Exercises in KS3 Mathematics Levels 7-8. R Joinson

Transcription

1 Exercises in KS Mthemtics Levels 7-8 R Joinson

2 Sumbooks Northwy Chester CH 8BB Exercises in KS Mthemtics - Levels 7 nd 8 First Published 00 Copyright R Joinson nd Sumbooks This pckge of worksheets is sold subject to the condition tht it is photocopied for eductionl purposes only on the premises of the purchser ISBN

3 Prefce The questions hve been rrnged, s fr s possible, ccording to level 7 nd level 8 of the Ntionl Curriculum. All level 7 questions re in the front of the book nd ll level 8 questions in the bck. Pges re lbelled L.7 or L.8 ccordingly. There my be some overlp of the levels where I hve found it unvoidble in order to keep the questions sensible. I would like to thnk my wife Jenny nd my dughters Abigil nd Hnnh for ll the help nd encourgement they hve given me. R Joinson September 00 Chester

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5 Contents Estimting 7 Powers of Numbers 8 Multiplying nd Dividing 9 Percentge Chnge 0 Frctions Rtio Rtio Odd nd Even Solutions Simplifying Simplifying 6 Multiplying Brckets Together 7 Fctorising 8 Solving Simple Equtions 9 Sequences 0 Tril nd Improvement Grphs Simultneous Equtions with Grphs Simultneous Equtions Solving Simultneous Equtions Inequlities 6 Pythgors Theorem 7 Ares of Right Angled Tringles 8 Ares of Plne Shpes 9 Volumes of Prisms 0 Enlrgement nd Similrity Routes Trees Rounding Off Imprecision of Mesurement Compound Mesure 6 Currency 7 Coch Journey 8 Trin Journey 9 Rod Rce 0 Men Men nd Rnge Sweets Flower Seeds Mesuring Sctter Reltive Frequency 6 Probbility 7 Powers 8 Stndrd Form 9 Stndrd Form 0 Questions in Stndrd Form Repeted Proportionl Chnge Clculting the Originl Amount

6 Proportion Letters nd % Substitution 6 How Mny Solutions? 7 Formule 8 Simultneous Eqution Problems 9 Equtions from Experimentl Dt 60 Solving Equtions 6 Fctorising Expressions 6 Tringulr Numbers 6 Grph of y = x 6 Inequlity Questions 6 Ares Bounded by Curves 66 Pythgors etc 67 Are 68 Ares nd Perimeters 69 Volume 70 Congruent Tringles 7 Similr Tringles 7 Angles 7 Sine, Cosine nd Tngent Rtios 7 Berings 7 Clculting Lengths in Tringles 76 More Similrity 77 The Cricket Scores 78 Cumultive Frequency 79 Cumultive Frequency 80 Cumultive Frequency 8 Probbility 8 Probbility 8

7 Sumbooks 00 Key Stge Estimting Do not use Clcultor L.7 ) Estimte ech of the following. ).8. b) c).7.6 d) 7..7 e) 8.. f) 9..0 g) 0.. h) 7.. i). 0. j) k) l) m). 0. n) o) p) q)..9 r)..7 s) 7.. t) 86.9 u) 8.97 v) 6.8. w) x) ) Estimte the sizes of the following. ) b) c) d) e) f) g) h).6 9. i) j) 7. k) l) m) n) o) p) q) r) ) In ech of the following write down the number you consider to be the best estimte. ).6.7 Estimtes b).7 0. Estimtes c). 0.8 Estimtes d) Estimtes e) Estimtes ,000 f) 0.0 Estimtes g) 0. Estimtes ,000 h). 0. Estimtes ,000 i) Estimtes j) 6 0. Estimtes k) Estimtes,

8 Sumbooks 00 Key Stge Powers of Numbers Do not use clcultor. ) Rerrnge the following into order of size, smllest first. L ) Which of the following re not squre numbers? ) Which of the following re equl to 6? ) If 0 = 909, write down the vlues of these ) If 0 = 0876, complete ech of the following. 6 =? 6 =? 90 =? 0876 =? 6) Which of the following re true? ) 0 = 0 b) 0 = 8 c) 0 = 6 d) 0 = 0 e) 0 = ( ) 0 f) 0 = 9 g) = h) = 8

9 Sumbooks 00 Key Stge Multiplying nd Dividing Do not use Clcultor L.7 ) In ech of these clcultions the nswer is. Write down the missing numbers = ) Look t these number crds ) Which two crds give the lowest nswer when multiplied together? b) Which two crds give n nswer of 0 when divided? c) Which two crds give the smllest possible nswer when divided? d) Which two crds give the gretest nswer when multiplied together? e) Which two crds give the gretest nswer when divided? f) Write down second wy in which 0 cn be obtined by dividing. g) How cn, 0.0 nd 0 be put together to get n nswer of 9.9? h) How cn 0., 0.0 nd 0. be put together to get n nswer of 00? i) How cn 0.0, 0 nd be put together to get n nswer of 0.0? ) Complete ech of the following. ) = 00 b) = 00 c) = 00 d) = 00 e)... = 0.8 f)... = 0. g)... = 0.0 h) = 0 i) = 00 j) = k).... = 0 l) = 00 m) = 700 n).... = 0. o) = 0 p) = 0 q)... =. r).... = 0.8 9

10 Sumbooks 00 Key Stge Percentge Chnge Round off your nswer sensibly wherever necessry. L.7 ) The popultion of town during the second hlf of the 0th century is shown in the tble below. Yer Popultion,0 8,8 7,0 6, 8,6,8 ) Wht ws the rise in popultion between 90 nd 000? b) Wht ws the percentge rise in popultion between 90 nd 000? c) There ws fll in the popultion between 970 nd 980. Wht ws this percentge fll? d) It is expected tht the popultion will fll by % between 000 nd 00. Wht is the expected popultion for 00? ) In the generl elections of 997 nd 00, the percentge of the voters who supported the three min prties re shown in the tble below. Prty Lbour Conservtive Liberl Democrt Other Prties % 0.9% 6.9% 8.99%.08%.79% 8.8% 6.7% ) Why does the totl percentge of votes cst in 997 not equl 00? b) In 997 the totl number of votes cst ws,60,8. How mny people voted for ech of the three min prties in 997? c) Wht ws the percentge increse in the Liberl Democrts shre of the vote in 00 compred with 997? ) In 999 compny mde profit of 0,. In 000 its profit ws,678. ) Wht ws its increse in profit? b) Wht ws it s percentge increse in profit? In the first hlf of 00 it mde profit of 7,0. It ws expected to mke the sme profit in the second hlf of the yer. c) Wht ws the expected profit for 00? d) Wht ws the expected percentge decrese in profit for 00 compred with 000? 0

11 Sumbooks 00 Key Stge Frctions L.7 ) A tnk contins 0,000 litres of wter when full. It begins to lek. After the first dy hlf of the wter is lost. After the second dy hlf of the reminder is lost. After the third dy hlf of the reminder from the second dy is lost. This continues, losing hlf of the reminder from the previous dy. At the end of dys the lek is discovered. ) Wht frction of the wter hs been lost? b) Wht frction of the wter remins? c) How much wter hs to be put bck into the tnk in order to fill it up? ) A cke is cut up into number of equl pieces. Aln, Bethn, Clive nd Deborh tke pieces of the cke. Aln hs -- of the cke. Bethn hs -- of the cke. Clive hs -- of the cke. Deborh 6 now tkes one third of the reminder. This leves two pieces. How mny pieces ws the cke cut into? ) Afrm trvels by cr to Itly. On the first dy he trvels 0 miles. On the second dy he trvels 0 miles nd on the third dy he trvels 80 miles. If he now hs of his journey left to do, wht is the totl length of his journey? ) The list below shows how Mrie spends her weekly wges. Rent Shopping Clothes Energy (Electricity etc) Trnsport Luxuries nd Entertinment Other Proportion of wges ) Wht frction of her weekly wges is spent on other? b) If Mrie spends 0 on trnsport, wht is her totl weekly wge? 7 ) Biscuits occupy -- th of the volume of their pcket. The remining -- is unused. It is 8 8 decided to re-design the pcket so tht the mount of unused spce is reduced by 0%. Wht frction of the pcket will the biscuits now tke up?

12 Sumbooks 00 Key Stge Rtio L.7 ) The tble below shows some informtion bout the 6th form students of school. Boys Girls Cn spek French Cn t spek French 8 7 ) How mny pupils re there in the 6th form? b) Wht is the rtio of those who cn spek French to those who cn t? :... ) The scle on mp is :,000. This indictes tht n ctul distnce of,000 centimetres (0 metres) is represented by centimetre on the mp. ) Wht distnce on the mp will represent n ctul distnce of kilometre? b) A rod mesures.6cm on the mp. Wht is its ctul length? c) Gwyn wlks distnce of 8.7km long the side of the cnl. Approximtely how long is this on the mp? ) Below re shown the res of the prts of the British Isles. (The Isle of Mn nd the Chnnel Islnds hve been left out) Country Wles Irelnd Scotlnd Englnd Are in squre kilometres 0,76 70,8 78,77 0,60 Complete this rtio for the four countries which shows their reltive sizes. Wles : Irelnd : Scotlnd : Englnd :... :... :... ) Four cubes, ech of exctly the sme size (congruent), re mde from four different metls. The rtio of their msses is shown below. Aluminium : Titnium : Copper : Led :.67 :. :. ) If the luminium cube hs mss of 0.7kg, wht re the msses of the other cubes? b) Another bigger shpe is mde. Agin exctly the sme size for ech of the mterils. If the titnium shpe hs mss of.kg, wht is the mss of the copper shpe?

13 Sumbooks 00 Key Stge Rtio L.7 ) Hll mixes pint. She wnts to mke ple green. These re the colours she uses. ml of blue 0ml of yellow ml of white. ) How much of ech colour is in 00ml of the mixture? Winston mixes pint to get ple green. These re the colours he uses ml of blue 0ml of yellow 0ml of white. b) How much of ech colour is in 00ml of the mixture? c) Which of the two mixtures is the pler? ) A biscuit br hs the following informtion printed on the side of its pcket. TYPICAL NUTRITION PER g BAR PER 00g Energy 8kj/97kC Protein b 8.g Crbohydrte 6.7g 9.g Ft 9.g c Fibre d 7.g Sodium 0.0g 0.06g Complete the tble by putting in the vlues, b, c nd d. ) Bridget buys longlife bulb. It costs. The pcket hs the following informtion printed on the side. A longlife bulb uses wtts of electricity per hour nd lsts for 8,000 hours. An ordinry bulb uses 7 wtts per hour nd lsts for,000 hours. ) How mny wtts of electricity does longlife bulb use in its lifetime? b) How mny wtts of electricity does norml bulb use in its lifetime? c) Complete this rtio for the mount of electricity used by ech type of bulb in 8,000 hours. Longlife bulb : Ordinry bulb :... d) An ordinry bulb costs p. Complete this rtio for the cost of the bulbs for 8,000 hours. Longlife bulb : Ordinry bulb... : e) Is it economicl to buy longlife bulb in preference to n ordinry one? Explin your nswer.

14 Sumbooks 00 Key Stge Odd nd Even Solutions L.7 ) n is n even number. Which of the following re even? ) n + b) n + c) n d) n + e) (n + ) f) n g) n h) (n ) i) (n + )(n ) j) n k) n l) n m) n n) n o) (n )(n ) p) (n + )(n ) ) If n is n odd number, wht kind of number, odd, even, either or neither, must m be in ech of the following in order for the expression to be even? ) n + m b) n m c) m + n d) (n + m) e) (n + m)(n m) f) n m g) n + m h) n + m i) n + m j) n + m k) (n m) l) m n ) In the following expressions x is n odd number greter thn. Which of the expressions lwys give whole number nswers nd which don t? x+ x x x + ) b) c) d) x + x 6x + 6x + e) f) g) h) ) Use this tble to nswer the questions below. n = n (n ) (n ) (n ) (n ) (n ) (n 6) (n 7) ) Complete the tble. b) Explin which expressions give odd nswers. c) Explin which expressions give even nswers. d) Explin wht is required in n expression to get 9 s n nswer. e) Wht type of numbers would n nd y hve to be for (n y) to be even?

15 Sumbooks 00 Key Stge Simplifying L.7 ) Simplify ech of the following expressions ) + 7 b) x 6x c) w + w 6w d) y 6y + 7y e) x + 7x x f) n + 7n 6n g) b b b h) x + x 7x i) p + 7p 6p j) z + z z k) x + y x + y l) p q p + q m) w + x w x n) f 7g + f + 7g o) k 7k m + m p) x + x q) m + 7m r) 7x x 6 ) Simplify ) b) y + y y + y c) b + b + 7b b d) + y + + y e) 6x + x x + x f) c + bc + c bc g) x + x + 7x + x h) 6b + b b + b i) 6c b + c b j) y + 6y y + y k) 6xy + y xy + 6y l) 7d cd + d cd m) y y + y + n) o) 7c c + 6c ) Simplify these frctions 8 ) b) --x + --x c) --y + --y d) 0 e) --c c f) --y --y g) h) 8 i) --x --x j) --c --c k) l) 7 0 m) n) -----x --x o) --c --c p) b --y b -----y b --b ) Simplify these frctions c c 0 b b 8 9y y 0 0 7c c 8 x x 6 ) b) c) d) 8 8 e) f) g) h) c c 0 i) j) k) l) y y 6 m) n) o) p) c x b c x 8 b 6 w w y y x x -- c c ) Which of these is equl to --c? c 8 c c c 6 ) b) c) d) c c c c 0 e) f) g) h) c c 8 c c i) j) k) l) c c c c m) n) o) p) c c 9c 0 7c 8 c 6 c 6 c c 8 c c c -- c -- c c c

16 Sumbooks 00 Key Stge ) Simplify these frctions Simplifying 8 ) -- b) c) -- d) -- e) f) g) h) i) j) k) l) m) n) L.7 ) Simplify these multiplictions 8 ) b) c) d) 6 7 e) f) g) h) 9 i) j) k) l) ) Simplify these frctions 6 0 x c 9 y 8 ) b) c) d) e) f) g) 8y 6 0 x h) i) j) k) l) m) n) x 8 7 y o) p) q) r) s) t) u) b c 0 8c 0 9x y y ) Simplify these frctions b b 9b xy xy ) b) c) d) e) f) b b b xy 9xy g) h) i) j) k) l) x y xy m) n) o) p) q) r) y 6xy x y xy y xy b b b 6b b x xyz xy xyz xy xy ) Arrnge the following into pirs tht re equl to ech other -- b b bc b y xy xy xy xy y -- y 8xy xy c bc x x y c c b b y xy c b b bc x x yz y xy z 6

17 Sumbooks 00 Key Stge Multiplying Brckets Together L.7 ) Remove the brckets nd simplify. ) (x + ) + (x + 6) b) (x + ) + (x + 7) c) (x + ) (x + ) d) (x + ) (x ) e) (x + ) + (x 6) f) 7(x + ) (x ) g) (x 0) + (x + ) h) 6(x ) + (x + ) i) (x ) (x + 9) j) 9(x ) + (x ) k) 7(x 7) (x ) l) 6(x 6) (x 7) m) (x ) + (x + 6) n) (x ) + 7(x + 7) o) (x ) 6(x + ) p) 8(x ) + (x 6) q) (x 8) (x ) r) 6(6x ) (x 8) ) Multiply together ech pir of brckets nd simplify your nswer ) (x + )(x + ) b) (x + )(x + ) c) (x + )(x + 7) d) (x + )(x 6) e) (x + 7 )(x ) f) (x + )(x 8) g) (x )(x + ) h) (x 8 )(x + 6) i) (x 0)(x + ) j) (x )(x 9) k) (x )(x 6) l) (x )(x ) ) Multiply together ech pir of brckets nd simplify your nswer ) (x + )(x + ) b) (x + )(x + ) c) (x + )(x + ) d) (x + )(x ) e) (x + )(x ) f) (x + )(x ) g) (x )(x + 6) h) (6x 8 )(x + ) i) (x 7)(x + ) j) (6x )(x ) k) (x 7 )(x ) l) (x )(x 7) ) Multiply together ech pir of brckets nd simplify your nswer ) (x + )(x + ) b) (x + )(x + ) c) (x + 6)(x + ) d) (x + )(x ) e) (x + 6 )(x ) f) (x + )(x ) g) (x )(x + ) h) (x 6 )(x + 9) i) (x )(6x + 9) j) (x )(9x ) k) (x )(x 8) l) (x 9)(6x 6) ) Multiply together ech pir of brckets nd simplify your nswer ) (x + )(x + 9) b) (x + )(x + 8) c) (6x + )(x + 6) d) (x + )(x 7) e) (6x + )(x 8) f) (6x + 9)(x 8) g) (x )(8x + ) h) (x 9 )(6x + 6) i) (8x )(x + ) j) (x 6)(x ) k) (x )(8x 6) l) (6x 7)(x ) 6) Multiply out these squres nd simplify your nswers ) (x + ) b) (x + ) c) (x ) d) (x ) e) (x + ) f) (x + ) g) (x 7) h) (x ) i) (x + ) j) (x + 6) k) (x ) l) (6x ) m) (x + ) n) (x + ) o) (x ) p) (x ) 7

18 Sumbooks 00 Key Stge Fctorising ) Write down the fctors of these. ) 6 b) c) b d) e) 6 L.7 f) g) b h) i) b j) b k) x l) 7b m) 6c n) 8xy o) b ) Write down the highest common fctor of ech of the following pirs of expressions. ) 8 nd b) 9 nd 8 c) 8 nd 0 d) b nd 9 e) b nd 9b f) nd g) b nd b h) 6b nd 9 i) b nd 6b j) 6 nd k) x nd x l) 6xy nd 9x y m) x y nd 8xy n) 8 b nd b o) 9c nd c ) Fctorise ech of the following expressions by finding the highest common fctor. ) + b) x + 6 c) x + 6 d) 6x e) xy + y f) b b g) b 0b h) 6c i) x 0xy j) b + k) xy y l) 6 m) bc n) x + 6x o) b + bc + c ) Fctorise ech of the following expressions by finding the highest common fctor. ) xy + x b) x y + y c) b c + d d) + b + 6c e) + 6b 8 b f) 6b c + bc g) x + x + 6x h) + b + c i) + 6 b 0b j) + x b k) xy + 6y y l) 6 b b m) + b + 6 c n) + 8b 0 b o) b 6 + bc p) x + 6xy + 9x q) b + b + 0bc r) + b b 8

19 Sumbooks 00 Key Stge Solving Simple Equtions ) Clculte the vlue of x in ech of the following. ) x + = 8 b) 9 x = c) x 9 = d) x + = 6 e) x = 7 f) x = 8 g) + x = 7 h) 6 x = 0 i) x + = L.7 ) Clculte the vlues of the letters in the following. ) + = 8 b) 9x 6 = 8 c) 6 + 7y = 7 d) 9 b = e) 6c = 6 f) w + 6 = 8 g) 6x = 8 h) 6x = 6 i) 7x = 60 j) 7 y = k) p = 0 l) w = 6 ) Clculte the vlue of the letters in ech of the following. ) x = b) = c) b + = 8 d) y + 6 = 9 e) w + = 9 f) x = 6 g) y = 9 h) = 6 i) = 7 x b j) = 0 k) = 9 l) + 6 = c ) Clculte the vlue of the letter in ech cse. ) (x + ) = b) (x + ) = c) (x + ) = d) 7(x ) = e) 6(x ) = 8 f) 8(x ) = 8 g) 6(x + ) = 6 h) 9(x ) = 90 i) 6(x ) = 7 j) (x + 7) = k) 8(x ) = 60 l) (x + ) = 7 ) Clculte the vlue of the letter in ech cse. ) x + = x + b) x + = x + c) x + = x + d) x = x + e) x + 7 = x f) 8x = x + g) x 6 = x 9 h) x = x + i) 6x + = 8x j) x = 6x k) 8x 8 = x l) x + = x 6 9

20 Sumbooks 00 Key Stge Sequences L.7 ) Grce rrnges discs into rows. She begins with discs in row. She then increses the number of rows by nd the number of discs in ech row by row discs rows 6 discs rows discs rows 0 discs ) How mny discs does she put into rows? b) Which of these rules will clculte the number of discs in n rrngement? d = r d = r d = r r + d = r(r + ) d = r + where d represents the number of discs nd r the number of rows. c) Use the rule to clculte the number of discs she needs for 0 rows. ) Brin writes down this sequence of numbers The rule for finding the next number is n + n, where n is the position of the number in the sequence. ) Use this rule to check which number in the sequence is incorrect. b) Clculte the next two numbers in the sequence. c) Brin sys tht ll the numbers in the sequence re even numbers. Explin whether you think he is right. ) Dve writes down this sequence of numbers The rule for finding the next number is in the sequence. n n + n +, where n is the position of the number ) Use this rule to check which number in the sequence is incorrect. b) Clculte the next two numbers in the sequence. c) Explin why the sequence of denomintors cn never be even. 0

21 Sumbooks 00 Key Stge Tril nd Improvement L.7 The eqution x 8x + = 0 hs two solutions for x. One solution is between nd nd the other is between 0. nd 0.. Derek clcultes the vlues of x by tril nd improvement method. These re his clcultions. The difference is obtined by subtrcting the vlue of x from 8x. x x 8x Difference ) Rewrite the eqution in the form x =... b) Why did Derek clculte the difference between x nd 8x? c) Between which two vlues does the solution lie? Explin your nswer. A more ccurte vlue cn be obtined by using vlues with deciml plces. x x 8x Difference d) Continue this tble until the difference is negtive. e) Wht two vlues does the solution now lie between? f) Write down the first solution to the eqution correct to deciml plces. Explin why you chose tht nswer. g) Use Derek s method to clculte the second solution to the eqution. Give your nswer correct to deciml plces.

22 Sumbooks 00 Key Stge Grphs L.7 ) Here re the equtions of eight grphs lbelled A to H. A y = x + B y = C y = x D x = E y x x + y = F x + y = G y = --x + H = 9 ) Which grph is prllel to F? b) Which grph is not stright line? c) Wht re the co-ordintes of the point where equtions C nd F cross? d) Which grph is prllel to the x xis? e) Which two grphs pss through the point (0,0)? f) Which grph goes through the point (,7)? g) Which eqution is the sme s y = 8 x? h) At which point do B nd D cross? i) Which grph is prllel to A? j) Which grph crosses D t right ngles? k) Which grph is prllel to y = 0.x? ) The digrm shows hexgon with corners lbelled A to F. y A F B E C x - D Use the digrm to nswer these questions. ) Wht is the eqution of the stright line through F nd A? b) Wht is the eqution of the stright line through F nd C? c) Wht is the eqution of the stright line through F nd B? d) Which two points on the hexgon does the line y =.( x + ) pss through? e) Wht re the co-ordintes of the point where the lines x + y = 6 nd x = cross? f) At wht point does the line through BC meet the line through ED? g) At wht point will the line through CB meet the line through EA?

23 Sumbooks 00 Key Stge Simultneous Equtions with Grphs ) The digrm below shows the grphs of the equtions y = - x + nd y = x + y 0 L Use the digrm to solve the simultneous equtions:- y - x = y x = x ) The digrm below shows the grphs of two equtions:- A y B x Complete these equtions for the two grphs:- A is y = B is y = Solve the simultneous equtions y x = nd x + y = 9 ) With scle of to on the y xis nd to on the x xis, drw the grphs of y = x + nd y = - x + Use the digrm to write down the solution to the simultneous equtions y x = nd y x =

24 Sumbooks 00 Key Stge Simultneous Equtions ) y L.7 B x - - A In the digrm bove ) Which grph represents the eqution y x =? b) Which grph represents the grph y+ x = 7? c) Show tht the point of intersection of the two grphs is the solution to the two simultneous equtions:- y x = y+ x = 7 ) With scle of to 7 on the y xis nd 0 to 9 on the x xis, drw the grphs of y = x nd y = --x + Use the digrm to write down the solution to the simultneous equtions:- y x = y x = ) With scle of - to 7 on the y xis nd - to on the x xis, drw the grphs of y = x + nd y = --x Use the digrm to write down the solution to the simultneous equtions:- y x = y x = ) With scle of 0 to 6 on the y xis nd -6 to 0 on the x xis, drw the grphs of y = x + 6 nd y = x Use the digrm to write down the solution to the simultneous equtions:- y x = 6 y + x =

25 Sumbooks 00 Key Stge Solving Simultneous Equtions Solve the following pirs of simultneous equtions ) ) x + y = b) x + y = c) x + y = x + y = x + y = 7 x + y = 7 d) x + y = e) x + y = 9 f) x + y = 6 x + y = x + y = 9 x + y = L.7 ) ) + y = 0 b) x + y = 0 c) x + y = y = x y = x y = d) 8x 6y = 8 e) x y = f) x + y = x + 6y = 7 x + y = x y = ) ) x y = b) x y = c) x y = x y = 0 x y = x y = d) x y = e) x y = f) x y = x + y = x + 6y = 0 x + y = ) ) x + y = b) x + y = 7 c) x y = 0 x y = x y = x y = d) x + y = 7 e) x + y = 8 f) x + y = 6 x y = x y = x y = ) ) x + y = 7 b) x + y = c) 7x y = 0 x + y = 8 x y = x + y = 6 d) x + y = e) x y = f) x y = x y = x + y = x y = 6) Clculte the coordintes of the point of intersection of the following pirs of grphs. ) y = x nd y = x 7 b) y = x nd y = --x x c) y = -- nd y = x d) y = x 8 nd y = --x + 8 e) y = x nd y = 8 x f) y = x 6 7 nd y = --x 7

26 Sumbooks 00 Key Stge Inequlities ) In ech of the following inequlities the vlues of x re integers. Write down the solutions in ech cse. ) < x < 9 b) 6 < x < 0 c) - < x < d) -8 < x < - e) - < x < - f) - < x < - g) < x + < 9 h) 6 < x + < 0 i) - < x + < j) < x + < 9 k) 6 < x + 6 < 0 l) - < x + < m) < x < 9 n) 6 < x < 0 o) - < x < p) < x < q) < x < r) < x < s) < x + < 9 t) < x < u) - < x + < 7 v) - < x < w) - < x < 0 x) -6 < x < ) In ech of the following digrms, the informtion given will eliminte ll the points except one. In ech cse write down the point. L.7 ) b) c) y y y x x x y > x x + y > y < x + y < 7 y > x > y x > x > - y < d) e) f) y y x 0 0 x x y x > - y < x + y > y > x y < x > - y x > x > - y < 6

27 Sumbooks 00 Key Stge Pythgors Theorem ) Clculte the length of the hypotenuse in ech of the following right ngled tringles. Give your nswers correct to the nerest millimetre. L.7 ) b) c) cm d) 7cm cm 9cm cm 0cm cm cm ) Clculte the length of the unknown side in ech of the following right ngled tringles. Give your nswers correct to the nerest millimetre. ) b) c) d) cm cm 6cm cm cm 0cm 8cm cm ) Explin why you know tht the three tringles shown below re right ngled. cm 0cm 6cm 8cm cm cm cm cm 7cm ) An isosceles tringle cn be mde into two congruent right ngled tringles like this. Wht re the length of the sides of the right ngled tringles? cm 6cm 6cm ) The digonls of kite cross t right ngles. The shorter one is bisected, the other is cut in two. The digonls of this kite mesure 0cm nd 6cm. If the smller sides of the kite mesure cm, wht re the lengths of its lrger sides? 7

28 Sumbooks 00 Key Stge Are of Right Angled Tringle ) Clculte the res of these tringles. ) b) c).cm d) 9cm 7cm 7.cm cm 6.cm L.7 cm 8cm ) Clculte the res of these tringles. ) c) b) cm cm 9cm 8.cm cm 9.cm ) Use the rule for finding the re of tringle to clculte the shded res in the following shpes. Digrm b is kite, c is rhombus nd d is prllelogrm. ) b) 9cm 7. cm 9. cm cm cm cm c) d) 7cm 7.cm 9.cm.cm ) Using the results of question, explin how you would clculte the res of:- ) kite b) rhombus c) prllelogrm 8

29 Sumbooks 00 Key Stge Ares of Plne Shpes ) Clculte the res of the trpezium, prllelogrm, kite nd rhombus shown below. cm ) b) L.7 cm 8cm cm 7cm c) cm d) cm 0cm ) Clculte the res of the shded prts of these shpes. cm ) b) cm 8cm rdius 6cm 6cm 6cm c) cm cm d) cm cm cm cm 7cm 0cm rdius 9

30 Sumbooks 00 Key Stge Volumes of Prisms ) 8cm cm L.7 cm The digrm on the left shows prism of height cm ) Clculte the re of its top. b) Wht is its volume? 9cm cm ) 6cm 9cm 8cm The digrm on the left shows trpezil prism of height 8cm. ) Clculte the re of its top. b) Wht is its volume? 7cm ) Clculte the volume of the cylinder on the left which hs dimeter of 7cm nd height of 9cm. ) The prism on the left is cm in height. Its top is in the shpe of tringle with smller similr tringle cut from it. The height of cm the lrger tringle is cm nd tht of the smller one is 7cm. ) Wht is the re of its top? cm b) Clculte the volume of the solid prt. 6cm ) Drinking glsses of dimeter 6cm nd depth cm re pcked into boxes with internl mesurements of 8.cm long, 9cm wide nd cm high. The spces between nd round the glsses re filled with polystyrene grnules. Clculte the volume the polystyrene hs to fill. 0

31 Sumbooks 00 Key Stge Enlrgement nd Similrity L.7 ) The digrm below shows two similr right ngled tringles. Tringle A hs been enlrged by fctor of -- to mke tringle B..9cm A B.cm b ) Wht re the dimensions of sides nd b? b) Wht re the res of tringles A nd B? c) Complete this rtio:- Are of tringle A : Are of tringle B :... ) The digrm below shows two similr tringles, one n enlrgement of the other.....8cm.0cm ) Wht is the scle fctor of the smller one to the lrger one? b) Wht is the scle fctor of the lrger one to the smller one? (give your nswer s frction) If the re of the smller tringle is.08cm c) Wht is its height? d) Wht is the re of the lrger tringle? ) The digrm shows two similr shpes. 0.6 The dimensions of the lrger shpe hve been multiplied by 0.6 to get those of the smller shpe. ) One of the dimensions on the lrger shpe is.cm. Wht is the size of the corresponding dimension on the smller shpe? b) One of the dimensions on the smller shpe is.cm. Wht is the corresponding dimension on the lrger shpe? c) If the re of the lrger shpe is 0cm, wht is the re of the smller one?

32 Sumbooks 00 Key Stge Routes ) The digrm below shows field mesuring 0 metres by 80 metres. L.7 E 0m D A Existing pipeline 80m B 0m Tree 0m C It hs tree growing ner to corner B, 0m from ech of the two sides. An existing pipeline enters the field t the mid point of side ED nd leves the field t corner C. It is proposed to run nother stright pipeline from point A, hlf wy long side EB to side BC. The pipeline must not be within 0 metres of the tree or metres of the existing pipeline. Mke n ccurte scle drwing of the field, using scle of cm to represent 0 metres. On your digrm shde in the re through which the pipe cn run. ) The digrm shows prt of lke. There re three dnger mrkers, A, B nd C on the lke nd it is recommended tht bots should keep well cler of them. N A 00m B º 70m 80m C A bot trvels between mrkers A nd C then lters course to go between A nd B. ) Drw n ccurte digrm of the reltive positions of the mrkers, using scle of cm to represent 0 metres. b) The bot trvels so tht it is equidistnt from A nd C, then it lters course so tht it is equidistnt from A nd B. Drw ccurtely on your digrm the route of the bot.

33 Sumbooks 00 Key Stge Trees ) The digrm below shows the pln of grden in the shpe of rectngle mesuring metres by metres. L.7 A D House m 8m Old tree B m C A tree is growing on the boundry DC, metres from the corner C. A new tree is to be plnted. It must not be within metres of the old tree. It is to be equidistnt from sides DC nd BC nd it must not be within metres of the house. ) Drw n ccurte digrm of the grden using scle of cm to represent m. d) Clerly indicte on the digrm where the tree cn be plnted. ) The digrm shows pln of smll public grden next to cnl. There re two trees, 0 metres prt nd both 8 metres from the cnl. 0 metres Tree Tree 8 metres Cnl A bench is to be plced in the grden. It must be within metres of ech of the trees but further thn metres from the cnl. ) Drw n ccurte sketch of the grden, using scle of cm to represent m. b) Clerly indicte on the digrm the re where the bench cn be plced.

34 Sumbooks 00 Key Stge Rounding Off L.7 ) Wht re the distnces mrked on the number line, correct to the nerest whole number? A B C D E F ) This rectngle hs dimensions mesured correct to the nerest cm. cm 9cm ) Clculte the minimum re of the rectngle. b) Clculte the mximum re of the rectngle. ) The digrm below shows the pln of running trck. It is mde up of two stright lengths of 00m nd two semicircles of 60m dimeter. The dimensions re given correct to the nerest metre. 00m 60m Wht is the minimum distnce round the trck? ) The length of piece of wood is given s 7cm correct to the nerest cm. Complete this sttement:-... Length of wood <... Explin why the signs nd < re used. ) The dily tempertures given by the Wether Bureu re lwys rounded to the nerest degree celsius. Wht re the mximum nd minimum vlues of temperture of 0ºC? 6) Five people get into lift. The lift will not move if their combined mss is greter thn 00kg. The msses of the people re 0kg, 9kg, 89kg, 09kg nd 0kg, ll mesured to the nerest kilogrm. Explin why the lift refuses to move.

35 Sumbooks 00 Key Stge Imprecision of Mesurement ) Boxes nd their lids re mde to these dimensions, correct to the nerest mm. L.7 Top of box Exterior dimensions Lid of box Interior dimensions 8mm 86mm 07mm 09mm When the lid is put on the box there is gp between them, s shown on the left. ) Wht is the mximum gp between lid nd box? b) Wht is the minimum gp between lid nd box? ) The timetble sys tht the buses rrive t the bus stop every 0 minutes, t 8:00, 8:0, 8:0, 8:0 nd so on. The bus compny sys tht they re lwys on time to the nerest minute. Jn rrives t the bus stop just s bus is leving. ) Wht is the mximum time she will hve to wit for the next bus? b) Wht is the minimum time she will hve to wit for the next bus? ) At n thletics meeting, the jvelin throws re mesured to the nerest centimetre. The winning throw ws 7. metres, equlling the record. Explin why this throw could hve been the new record. ) At the sme thletics meeting the 00 metres rely rce ws won in time of 8. seconds, correct to the nerest th of second. Between wht two vlues does the ctul time lie? ) Wter tnks re mde in the shpe of open cuboids. They re mde 9cm tll, 00cm wide nd cm long. Ech dimension is mesured to the nerest centimetre. 9cm The mkers dvertise them s cpble of holding up to 068 litres. Is this good estimte? Explin your nswer. 00cm cm

36 Sumbooks 00 Key Stge Compound Mesure L.7 ) A smll cr hs n verge fuel consumption of 8 miles per gllon. A lrge cr hs fuel consumption of miles per gllon. Jspl clcultes tht he trvels 9,00 miles ech yer. ) How mny gllons of petrol would he use in yer if he bought the smll cr? b) How mny gllons of petrol would he use in yer if he bought the lrge cr? c) A third cr is medium sized nd the fuel consumption is 0 kilometres per litre. How mny gllons of petrol would he use in yer if he bought this cr? ) The outside wlls of house re to be pinted. The pln of the house is rectngle mesuring metres by 0 metres. The wlls re metres tll. m metres 0m ) Clculte the totl re of the four wlls. The house hs windows in it nd doors. Four of the windows mesure 0cm by 0cm nd six others mesure 0cm by 0cm. The remining two windows mesure 0cm by 60cm. The doors mesure 90cm by m. b) Clculte the totl re of the windows nd doors in m. c) Wht is the totl re of wll needing to be pinted? d) Pint is bought in cns contining 0 litres nd litre is sufficient to cover 8.m. How mny cns of pint re needed? ) The distnce from the bus terminus to Am s house is. kilometres. The journey tkes 8 minutes. Clculte the verge speed of the bus in kilometres per hour. ) The velocity of sound through ir is pproximtely 760 miles per hour. If the noise of thunder tkes 8 seconds to rech the listener pproximtely how fr wy will it be in metres? ) A hosepipe feeds wter into tnk of height metres nd internl dimeter of.6m. ) Clculte the volume of wter in the tnk when it is full. The hosepipe hs n internl dimeter of.cm. b) Clculte the volume of metre of wter in the pipe. The tnk tkes 0 minutes to fill up. c) How much wter enters the tnk in second? d) Clculte the speed of the wter in the pipe in metres per second. 6

37 Sumbooks 00 Key Stge Currency L.7 ) Donn goes to Florid on holidy. She tkes 600 dollrs with her to spend. She buys this money t rte of $.7 for.00. Clculte how much it costs, to the nerest penny. She buys the money from trvel gent who dds on nother.% commission. Wht is her totl bill? ) On the bck of book the price is written in three wys..99 in UK $7.99 in USA $.99 in Austrli. If the rte of exchnge is.7 US dollrs to pound nd.67 Austrlin dollrs to pound, in which country will the book cost most nd in which will it cost lest? ) Dn trvels to Cnd for holidy. He chnges 00 into Cndin dollrs before he goes t rte of $. for.00. He spends week in Vncouver then trvels on to the USA. He decides to chnge 00 of his Cndin dollrs into Americn dollrs. He knows tht in the UK he cn get.7 Americn dollrs for.00. How mny US dollrs does he expect to get? ) The exchnge rte between the UK pound nd the Turkish lir is.00 equls,877 lir. Donn goes on holidy to Turkey. How mny lir cn she buy for 0? When Donn gets to Turkey she finds tht the exchnge rte hs chnged to,96 lir to pound. How mny more lir could she hve gined if she hd chnged her money in Turkey? ) The cr Mrs Lee wnts to buy costs 7,890 in her town. She finds tht in Europe the sme cr costs 9,00 euros. If euro is worth 66p, how much money does Mrs Lee sve by buying it in Europe? 6) Rik wnts to go on trvelling holidy to New Zelnd. It costs 0 to trvel from the UK to New Zelnd or 790 return. However, he is told tht the one wy fre from New Zelnd bck to the UK is $000. If.00 buys.9 New Zelnd dollrs, is it more economicl to buy return fre or two one wy fres? 7) In 00 Erol bought pir of sndls in Portugl for,00 escudos. On the bottom of his receipt it sys 0 escudos = euro. Erol knows tht euro is worth 69p. Wht is the cost of his shoes in pounds? 7

38 Sumbooks 00 Key Stge Coch Journey The simplified grph shows the journey coch mkes between Mnchester nd London. L.7 London Distnce from Mnchester in miles 60 Oxford Birminghm 0 0 Mnchester 0:00 m :00 :00 pm :00 Time ) Wht distnce does the coch trvel between Mnchester nd Birminghm? b) Wht is the verge speed of the coch between Mnchester nd Birminghm? c) For how long does the coch stop in Birminghm? d) Wht is the distnce trvelled by the coch between Birminghm nd Oxford? e) Wht is the verge speed of the coch between Birminghm nd Oxford? f) For how long does the coch stop in Oxford? g) At wht time does the coch leve Oxford? h) Wht is the distnce between Oxford nd London? i) Wht is the verge speed of the coch between Oxford nd London? j) At wht time does the coch rrive in London? 8

39 Sumbooks 00 Key Stge Trin Journey Mir tkes trin journey to Glsgow from Crdiff. She hs to chnge trins t Birminghm. Below is shown simplified grph of her journey. L.7 Glsgow 600 Distnce from Crdiff in km Birminghm 00 Crdiff :00 :00 7:00 9:00 Time ) Without clculting, sy over which prt of her journey the trin trvelled t the gretest speed. b) Wht were the verge speeds over the two prts of the journey? c) Wht is the distnce from Birminghm to Glsgow? d) Wht ws the totl time for her journey? e) How long did she hve to wit t Birminghm sttion? f) Another trin leves Glsgow for Birminghm t :7. It rrives t Birminghm t 7:. At pproximtely wht time do the trins pss? g) How fr from Glsgow is Mir when the two trins pss? 9

40 Sumbooks 00 Key Stge Rod Rce L.7 Two friends, Brody nd Hri run 0 kilometre rce from Ambridge to Blconsfield nd bck. The digrm below shows rough sketch of their journeys. 0 Brody s rce Hri s rce Distnce from the strt of the rce in km. 8 6 Strt hour hours Time from the strt of the rce ) Which of the two friends first tkes the led? b) Along the journey they encounter hill. Approximtely how fr from Ambridge is the beginning of the hill? c) At wht time did the led first chnge? d) How mny times did they pss ech other? e) How mny times did the led chnge? f) Who ws in the led t the hour point? g) Who ws running the fstest just fter the hlf wy point? h) Why did their speed increse between the hr min nd hr points? i) Who won the rce nd by wht time intervl? j) Wht ws Brody s pproximte verge speed for the whole rce? k) Give n explntion of the drmtic events t the 8km point. 0

41 Sumbooks 00 Key Stge Men L.7 ) Joe grows plnts in his greenhouse. After one week he mesures the heights of them. These re the results he gets, correct to the nerest cm. Height of plnt cms Number of plnts 8 9 ) Clculte the men height of the plnts, correct to the nerest millimetre. b) Wht is the modl height of the plnts? c) Wht is the medin height of the plnts? d) Wht is the rnge of their heights? ) The tble below shows the sles of two books in 0 stores throughout the country. Number of books sold Number of shops selling book A Number of shops selling book B For exmple, shops sold no book A s nd 7 shops sold no book B s. ) For ech of the two books, clculte the men number sold t the stores. b) For ech book, how mny shops sold less thn the men? These stores re prt of lrger group of 0 stores. c) For ech book, clculte the pproximte number of books the compny sold in ll its stores.

42 Sumbooks 00 Key Stge Men nd Rnge L.7 ) The men nd rnge of these numbers re equl. Wht is the vlue of the missing number? 6 6? ) The ges of 8 children re shown below. If the men is 7 wht is the rnge? ? ) Crd number 8 will increse the men of these numbers by. Wht number is on the new crd? 8 6 6? ) The men of these 8 numbers is 9 nd their rnge is 8. Wht re the two missing numbers? ?? ) The men of these 8 numbers is nd their rnge is. Wht re the two missing numbers? 6?? 6) The ges of 8 children re shown below. If the men nd rnge re equl nd ll re below 0, wht re the missing ges? ?? 7) The crds below hve 8 numbers on them. The men nd rnge of these numbers re equl. Wht re the missing crd numbers if they re equl to ech other? ??

43 Sumbooks 00 Key Stge Sweets L.7 A compny mke pckets of coloured sweets. They counted the number of red nd yellow sweets in 0 pckets. The results re shown in the digrm below. 7 Number of 0 pckets 6 0 Number of 0 Pckets Number of red sweets in ech pcket Number of yellow sweets in ech pcket ) Complete the tble below. Use it to estimte the men number of red sweets in pcket. Number of red sweets Mid point Number of of br ( x ) pckets ( f ) xf 6 68 b) Drw similr tble nd estimte the men number of yellow sweets in pcket. c) Ech dy the compny produces,000 pckets of sweets. Approximtely how mny red nd yellow sweets does it mke? d) Approximtely how mny pckets contin 0 or less red sweets?

44 Sumbooks 00 Key Stge Flower Seeds L.7 A compny produce pckets of seeds tht will grow into mixture of blue nd white flowers. 00 pckets were sown nd the resulting colour of the flowers were recorded. The tble below shows the results Number of Pckets of Seeds 0 0 Number of Pckets of Seeds Number of blue flowers Number of white flowers -7 ) Complete the tble below nd estimte the men number of blue flowers pcket of seeds will produce. Number of blue flowers Mid point Number of of br ( x ) pckets ( f ) 7 0 xf b) Drw similr tble nd estimte the men number of white flowers pcket of seeds will produce. c) Ech yer the compny produces,000 pckets of these seeds. Approximtely how mny blue nd white flowers will the pckets produce? d) Approximtely how mny pckets produce more thn white flowers? e) Which of the two chrts shows greter rnge? Explin your nswer. f) Fill in the blnks in this sentence A pcket of seeds usully hs more... seeds in it thn... seeds.

45 Sumbooks 00 Key Stge Mesuring Sctter L.7 ) At The Cstle Cfe they sell soup to their lunchtime customers. The sctter digrm below shows the number of bowls sold in My plotted ginst the lunchtime outdoor tempertures. 0 Number of bowls sold Lunchtime temperture ºC ) Drw in line of best fit. b) How mny bowls of soup would you expect to sell when the temperture is 9ºC? c) Would you expect to sell more or less soup in Jnury? ) A spring is hung from hook nd msses ttched to it. The length of the spring is mesured ech time mss is ttched to it. The results re then plotted. These re shown below. Mss ttched kg Length of spring in cms ) Drw line of best fit. b) An object is hung on the bottom of the spring. The length of the spring increses to 7.cm. Wht is the mss of the object? c) An object hs mss of.kg. Wht will be the pproximte length of the spring?

46 Sumbooks 00 Key Stge Reltive Frequency L.7 ) A die is rolled 00 times nd the number of sixes recorded. How mny times would you expect the 6 to occur? ) A bg contins 9 discs, ll similr to the touch. Some of the discs re blue, some re green nd some re red. Abi tkes disc from the bg nd records the colour. She then replces the disc. She does this 00 times recording ll the results in the tble below. Blue Green Red How mny discs of ech colour do you think re in the bg? ) A smll cube hs red sides, two blue sides nd yellow sides. yellow blue red Some friends do n experiment to decide whether this cube is bised. They ech roll the cube nd record the colour of the top fce. These re the results they get. Nme Emm Lim Hrriet Jude Number Results of Throws Red Blue Yellow ) Whose dt re more likely to give the most ccurte estimte of the probbility of getting ech result? Explin your nswer. b) Is the cube bised? Explin your nswer. The friends combine their results. Number Results of Throws Red Blue Yellow c) Use these results to clculte the probbility of getting yellow. d) Use these results to clculte the probbility of getting red. 6

47 Sumbooks 00 Key Stge Probbility L.7 ) Eun plys chess ginst his friend Joy. Over the lst month he hs won 8 times. He sys tht his chnce of winning the next gme is 0.. ) Wht is his chnce of not winning? b) How mny gmes hve they plyed ltogether? c) If Joy s chnce of winning is 0. how mny gmes did they drw? ) Two bgs contin red, yellow nd blue cubes. All the cubes re the sme to the touch. Bg A contins red 6 yellow nd blue cubes A Bg B contins red yellow nd 0 blue cubes B Triq tkes cube from one of the bgs. He wnts to choose yellow cube. Which bg should he choose? Explin your nswer. ) Bello plys cricket for his school tem. Lst seson they won gmes, lost 7 nd drew. ) Wht ws his tem s chnce of winning gme lst yer? He sys tht this yer they hve better chnce of winning. He estimtes tht they should hve t lest 0% chnce of winning their mtches. b) If they ply the sme number of mtches this seson, how mny would you expect Bello s tem to win? c) Hlf wy through the seson Bello s tem hs won gmes, lost nd drwn. He dds these vlues to lst yers results nd clcultes new probbility of the tem winning. Results Win Lose Drw Wht did Bello clculte the new probbility to be? d) Bello uses this vlue to estimte the number of mtches he will win in the second hlf of the seson. Wht vlue did Bello get? 7

48 Sumbooks 00 Key Stge Powers Do not use clcultor ) This tble shows the powers of 0 = = = 6 = 6 = 6 = 0 6 = = 68 8 = 66 9 = 6 0 = 0876 = 90 = L.8 ) Explin how the tble shows tht 6 0 = 6 b) Explin how the tble shows tht 6 6 = c) Explin how the tble shows tht = 6 d) Explin how the tble shows tht = 6 90 e) Use the tble to work out f) Use the tble to work out ) 8 6 = 6. Use this informtion to write down the following. ) Wht is the units digit of 8? b) Wht is the units digit of 8? c) Wht could the units digit of 8 be? d) Wht could the units digit of 8 be? ) Which of the following re true? Give the correct nswer when they re not, or explin why. ) 6 0 = 6 b) 0 = c) 9 = 6 8 d) = 7 9 e) 6 8 = 8 f) = 8 6 g) 7 = 6 0 h) 0 = 8 i) = 8 6 j) 6 = k) = l) = 0 8

49 Sumbooks 00 Key Stge Stndrd Form Do not use clcultor L.8 ) Write down these numbers in stndrd form. ) 6 b),7 c) 7,8 d) 8,000 e),000 f),00 g),800,000 h),80 i),60,000 j) k),90,000 l) 6,700,000 ) Write down these numbers in stndrd form. ) 0.00 b) c) d) e) 0.00 f) 0.08 g) h) i) j) k) l) 0. ) Chnge these numbers from stndrd form. ). 0 b). 0 c).8 0 d) 6. 0 e).6 0 f) g) h) 7. 0 i).67 0 j).68 0 k) l).6 0 ) Chnge these numbers from stndrd form. ). 0 - b) c) d) e) f) g) h) i) j) k) l) ) Write down these numbers in order of size, smllest first ) Write down these numbers in order of size, smllest first ) Which of the following hve the sme vlue s. 0? ) Which of the following hve the sme vlue s. 0-6? ,0, ) Which of the following hve the sme vlues s.8 0?.8 8. (.8 0)

50 Sumbooks 00 Key Stge Stndrd Form Do not use clcultor ) ) If = write down nd in stndrd form L.8 b) Clculte (i) nd (ii) leving your nswer in stndrd form ) Clculte ech of the following, leving your nswer in stndrd form. ) b) c) d) e) f) ) Write down ech of the following s simply s possible in stndrd form. ) ( 0 ) ( 0 ) b) ( 0 ) ( 0 ) c) ( 0 ) ( 0 ) d) (. 0 ) ( 0 ) e) ( 0 ) ( 0 7 ) f) ( 0 ) ( 0 - ) g) ( 0 ) (7 0 - ) h) (6 0 - ) (8 0 ) i) (7 0 - ) ( 0 ) j) ( 0 6 ) (8 0 - ) ) Write down ech of the following s simply s possible in stndrd form ) b) c) d) e) f) g) h) i) j) k) l) ) cn be written more simply s 0. Simplify these ) b) c) d) ) cn be written more simply s Simplify these ) b) c) d)

51 Sumbooks 00 Key Stge Question in Stndrd Form L.8 ) The pproximte distnces of the plnets from the Sun re given in the tble below. Plnet Mercury Venus Erth Mrs Jupiter Sturn Urnus Neptune Pluto Distnce from the Sun in km Distnce compred to Erth The finl column compres the distnce of the erth from the Sun with the distnces of the other plnets from the Sun. ) Complete the tble. b) The speed of light is pproximtely 0 8 metres per second. Use the vlues bove to clculte how long it tkes for light to trvel from the Sun to the Erth. c) How long will it tke for light to trvel from the Sun to Pluto? ) The dimeter of Mrs is metres. Two mn mde stellites circle the plnet t different ltitudes nd t different velocities. The stellites re circling t heights of 0km nd 60 km bove the surfce of Mrs. ) Wht is the mximum possible distnce between the stellites? b) Wht is the minimum possible distnce between the two stellites? ) If cm is pproximtely equl to 0.9 inches, how mny cubic centimetres re there in cubic foot? Give your nswer in stndrd form.

52 Sumbooks 00 Key Stge Repeted Proportionl Chnge L.8 ) The popultion of villge t the end of 998 ws,0. At the end of the next yer it ws found to hve risen by 0%. At the end of the next yer it rose by further 8%. Wht ws the popultion t the end of 000? ) Arln puts 000 into bnk ccount. He plns to leve it there for three yers. He is told when he puts the money in tht it will grow by % ech yer. Arln sys After yers I will hve 0 in the bnk ) Explin why Arln is wrong. b) Clculte the true mount of money Arln will hve in the bnk fter yers. ) A cr costs 8,000. At the end of the first yer its vlue deprecites by %. ) Which of the following clcultions will work out its new vlue? b) The next yer it will deprecite in vlue by further 9%. Wht clcultion must be crried out in order to find its new vlue? c) Wht is its vlue t the end of the second yer? ) A business employed 000 people t the end of 99. The tble below shows the number of employees t the end of subsequent yers. End of 99 End of 996 End of 997 End of % more 0% more 0% more ) Which of the following is used to clculte the number of employees in the compny t the end of 998? (000.) b) Clculte the number of people employed by the compny t the end of 998. ) Two people go to resturnt. The food costs 60. To tht is dded service chrge of 0%. To the new totl tx (VAT) of 7 -- % dded. ) Which of the following clcultions will work out their finl bill? b) Explin how this clcultion is rrived t.

53 Sumbooks 00 Key Stge Clculting the Originl Amount ) A bicycle shop increses ll its prices by %. One of their bicycles now costs.0. Wht ws its price before the increse? L.8 ) A compny reduced its number of employees by tenth to 67. How mny employees did they hve before the reduction? ) At the end of the seson grden centre reduced the prices of ll its spring plnts by 0%. If plnt now costs 7.0, wht ws its price before the sle? ) A shop hd sle. All its prices were reduced by 0%. A cot costs 6 in the sle. Wht ws its price before the sle? ) A length of wood hs -- cut wy. It now mesures 8cm. Wht ws the originl 8 length of the wood? 6) The cost of ril journey is incresed by % to Wht ws its cost before the increse in price? 7) A crowd of 8,70 t Premier Division footbll mtch ws % fewer thn the previous week. How mny went to the previous week s mtch? 8) Kml gives hlf of her weekly wges to her mum for her keep. One third of the reminder she sves nd the rest,, she spends on herself. How much money does Kml ern in week? 9) The height of tree incresed by 6% over period of yer to 6.9 metres. Bob wnts to clculte its height t the beginning of the yer. ) Which of the following clcultions should he do? b) Wht ws the height of the tree t the beginning of the yer? 0) Gwyneth invested some money in bnk ccount. She left the money in for two yers. At the end of the first yer her investment hd interest of % dded to it. At the end of the second yer further % ws dded to it. She then hd,6.0 in her ccount. ) Clculte the mount in her ccount t the end of the first yer. b) Wht ws her originl investment?

54 Sumbooks 00 Key Stge Proportion L.8 ) The tble below shows the popultion of two towns, Greystock nd Thrushm in 980 nd 000. Greystock Thrushm ,0 7,80 6,80 ) In Greystock the popultion fell by.% between 980 nd 000. Wht ws the popultion in Greystock in 000? b) In Thrushm the popultion incresed between 980 nd 000. Clculte the percentge increse to deciml plce. c) Between 980 nd 000 the popultion of two other towns, Kinster nd Flockborough incresed by the sme mount. The percentge increse in Kinster ws greter thn the percentge increse in Flockborough. Which of the following sttements below is true? In 980 the popultion in Kinster ws higher thn in Flockborough In 980 the popultion in Kinster ws lower thn in Flockborough In 980 the popultion in Kinster ws the sme s tht in Flockborough From the informtion given you cnnot sy whether Kinster or Flockborough hd the higher popultion ) A compny mkes lptop computers nd mobile phones. The tble below shows the vlue of their sles in thousnds of pounds for 99 nd 000. Lptop Computers Mobile Phones ,00,00,00 ) Wht ws the percentge increse in the vlue of the compny s lptop computer sles between 99 nd 000? b) The compny s sles of mobile phones incresed by 00% between 99 nd 000. Wht ws the vlue of their sles in 000? c) Wht proportion of their 99 sles were mobile phones? d) Wht proportion of their 000 sles were mobile phones?

55 Sumbooks 00 Key Stge Letters nd % L.8 ) A length of string is xcm. Another piece mesures x + cm. If the second piece is 0% longer thn the first, clculte the vlue of x. ) In 998 the cost of bus fre ws x pence. In 999 it incresed by 0%. ) Wht ws its price in 999 in terms of x? In 000 the price incresed by further 8%. b) Wht ws the new price in terms of x? c) If bus ticket cost.0 in 998, how much did it cost in 000? (correct to the nerest penny) ) A length of string mesuring y centimetres is cut in hlf. One of the pieces is discrded nd the other is cut into thirds. Two of these pieces re discrded nd the remining one is cut in hlf. ) Wht is the length of one of these pieces in terms of y? b) If the originl length of string ws 600cms, wht were the lengths of ech of the two finl pieces of string? ) The length of rectngulr piece of wood is xcm nd its width is ycm. The rectngle is mde smller by cutting 0% off its length nd 0% from its width. ) By wht percentge does its re decrese? Another piece of wood with the sme dimensions hs 0% cut from its length nd 0% cut from its width. b) By wht percent does its re decrese? c) If the originl length ws 0cm nd its width ws 0cm, clculte their finl res in ech cse. ) The popultion of town in 998 ws n people. During 999 the popultion incresed by 8%. During 000 the popultion decresed by %. Wht ws the popultion of the town t the end of 000 s percentge of n? 6) A rectngle hs length of xcm nd width of ycm. ) Wht is its re in terms of x nd y? Another rectngle hs the sme re, but its width is 0% greter. b) By wht percentge is its length smller? A rectngle mesures 0cm by 00cm. c) Wht re the dimensions of rectngle hving the sme re with one side 0% greter?

56 Sumbooks 00 Key Stge Substitution L.8 ) If = 0., b =.8, c =. nd d = 0. clculte the vlue of ech of the following giving your nswer correct to deciml plces wherever necessry. ) + c b) b + d c) c d) d e) c + b f) b g) + 7b h) b i) (c ) j) c + k) b + c l) c+ d m) b( + b) + b b ( b + c ) n) o) (b + c) p) c b ( + b ) b + c q) r) s) c(b d) t) c d d + ( + d ) c bc u) c + ( d) v) w) c(b ) ( + d ) x) c b ) The solution to the qudrtic eqution x + bx + c = 0 cn be found by using the eqution:- b ± b c x = For exmple, the solution to x + 6x = 0 is:- 6 ± 6 ( ) 6 ± x = = ± = = or so x = 0.6 or -.6 correct to deciml plces i.e. the qudrtic hs two solutions, either x = 0.6 or x = -.6 b ± b c Use the formul x = to solve the following qudrtics ) x 7x + 6 = 0 b) x x 0 = 0 c) x + x = 0 d) x x = 0 e) x 7x + = 0 f) 0x + x 7 = 0 g) x 7x = 0 h) x x + = 0 i) x + x 7 = 0 j) x x + = 0 k) x x = 0 l) 9x x 8 = 0 6

57 Sumbooks 00 Key Stge How mny Solutions? L.8 ) Equtions cn hve different numbers of outcomes. For exmple:- x = hs one solution, x = x = x + x is correct for ll numbers x = 9 hs solutions, nd - Sy whether the following re true for (i) one vlue, (ii) two vlues or (iii) ll vlues of x ) x + = b) x = c) x = x + d) -- x = 9 e) = 7 f) x = x + x g) = 6 h) x x 7 x = i) = x x j) = k) + 6x = l) x = m) -- x = 7 n) x = 6 o) x + 7 = x + 0 x + 7 p) x x+ = 98 q) = 7 r) x 7 = x 9 s) x + = x t) x = x + u) = ) Clculte the vlues of x which stisfy the following equtions. ) x = 00 b) x 7 = 8 c) x = d) x + 7 = 8 e) 8 x = 0 f) + x = 9 g) (x + ) = 00 h) (0 x) = 6 i) ( + x) = x x + j) = k) x = l) = x + x 0 x 0 m) = 7 n) = 0 o) = p) = x + q) = x r) x+ x x+ = + x ) Which of the following equtions hve only one solution? ) x = 6 b) x + 6 = 6 c) x = d) x + = 96 e) x = 7 f) + x = x + x + 9 g) = h) x = 9 i) = x + x 9 x + 7 j) = 7 k) = 0 l) = 0 7

58 Sumbooks 00 Key Stge Formule L.8 ) Rerrnge the following formule to mke the letter in the brckets the subject. C D ) A = LB (L) b) π = --- (C) c) y = -- () d) v = u + t (u) e) v = u + t () f) y = x( + b) (x) g) y = x( + b) (b) h) A = πr (r) i) I = xy w (w) x ) r h The volume of cylinder is clculted with the formul V = πr h. d ) If r = --, substitute this in the formul nd simplify your nswer. b) If the height of the cylinder is the sme s the rdius, wht is its volume in terms of the dimeter? ) d b h This regulr trpezil prism hs height of h centimetres nd depth of d centimetres. The two opposite edges of the trpezium re nd b centimetres. The volume of this shpe is given by the formul:- V = -- ( + b)dh ) Wht is its volume if the height nd depth re equl? b) Wht is its volume if, d nd h re equl nd = -- b? Give your nswer in terms of. ) The formul for clculting the volume of prism or cone like these is Volume = re of bse height -- ) Wht is the volume of cone whose height is h nd bse rdius is r? b) Wht is the volume of cone whose height nd bse dimeter d re equl? c) Wht is the volume of pyrmid with bse of sides x nd y nd height h? d) Wht is the volume of pyrmid with bse of sides x nd height of x? In ech cse simplify your nswer s fr s possible. 8

59 Sumbooks 00 Key Stge Simultneous Eqution Problems L.8 ) In September, the mths deprtment bought rems of lined pper nd rems of grph pper for. In Jnury, they bought 6 rems of lined pper nd rems of grph pper for 8. Write down two simultneous equtions, letting x represent the cost of rem of lined pper nd y the cost of rem of grph pper. Use these equtions to clculte the vlues of x nd y. In My they bought 6 rems of lined pper nd rems of grph pper. Wht did it cost? ) Mrs. Jenkins buys kg of pottoes nd kg of crrots for.8. Mr Prry buys 8kg of pottoes nd kg of crrots for.0. Letting x represent the cost of the pottoes nd y the cost of the crrots, write down two simultneous equtions. Showing ll your workings, clculte the vlues of x nd y. Wht will Mr Pugh hve to py for 7kg of pottoes nd kg of crrots? ) Den hs number of smll weights ll of the sme mss, nd some lrger weights ll of the sme mss. He tries to clculte their sizes by weighing them ginst two pckets of cheese he hs. The 0g block of cheese weighs the sme s smll weights nd lrge weights. The 0g block of cheese weighs the sme s smll weights nd lrge weights. 0g 0g Letting x represent the mss of smll weight nd y the mss of lrge weight, write down two simultneous equtions. Use the equtions to clculte the msses of the two sizes of weights. ) A quiz gme hs two types of question, hrd nd esy. Tem A nswers hrd questions nd esy questions correctly to get points. Tem B nswers hrd questions nd esy questions correctly to get points. Write down two simultneous equtions using h to represent the points scored for nswering hrd question correctly nd e to represent the points scored when nswering n esy question correctly. Use the equtions to clculte the vlues of h nd e. Tem C nswers 6 hrd questions correctly nd esy question correctly. How mny points do they score? 9

60 Sumbooks 00 Key Stge Equtions from Experimentl Dt ) A grge hires out minibus. The dily chrge is shown in the tble below. L.8 Number of dys d Cost in pounds C ) Complete the tble. b) Write down n eqution for C, the cost to hire the bus, in terms of the number of dys d it is hired for. C =... c) Use the formul to clculte the cost of hiring the minibus for 0 dys. d) How mny dys cn the bus be hired for it to cost? ) Wter is put into lrge tnk through hosepipe. The supply of wter entering the tnk never vries. The tnk hs circulr cross section nd its sides re verticl. The tnk hs some wter in it before the hosepipe is turned on. The tble below shows the depth of the wter t minute intervls. Time in minutes t Depth in cm D ) Complete the tble. b) Write down n eqution linking the depth of wter D to the time tken t minutes. D =... c) Use the formul to clculte the depth of wter in the tnk fter it hs been running for minutes. d) The tnk hs depth of 0 centimetres. How long will it tke to fill the tnk? ) A metl continer is to be designed in the shpe of cylinder, open t the top. It s cpcity is to be 0 litres. The tble below shows the vlues of heights nd bse res tht give 0 litre cpcity. Height of Cn H cm Are of Bse A cm ) Complete the tble. b) Write down n eqution linking the cpcity of the cn, C litres, to the height of the cn, Hcm, nd the re of the bse, Acm. C =... c) The size which the designer chooses hs bse re of 00cm. Wht is its height? d) Another cn is designed so tht its height nd dimeter re equl. Clculte its height, correct to the nerest 0.mm. 60

61 Sumbooks 00 Key Stge Solving Equtions L.8 ) Clculte the vlue of x in ech of the following. ) (x + ) + = 0 b) (x ) + 7 = c) (x ) 6 = d) (x + ) + x = e) (x ) x = f) x + (x + ) = 80 g) x + (x ) = h) (x + ) x = i) (x + ) x = 6 j) (x + ) (x ) = k) (x + ) + (x + ) = 7 l) (x ) (x + ) = m) (x + ) = (x + ) n) (x + ) = 9(x ) o) (x 7) = (x + ) p) 7(x + ) = 8(x ) ) Clculte the vlue of x in ech of the following. x x ) = b) = c) x + x 6 d) = 6 e) = f) x + x 6 g) = x h) 7 = x i) x + = x + = 0 x + 6 = x 0 + x 8 x j) = x k) = x + x l) = x x 6 x m) x = n) x = o) x p) x = q) x + = r) x 6 + x x = 0 + x x = ) Clculte the vlue of x in ech of the following. x + x + x + + x + ) = b) = c) x + x + 7 = x + x + x + + x d) = 7 e) = 8 f) x + x + 9 = 8 x + x + x + + x + 6 g) = 8 h) = i) x + x + = 6 x 6 = x + x + = x + j) k) l) x = x + x = x + 6 x + = x + m) n) o) x = x + 6

62 Sumbooks 00 Key Stge Fctorising Expressions L.8 ) If b = ( b)( + b), fctorise ech of the following nd simplify further wherever possible. ) x y b) m n c) c d d) x e) m f) c g) x 9 h) m 6 i) c j) 7 k) 7 l) 6 m) 9x y n) 6m n o) c d p) x y q) 6m 9n r) 8c d s) b t) b 9 u) b ) Simplify ech of the following by first finding common fctors. ) b b) -- b + -- c) -- xy -- y d) x + x e) + b f) b b g) b h) -- b -- b i) -- y -- y j) + b k) b + b l) + m) b + b n) o) -- x + x p) b b q) x xy r) b b ) Fctorise ech of the following expressions. b b 8 bc b ) b) c) d) + e) + f) + b b xy 8 g) h) i) j) + k) + l) + b m) + n) + o) + b p) + q) + r) + c b c y s) t) u) b 8 y b b 7 8 b y x xy xy b -- b 6 y -- xy xyz b

63 Sumbooks 00 Key Stge Tringulr Numbers The rrngements of discs below show the squre numbers. L.8 Sequence position n disc discs 9 discs 6 discs ) Wht re the next two numbers of discs in the sequence? The eqution for finding the number of discs in n rrngement is D = n where D is the number of discs nd n is the sequence position b) Write down the vlues of n for the inequlity:- 000 < D < 00 Grce wnts to find n eqution for tringulr numbers. She sys tht she cn do this by considering the squre numbers. The grey discs below represent the series of tringulr numbers. Grce hs tken some discs wy from the squre sequence to get the tringulr sequence. grey disc grey discs white disc 6 grey discs white discs 0 grey discs 6 white discs c) Which of the following equtions represent the white discs? W = n(n ) W = n(n n) W = n W = n n W = n(n ) W = n(n + ) Grce now writes this eqution for the sequence of tringulr numbers. G = (n + n) d) Show how Grce gets this result. 6

64 Sumbooks 00 Key Stge The Grph of y = x ) The digrm on the right shows the grph of y = x nd its reflection in the x xis. Write down the co-ordintes of the points A, B, C nd D. D C.. y.. A B x L.8 ) The digrm on the right shows the grphs of y = x nd y = (x ). Write down the co-ordintes of the points A nd B. y B.. A x ) The digrm on the right shows the grphs of y = x nd its reflection in the line x = -. ) Write down the co-ordintes of the points A nd B. b) Wht is the eqution of the reflected grph? B. - y. A x y ) The digrm on the right shows the grphs of y = x nd its reflection in the line y = 9. ) Write down the co-ordintes of the points of intersection of the two grphs. y = 9 b) Wht is the eqution of the reflection? x ) The digrm on the right shows the grphs of y y = x nd its trnsltion units in the y direction. ) Write down the co-ordintes of the points A nd B.. b) Wht is the eqution of the trnslted grph?. A B x - 6

65 Sumbooks 00 Key Stge Inequlity Questions L.8 ) A number in the series 0, 0,,, 6... cn be clculted by using the expression ( n ) ( n ) where n is whole number. 9 8 For exmple the 0th number in the series is = 6 ) By using tril nd improvement method, clculte the three vlues of n which stisfy the inequlity:- ( n ) ( n ) 00 < < 600 b) By using tril nd improvement method, clculte the smllest number in the series which stisfies the inequlity:- ( n ) ( n ) > 00 ( n ) ( n ) ( n ) ( n ) c) By compring nd , write down the first numbers in the series formed by the expression substitution. ( n ) ( n ) Check your nswers by ) A number in the series 0,, 9,, 0... cn be clculted by using the expression n ( n ) where n is whole number. 00( 0 ) For exmple the 0th number in the series is = 0 ) By using tril nd improvement method, clculte the two vlues of n which stisfy the inequlity:- n ( n ) 000 < < 6000 b) By using tril nd improvement method, clculte the smllest number in the series which stisfies the inequlity:- n ( n ) > 00,000 n ( n ) n ( n ) c) By compring nd , write down the first numbers in the n ( n ) series formed by the expression Check your nswers by substitution. 6

66 Sumbooks 00 Key Stge Ares Bounded by Curves ) The digrm on the right shows the grphs of y = x. Which of the two inequlities below cn be used to describe the shded re below the x xis? y > x y < 0 y > y > x y > x y - x L.8 ) The digrm on the right show the grphs of y = 7 x. Which of the two inequlities below cn be used to describe the shded re bove the x xis? x < 0 y > 0 y < 0 y > 7 x y < 7 x y 7 x ) The digrm on the right shows the grph of y = x nd the line y = Which of the two inequlities below cn be used to describe the shded re bove the x xis? y < x < y > y < x y > x y x y = ) The digrm on the right shows the grph of y = (x + ) nd the line y = 9 Which three of the inequlities below cn be used to describe the shded re to the left of the y xis? y < 9 x < 0 y > 9 x < - y < (x + ) y < x y > (x + ) y y = 9 x ) The digrm on the right shows the grph of y = -(x + ) nd the lines x = - nd x =. Which four of the inequlities below cn be used to describe the shded re below the x xis? x > y < 0 x < - x > - x < y < -(x + ) y < x y > -(x + ) y - x 66

67 Sumbooks 00 Key Stge Pythgors etc ) ) c In this right ngled tringle two sides re of the sme length. c (i) Show tht = (ii) Wht is the re of the tringle in terms of c? L.8 b) c This digrm shows regulr octgon with ech side mesuring c centimetres. Using the result from prt, clculte its re in terms of c. ) A B The digrm shows n equilterl tringle with sides of. ) Show tht the length of the perpendiculr AB is b) Write down the re of the tringle in terms of 6 This regulr hexgon hs sides of 6 centimetres. c) Use the results bove to clculte its re ) 0cm 0cm 00cm Clculte the re of this kite. 0cm 0cm 00cm 67

68 Sumbooks 00 Key Stge Ares ) Clculte the res of the shded prts of these shpes. L.8 ) b) cm 8cm.cm ) The digrm shows circle with sector shded in. The ngle of the sector t the centre is 60º nd the rdius of the circle is cm. ) Wht frction of the circle hs been shded in? b) Wht is the re of the circle? c) Wht is the re of the sector? 0º 9cm 0. cm This digrm shows two concentric circles of rdii 9cm nd 0.cm. A sector with centre ngle of 0º cuts the circles. d) Clculte the re of the shded prt. ) A O cm B The digrm on the left shows circle of rdius cm nd squre with digonls of cm. The corners of the squre touch the circle. ) Clculte the re of the tringle AOB. b) Clculte the re of the shded prt of the circle. 68

69 Sumbooks 00 Key Stge Ares nd Perimeters ) L.8 The two circles shown in the digrm hve dimeters of nd. Their edges touch nd their dimeters re on the sme line. Show tht the re of the shded prt is 7 π -- ) x The digrm shows circle of rdius centimetres. The sector hs right ngle t the centre of the circle. ) Wht is the re of the sector in terms of? b) Show tht the length of the chord x is c) Show tht the re of the shded segment is (π ) ) This shpe is mde up of semicircles. A B Show tht the distnce from A to B, long the curve, is π centimetres. 69

70 Sumbooks 00 Key Stge Volume L.8 ) A biscuit pcket is in the shpe of n octgonl prism. One end of the pcket is shown. Four sides re ech cm long. The height of the pcket is 8cm nd its width is 8cm. The other four sides re equl. It is filled with round flt biscuits. cm cm cm 8cm cm ) Wht is the re of the end of the pcket? b) Wht is the mximum dimeter of the biscuits tht re put in the pcket? c) A pcket holds biscuits. Ech biscuit is 6mm thick. Wht is the volume of the pcket? d) Wht percentge of the pcket is tken up with biscuits? e) The pckets re put into cuboid shped boxes designed to hold 00 pckets. Wht is the size of the box? (You my ignore the thickness of the pckging) 8cm ) Prt of child s toy is plstic peg in the shpe of cylinder with squre hole through the middle. The minimum dimension between the hole nd the outside is centimetre. cm cm The sides of the squre re cm. ) Use Pythgors theorem to clculte the dimeter of the peg. b) Wht is the re of the end of the peg? (The shded prt of the first digrm) c) If the peg is 0cm long, wht volume of plstic is needed to mke the peg? d) If cm of the plstic hs mss of 0.9g, clculte the mss of one of the pegs. e) If btch of pegs re mde, wht will be the totl mss of plstic needed? 70

71 Sumbooks 00 Key Stge Congruent Tringles ) Which three of these tringles re congruent? L.8.cm.cm.cm 6.0cm b.cm.cm.cm c.cm.8cm.cm d.cm.0cm.cm e.cm.cm.cm.cm f.0cm.cm.cm g.cm.cm h.cm.0cm ) Which three of these tringles re congruent? 7cm 60º 6cm 60º 7cm 6cm 60º 6cm b c d 6cm 60º 7cm 7cm 6cm 60º 7cm 7º 60º e f g h 60º 6cm 0º 6cm 7cm 60º 6cm ) º º 60º 60º 60º b c d 66º 66º º e 66º 7 º g f 6 º h 6 60º 60º Which, if ny, of the following sttements re true for these digrms? (i) Tringles c, e nd h re congruent. (ii) Tringles b, c nd h re congruent. (iii) Tringles nd g re congruent. (iv) Tringles c, d nd e re congruent. (v) Tringles b nd h re congruent. (vi) Tringles, c nd h re congruent. 7

72 Sumbooks 00 Key Stge Similr Tringles ) L.8 0cm y 8cm cm cm x These tringles re similr. Clculte:- ) The length of x b) The length of y ) B A X Y º bº º bº Z C In the tringle ABC, XY is prllel to BC nd hlf its length ) Wht is the size of ngle ZXY? b) Wht is the size of ngle XYZ? c) How mny similr tringles re there in this digrm? d) If the length of AB is 00cm, wht is the length of YZ? e) If the length of BZ is 0cm, wht is the length of BC? ) A 0cm B 0cm E 00cm C 0cm In this shpe, AB is prllel to CD. ) Which ngle is equl to ngle ABE? b) Which ngle is equl to ngle ADC? c) Clculte the length of AE. d) Clculte the length of BE. D 7

73 Sumbooks 00 Key Stge Angles L.8 ) º xº xº The digrm shows rectngle with its digonls. Two ngles of xº nd xº re indicted. Clculte the size of the ngle mrked º in terms of x. ) A B xº xº D In this shpe, AC = BC nd AB = AD Two ngles, x nd x re mrked. Clculte the size of ngle x. C ) A B E xº xº D The digrm shows kite ABCD. Tringle ABE is similr to tringle BEC. Two ngles of size xº nd xº re shown. ) Clculte the size of x. b) Wht re the sizes of the four ngles of the kite? C ) B D 6xº F xº A 7xº E C In the digrm, DE is prllel to BC nd FD is prllel to CA. Three ngles of 6xº nd xº nd 7xº re shown. Angle EFC is twice ngle DBF. Clculte the sizes of the ngles of tringle DEF. 7

74 Sumbooks 00 Key Stge Sine, Cosine nd Tngent Rtios L.8 ) In ech of the following right ngled tringles, clculte the size of the unknown side x. Write down your nswer correct to the nerest 0.mm. ) b) x c) x 6cm 8º cm 7º cm º x d) e) x cm x 7cm º º f) x 6º cm g) cm 7º x ) In ech of the following right ngled tringles, clculte the size of the unknown ngle x. Write down your nswer correct to the nerest 0.º. 7cm ) b) c) d) 8cm xº 7cm 8cm 6cm 9cm xº xº cm xº cm e) 9.cm f) g).9cm 8.cm xº xº 7.cm xº cm cm ) cm cm Clculte the size of the ngle mrked x. 6cm xº cm 7

75 Sumbooks 00 Key Stge Berings ) In the digrm below, clculte:- ) The bering of Port Benon from the lighthouse. b) The bering of the lighthouse from port Benon. L.8 N Lnd Port Benon.8km Lighthouse.km Se ) Bz stnds on Angus Cliff nd observes ship nd Regis Hed through his binoculrs. Se N Ship Regis Hed.9km.6km.km Lnd.7km Angus Cliff ) Wht is the bering of the ship from Angus Cliff? b) Wht is the bering of Regis hed from Angus Cliff? 7

76 Sumbooks 00 Key Stge Clculting Lengths in Tringles ) The digrm below shows kite. A L.8 9cm Clculte:- D 6º E º B ) The length of EB. b) The length of AE. c) The length of DE. d) Wht re the lengths of its digonls? C ) In the shpe below, two right ngled tringles ADB nd DBC mke third right ngled tringle ABC. cm A D ) Clculte the size of the ngle mrked x. b) Wht is the size of ngle ABD? c) Clculte the length of AD. B cm xº C ) The tringle ABC hs two ngles of 8º nd º. Its height is 6cm. Clculte the length of its side BC. A 6cm B 8º º C 76

77 Sumbooks 00 Key Stge More Similrity ) The digrm shows n equilterl tringle with sides mesuring cm. The perpendiculr height of this tringle is hcm. L.8 h ) Use your knowledge of Pythgors theorem to clculte the vlue of h in terms of. b) A tetrhedron is mde from four of these tringles. Wht is the surfce re of the tetrhedron in terms of? c) A tetrhedron hs edges of length cm. Clculte its surfce re. d) Another tetrhedron hs edges of length cms. Wht is the rtio of the surfce re of the tetrhedron with sides of cm to tht of this lrger one? ) The digrm below shows two spheres, one with rdius of cms nd the other with rdius of cms. ) The surfce re of the smller sphere is A s = π. Wht is the surfce re, A l, of the lrger sphere? b) The volume of the smller sphere is V s = -- π. 6 Write down formul for the volume V l of the lrger sphere. c) The dimeter of sphere is cms. Clculte its surfce re nd volume. d) The dimeter of smll sphere is cm nd tht of lrge sphere is 7cm. Explin why the rtio of their surfce res is : 9. e) A sphere hs rdius of cm nd lrger sphere hs rdius of 0cm. Explin why the rtio of their volumes is 7 : 6. 77

78 Sumbooks 00 Key Stge The Cricket Scores L.8 ) In the Brsetshire cricket legue, the tems ply two gmes week for 0 weeks. The frequency tble below shows the scores of Eggwold Cricket Club for 00. Runs Scored > 0 nd 00 > 00 nd 0 > 0 nd 00 > 00 nd 0 > 0 nd 00 > 00 nd 0 Number of Gmes 7 6 Cumultive Frequency Grph Copy nd complete the cumultive frequency grph for Eggwold. b) The digrm below shows the cumultive frequency curve for Eggwold s rch rivl Feldown. Use it to complete the frequency tble for their scores. 0 Runs Scored > 0 nd 00 > 00 nd 0 > 0 nd 00 > 00 nd 0 > 0 nd 00 > 00 nd 0 Number of Gmes c) Which tem hd the better medin score? d) Clculte pproximte vlues for the men scores for both tems. Which tem hd the highest men score? 78

79 Sumbooks 00 Key Stge Cumultive Frequency L.8 ) The grph below shows the cumultive frequency distribution of the mrks scored by 0 pupils in mthemtics exmintion. The mrks re out of Cumultive Frequency 0 From the grph estimte the following ) Wht is the medin mrk? b) How mny pupils got more thn 0%? c) How mny pupils got more thn 9%? 0 Mrk 00 ) The pupils in 9W were sked how much pocket money they were given ech week. The results re shown on the frequency grphs below. 0 Number of Pupils 8 6 Cumultive Frequency Pocket Money Pocket Money 0 ) Complete the cumultive frequency grph. b) Use the grph to estimte the medin mount of pocket money the clss gets. c) Estimte the percentge of pupils who get more thn 0 per week. 79

80 Sumbooks 00 Key Stge Cumultive Frequency ) The cumultive frequency grph shows the heights of 0 pupils in clss. L.8 Cumultive Frequency Grph 0 A B 0 0 C D 0cm 0cm ) Which of the four frequency grphs on the right shows this informtion? b) Drw cumultive frequency grph for ech of the other three frequency grphs. ) The mnufcturer of new chemicl fertiliser sys tht plnts will produce t lest % more fruit when fed on it. They do n experiment to test this sttement on two sets of plnts. One set they give the fertiliser to, but the second set they don t. The digrm below shows cumultive frequency curves for the two sets of plnts. 0 Number of Plnts A B 0 6 Amount of Fruit per Plnt in kg ) Which grph, A or B, represents the plnts which hve hd fertiliser? b) Wht is the medin mount of fruit picked from ech group of plnts? c) Wht ws the rnge of weights for ech of the two groups? d) Do you think tht they re justified in climing % increse in production? Explin your nswer. 7 80

81 Sumbooks 00 Key Stge Cumultive Frequency ) 00 pupils from yer 9 were sked wht time they got out of bed lst Sturdy morning. The results re shown in the tbles below. L.8 Tble A Tble B Cumultive Frequency Time Frequency 06: :00 time < 07:00 07:00 07:00 time < 08: : :00 time < 09:00 09:00 09:00 time < 0:00 7 0:00 0:00 time < :00 0 :00 ) Use tble A to show tht the men time they got out of bed ws pproximtely 09: b) Complete the cumultive frequency tble for the dt. c) Drw cumultive grph for the dt. d) From your grph estimte the medin time the pupils got out of bed. ) A computer shop sells 70 different kinds of gmes. The frequency grph below shows their prices. Cumultive 0 Frequency > 0 > 0 > > 0 > > 0 > ) Show tht the men price of computer gme in the shop is pproximtely 9.9 b) Complete the cumultive frequency tble for the dt. c) Drw cumultive frequency grph nd from it estimte the medin price of the computer gmes. 8

82 Sumbooks 00 Key Stge Probbility L.8 ) Tony hs fir die. He rolls it nd records the result. ) Wht is the probbility of him getting when he rolls it once? b) Wht is the probbility of him getting two s when he rolls it twice? c) Wht is the probbility of him getting three s when he rolls it three times? d) Wht is the probbility of him getting followed by when he rolls it twice? e) Wht is the probbility of him not getting when he rolls it twice? ) I hve two bgs contining coloured discs. Bg contins red discs yellow discs 6 white discs Bg contins red discs yellow discs Bg white discs Bg Discs re withdrwn from the bgs. ) Wht is the probbility of withdrwing yellow disc from bg? b) Wht is the probbility of withdrwing yellow disc from bg? c) I withdrw two discs, one from bg nd one from bg. Which of the clcultions below shows the probbility of getting white disc followed by red disc? d) Chen tkes disc from bg then disc from bg. Wht is the probbility tht he tkes yellow disc ech time? ) In 7D there re boys nd girls. In 7F there re boys nd girls. Two people re to be chosen t rndom by the hed of yer, one from ech group. ) Wht is the probbility tht they re both boys? b) Wht is the probbility tht they re both girls? c) Wht is the probbility tht one boy nd one girl re chosen? ) At the inter-schools thletics meeting, Gom is entered for the 00 metres nd the high jump finls. She knows from pst experience tht her chnce of winning the 00 metres is 0.6 nd her chnce of winning the high jump is 0.. ) Wht is her chnce of winning both events? b) Wht is her chnce of winning just the high jump? c) Wht is her chnce of winning just the 00 metres? d) Wht is her chnce of winning t lest one of the events? 8

83 Sumbooks 00 Key Stge Probbility L.8 ) In clss of 8 pupils, some hve brothers, some hve sisters, some hve both nd some hve neither. The digrm below shows this. There re 7 pupils who hve both brothers nd sisters. Those with brothers Those with sisters ) How mny pupils hve brother? b) Wht is the probbility tht pupil, chosen t rndom, will hve brother? c) Wht is the probbility tht pupil, chosen t rndom, will hve sister? d) Wht is the probbility tht pupil, chosen t rndom, will not hve brother or sister? e) Wht is the probbility tht pupil who hs brother lso hs sister? ) In order to get from her home to her Grns, Cin hs to ctch two busses. She knows tht when she wits for bus t the first stop there is probbility of 0.7 tht she will hve to wit more thn minutes. At the second stop, the probbility is 0.. ) Clculte the probbility tht she will hve to wit more thn minutes t both stops. b) She visits her Grn every Sturdy for 0 weeks. How mny times would you expect her to wit for both buses for more thn minutes ech? ) George hs bised die. He clcultes tht the probbility of getting, or re ech 0.. ) The probbility of him getting followed by is 0.0. Wht is the probbility of him getting with one roll of the die? b) Wht is the probbility of getting if it is the sme s the probbility of getting 6? ) Six crds hve the numbers to 6 written on them. 6 The crds re shuffled nd plced fce down on tble, one on top of the other. Clculte the following probbilities. ) The top crd hs on it. b) The top crd is nd the next crd is. c) The top two crds re nd in ny order. 8

84 8

85 Sumbooks 00 Key Stge Estimting - Pge 7 Answers ) ) 6 b) 6 c) 0 d) e) f) g) h) i) 0. j) k).8 l).6 m) 0 n) o) 0 p) q) 70 r) 90 s) 00 t) 70 u) 6 v) 0 w) 0 x) ) ) b) c) d) e) f) 6 g) 0 h) 0 i) 7 j) 0 k) 0 l) 60 m) n) o) p) q) r) ) ) 9 b) c). d) 0. e) 00 f) 0.7 g) 0 h) i) 00 j) 00 k) 0 Powers of Numbers - Pge 8 ),,,,, 7, (=)8,,,,,, 6 ) 7, 9, 6, 7, 7 ), 8 ) 9,68 6,6 77,7,, 9,09 6,6, ) 9, 8,, 9 6), f, h Multiplying nd Dividing - Pge 9 ) From the top, clockwise, 0.0, 0.,., 0., 0.0, 0 0, 000, 00 ) ) 0.0 nd 0.0 b) nd 0. or nd 0. c) d) nd 0 e) f) nd 0. or nd 0. g) h) 0. (0.0 0.) i) ) ) 0,000 b) c),000 d) e) 0.06 f) 0.9 g) 0.00 h) 0.0 i) 00 j).0 k) 0 l) m),000 n).0 o),00 p) 0.0 q) 0. r).0 Percentge Chnge - pge 0 ) ) 0, b) % c).% d), ) ) The numbers hve been rounded off, thereby gining nd losing smll mounts. b),6,6 9,6,96,7,9 c).% ) ), b) 0.6% c) 9,900 d).9% Frctions - Pge ) ) b) c) 9,687. litres 7 ) pieces ),00 miles ) ) b) 80 ) ths 0 Rtio - Pge ) ) 0 b) :.68 ) ) cm b).km c).8cm ) :. :.8 : 6. ) ).69kg,.7,.9 b) 8.9kg Rtio - Pge ) ) ml, 0ml, ml b) 6ml, ml, ml c) Hll s ) ) 8/8 b).78g c) 0.7 d). ) ) 0,000 wtts b) 7,000 wtts c) : d).: e) Probbly. The cost of longlife bulb is. times s much s n ordinry one. However the long life bulb uses only fifth of the electricity of n ordinry one. The vlue of this sving outweighs the cost of the more expensive bulb. Odd nd Even Solutions - Pge ) b,c,g,h,k,l,o,p ) ) odd b) odd c) even d) odd e) odd f) even g) odd h) either i) odd j) neither k) odd l) odd ) ) whole b) whole c) no d) no e) whole f) no g) no h) no ) ) b) When the difference in the brcket is odd c) When the difference in the brcket is even d) Either or (-) e) Both even or both odd Simplifying - Pge ) ) b) 6x c) w d) y e) 60x f) -n g) -6b h) 7x i) -p j) -7z k) x + y l) p + q m) w n) -f o) -k m p) -x q) 0m r) x 8 ) ) b) 7y + y c) b b d) + y e) 7x + x f) 7c bc g) x + x h) b + b i) -c b j) y + 0y k) 8y + xy l) 0d cd m) y + y + n) 0 o) 7c + c ) ) -- b) x c) -- y d) -- e) -- c f) -- y g) -- h) -- b i) -- x 8 j) -- c k) - -- l) -- y m) - -- n) -- x o) -- c p) - -- b c x c 8w b x y ) ) -- b) c) d) e) f) g) h) y c x c y b c i) j) k) -- l) -- m) n) -- o) -- p) ) b, d, f, k, l, n, o, p Simplifying - Pge 6 ) ) -- b) -- c) -- d) -- e) -- f) -- g) -- h) -- i) -- j) k) -- l) -- m) -- n) ) ) -- b) -- c) 6 d) e) f) g) h) i) j) k) l) x c y b x y ) ) -- b) -- c) -- d) -- e) -- f) -- g) h) i) x j) k) c y x l) m) n) o) p) -- q) y c y r) s) -- t) u) ) ) b b) -- c) -- d) e) -- f) ---- g) b h) -- i) 9 6x yz x j) k) l) m) n) o) x p) q) b z x y r) -- 7 ) = y xy y = b b y xy 9xy = c c = b c 8xy = b bc b c = b b x y = = = bc bc x yz xy z xy y xy xy x x y Multiplying Brckets Together - Pge 7 ) ) x + b) x + 6 c) x + 7 d) x + 9 e) x f) x + g) 8x h) 0x 0 i) -0 j) x 7 k) 6x l) x 8 m) x + 0 n) 9x + o) -x 9 p) 6x q) x r) 8x + ) ) ) x + x + 6 b) x + 9x + 0 c) x + 0x + d) x x 0 e) x + x 8 f) x 6x 6 g) x 0x h) x x 8 i ) x 7x 0 j) x x + 6 k) x 9x + 8 l) x 9x + 0 ) ) x + 9x + b) x + x + c) x + 9x + 0 d) x 0x 6 e) x x f) x x g) x + 7x 8 h) 6x + x 6 i) x + x

86 Sumbooks 00 Key Stge j) 6x 0x + 6 k) x x + 7 l) x x + 8 ) ) x + 9x + 0 b) x + x + 6 c) x + x + 8 d) x e) x + 8x f) x + x 6 g) x x h) x 9x i) 6x 9x 7 j) 9x x + 0 k) x x + l) 6x 60x + ) )x + x + 6 b) 0x + 8x + c) x + x + d) 0x x e) x 6x f) x x 7 g) 0x + x h) x 0x i) x + x j) x x + 8 k) x x + 8 l) x 8x + 6) ) x + x + b) x + 0x + c) x x + d) x 8x + 6 e) x + x + f) x + x + g) x x + 9 h) x 0x + i) 9x + 8x + 9 j) x + 60x + 6 k) 6x x + 6 l) 6x 6x + 9 m) x + 8x + n) 9x + x + o) x 0x + p) 6x x + 9 Fctorising - Pge 8 ) ),,, 6 b),,,, 6, c),, b, b d),,, e),,, 6,,,, 6 f),, g),,,, 6,, b. b, b, b, 6b, b h),,,,,,,, i),,,, b, b, b, b j),,,,,, b, b, b, b, b, b k),,, x, x, x, x, x, x l), 7, b, 7b m),,, 6, c, c, c, 6c, c, c, c, 6c n),,, 8, x, x, x, 8x, y, y, y, 8y, xy, xy, xy, 8xy o),,,,,, b, b, b, b, b, b ) ) b) 9 c) d) e) b f) g) b h) i) b j) k) x l) xy m) xy n) b o) c ) ) ( + ) b) (x + ) c) (7x + 8) d) (x ) e) y(x + ) f) b( ) g) b( ) h) 6(c ) i) x(x y) j) (b + ) k) y(x y) l) ( ) m) ( bc) n) 6x( x + ) o) (b + bc + c) ) ) x(y + x) b) y(x + ) c) (b c + d) d) ( + b + c) e) ( + b b) f) (6b c + bc) g) x( + x + x ) h) ( + b + c) i) ( + b b ) j) ( + x b) k) y(x + y) l) b( b) m) ( + b + 6c) n) ( + b b) o) (b 8 + bc) p) x(x + y + x) q) b(b + + c ) r) ( + b b ) Solving Simple Equtions - Pge 9 ) ) b) c) d) - e) -0 f) g) h) 6 i) ) ) b) -- c) d) e) f) -- g) -- h) -6 i) 9 j) 9 k) l) 6 ) ) 8 b) c) d) e) 6 f) 8 g) h) - i) 8 j) 0 k) l) 0 ) ) b) c) d) 7 e) 0 f) 8 g) h) i) 8 j) k) 7 l) 0 ) ) b) c) d) e) 6 f) g) h) i) -- j) 7 k) l) 0 -- Sequences - Pge 0 ) ) 0 b) d = r(r + ) c) 0 discs ) ) b), 6 c) Yes. When n is odd, n is odd. So n + n is odd + odd = even. When n is even, n is even. So n + n is even + even = even. Therefore the nswer is lwys even. 7 8 ) ) b) -----, c) As in question, n + n is lwys even therefore n + n + must lwys be odd. Tril nd Improvement - Pge ) x = 8x b) The solution will occur when x = 8x i.e. when the difference is zero. c). nd. The difference chnges from + to so difference of 0 is between. nd.. d) x x 8x Difference e).8 nd.9 f) When x is.8 the difference is 0.0. This mens tht when the difference is 0, x lies between.8 nd.9. Therefore.9 is the solution correct to two deciml plces. g) 0.8 Grphs - Pge ) ) H b) E c) (,9) d) B e) C nd E f) G g) H h) (,) i) C j) B k) G ) ) y = x + b) y = 9 x c) y = d) A nd E e) (,) f) (,-) g) (,0) Simultneous Equtions - Grphs - Pge ) x = 8, y = 9 ) y = 9 x y = x + x =. y =. ) y = 0, x = -. Simultneous Equtions - Pge ) ) A b) B c) y x = + 6 = y + x = - = -7 ) x = 8, y = 6 ) x = -, y = - ) x = -., y =. Solving Simultneous Equtions - Pge ) ) y = x = b) y = x = c) y = x = d) x = y = e) x = y = f) y = x = ) ) x = 7 y = b) x = y = c) x = y = d) x = y = e) x = y = f) x = y =. ) ) x = 6 y = b) x = y = c) x = y = d) x = 6 y = e) x = 7 y = f) x = y = 6 ) ) x = y = b) x = y = c) x = 6 y = d) x = y = e) x = y = f) x = y = ) ) x = -9 y = b) x = y = c) x = - y = d) x = y = - e) x = -6 y = f) x = y = 0 6) ) x = 7 y = b) x = 6 y = 8 c) x = 8 y = - d) x = - y = e) x = y = 8 f) x = - y = Inequlities - Pge 6 ) ) 6, 7, 8 b) 7, 8, 9 c) -, -, 0 d) -7, -6 e) -, - f) -, - g), 6, 7 h) 6, 7, 8 i) -, -, - j),, k),, l) -6, -, - m) 7, 8, 9 n) 0,, o),, p),,, q),,, r),, s),, t),,, 6 u) -, 0 v) 0,,,,,, 6, 7 w),,,,, 6, x) -, 0, ) ), b), c) -, d), e) 0, f) -, Pythgors Theorem - Pge 7 ) ).6cm b) 9.8cm c).9cm d).9cm ) ) 8.cm b).6cm c) 8.9cm d) 9.8cm ) In ech cse the squre on the hypotenuse is equl to the sum of the squres on the other two sides. i.e. 0 = = + = + 7 ) 6cm, cm nd.7cm ) 9cm 86

87 Sumbooks 00 Key Stge Ares of Right Angled Tringles - Pge 8 ) ).cm b) cm c) 7.87cm d) 8.8cm ) ) 8.cm b) 0.7cm c) 8.cm ) ).cm b) 66.cm c).cm d) 80.7cm ) ) Multiply the digonls together, then divide by. b) Multiply the digonls together, then divide by. c) Bse perpendiculr height ) Ares of Plne Shpes - Pge 9 ) ) 98cm b) 87cm c) 0cm d) 9.cm ) ).cm b).9cm c) 8cm d).6cm Volumes of Prisms - Pge 0 ) ) cm b) 6cm ) ) 8cm b) 8cm ) 6.cm ) ) 8cm b) 09cm ) 968cm Enlrgement nd Similrity - Pge ) ).cm nd 6.cm b) 6.09cm nd.70cm c) :. ) ). b) -- c).cm d).67cm 9 ) ).7cm b).6cm c).cm Routes - Pge ) Rounding Off - Pge ) A - B - 6 C - 7 D - 9 E - 0 F - ) ) 97.7cm b) 8.7cm ) 8.9m ) 6. Length of wood < 7.. indictes tht the length of the wood is greter thn or equl to the first vlue. The < indictes tht the length is less thn nd not equl to the second vlue. ) 9.ºC nd 0.ºC 6) The totl mss is 99kg when ech is rounded to the nerest kilogrm. However the minimum nd mximum totl msses re 96.kg nd 0.kg. In this cse the totl mss ws ner the top end of the rnge. Imprecision of Mesurement - Pge ) ) mm b) mm ) ) minutes b) 9 minutes ) The old record could be smller thn the new one but when rounded off they re both 7.. ) 8. nd 8. seconds. ) This is bsed on its upper limit. If the dimensions re not on the upper limit then it will not hold this mount. Better to use the bottom limit i.e. 07 litres ) Compound Mesure - Pge 6 ) ) 98 gllons b) gllons c) gllons (pprox) ) ) 0m b) 9.86m c) 00.m d) tins ) 6.km/hr ),700 metres ) ).0m b) 9cm c). litres d). metres per second Currency - Pge 7 ) 7.96, 8.9 ) Most in UK. Lest,.6, in Austrli ) $9.86 ) 69,0 Lir.,70 Lir ) 686 6) It is more economicl to buy two tickets s they will cost 7.9 ltogether, sving 6.0 7) 8. Trees - Pge ) Coch Journey - Pge 8 ) 80 miles b) 0mph c) 0 minutes d) 6 miles e).7mph f) 6 minutes g) :6pm h) miles i) 7.mph j) :pm Trin Journey - Pge 9 ) Birminghm to Glsgow b) 97.0kph nd 7.kph. c) 60km d) hrs 7mins e) 7mins f) 6:0 g) 0km Rod Rce - Pge 0 ) Hri b) km c) After bout 0/ minutes d) e) f) Brody g) Brody h) going down hill i) Brody by bout 0 minutes j) 8kph k) Hri suddenly stopped, probbly becuse of n injury. He strted gin some time lter but rn t slower speed. 87

88 Sumbooks 00 Key Stge Men - Pge ) ) 7.cm b) 8cm c) 8cm d) 6cm ) ). nd.78 b) 7 nd c) 7 nd 79 Men nd Rnge - Pge ) ) 6 ) ) nd ) nd 6) nd 7) 7 Sweets - Pge ) b) 6.88 c) 60 nd 6880 d) 8 Flower Seeds - Pge ) 0. b) c),800 nd 0,00 d) 6,0 e) White. Rnge is 7 =. Rnge for blue is 7 = f) A pcket of seeds usully hs more white seeds thn blue seeds Mesuring Sctter - Pge ) ) b) bout or c) More ) ) b) About.7kg c) About 6.cm Reltive Frequency - Pge 6 ) 6 or 7 ) blue, green nd red ) ) Lim s becuse he hs done it the most number of times b) Yes. The totl result for ech colour should be bout the sme. However the red occurs nerly times more often thn the yellow nd nerly twice s often s the blue c) or bout 0. d) or bout Probbility - Pge 7 ) ) 0.6 b) 0 c) ) Bg A. His chnce of getting yellow is 0. in bg A nd 0. in bg B ) ) b) t lest 7 c) 0.7 or 7.% d) 6 Powers - Pge 8 ) ) = + = 9 b) 9 = +9 = c) 0 7 = 0 7 = d) 0 = 0 = e) 7 = = 6 f) 0 = = 6 ) ) 6 b) 6 c) or 8 d) or 8 ) ) b) true c) d) true e) 6 8 = ( ) ( ) = 6 6 = 0 but 8 = ( ) = 6 f) 8 g) Becuse = 6 0 h) true i) 8 j) true k) l) Stndrd Form - Pge 9 ) ).6 0 b).7 0 c) d) 8. 0 e). 0 f). 0 g) h).8 0 i) j). 0 k) l) ) ). 0 - b) c). 0 - d). 0 - e). 0 - f) g). 0 - h) i). 0-7 j) k) l) 0 - ) ),00 b) 0,000 c) 8,000 d) 6,00 e) 6,00 f) 67,00,000 g),80,000 h) 70 i) 67,000 j),680 k),80,000 l) 6,00 ) ) 0.0 b) c) 0.8 d) e) f) g) h) i) j) k) l) ) 6.7 0, 9. 0,.6 0, 6.8 0,.76 0,. 0 6). 0 -, ,. 0 -,. 0 -, , ) ,,000, 0 8) 0-8, 0 0-9, ) 8. 0,

89 Sumbooks 00 Key Stge Stndrd Form - Pge 0 ) ) 0 - nd 0 - b) (i). 0 - (ii) ) ).6 0 b) c). 0 d) e).79 0 f) ) ) b) c) d) e). 0 0 f). 0 g). 0 h).8 0 i).8 0 j) 0 ) ) 0 b) 0 c) 0 d) 0 e) 0 f) 0 g) 0 h) 7 0 i) 0 j) 9 0 k). 0 l) 0 ) ) 0 b). 0 7 c) 0 9 d) 9 0 6) ) 0 - b). 0-8 c) d) Questions in Stndrd Form - Pge ) ) Mercury 0.9 Venus 0.7 Erth Mrs. Jupiter. Sturn 9. Urnus 9. Neptune 0 Pluto 9. b) 00 seconds or 8mins 0secs c) Approx hrs 8mins ) ) metres b) 0 metres ).80 0 Repeted Proportionl Chnge - Pge ) 7 ) ) % interest is dded t the end of ech yer on wht ws in the ccount t the beginning of tht yer, not the beginning of the ccount. b) 7.6 ) ) 8, b) 8, or c) 6,06.0 ) ),000. b) 66 ) ) 60.9 b) With service chrge the bill is multiplied by.. For VAT the bill is multiplied by.7. With both it is multiplied by..7 or.9 Clculting the Originl Amount - Pge ) 0 ) 70 ).0 ) 70 ) 6cm 6) 7.0 7),00 8) 6 9) ) b).97 0) ) 60 b) 00 Proportion - Pge ) ) 6,88 b).0% c) In 980 the popultion of Kinster ws lower thn in Flockborough. ) ) 7.7% b),000,000 c).% d) 7% Letters nd % - Pge y ) cm ) ).x b).88x c).78 ) ) b) 0cm ) ) 8% b) 8% c) 0cm ) 0.8% 6) ) xycm b) 9.% c) cm 90.9cm or 00cm 0cm Substitution - Pge 6 ) ). b) -.8 c) - d) 0.9 e) 0.76 f).66 g) -7. h) 8.7 i) 6 j).7 k).0 l) m) -.0 n) 0.7 o) -. p) q) -.7 r) 68.8 s) 9.09 t) 0.06 u).7 v) w) x) ) ) or. b). or - c) or - d).66 or 0.66 e).9 or 0.7 f) 0.7 or -0.9 g).886 or 0.86 h). or 0. i) 0.89 or -.69 j).0 or k).7 or l) or - 8 How Mny Solutions? - Pge 7 ) ) one vlue b) one vlue c) vlues d) one vlue -- 9 e) vlues f) one vlue g) one vlue h) vlues i) one vlue j) ll vlues k) one vlue l) vlues m) one vlue n) vlues o) ll vlues p) vlues q) one vlue r) vlues s) one vlue t) one vlue u) vlues ) ) 0 or -0 b) or - c) 7 or -7 d) or - e) ±8 f) ±9 g) 7 or - h) 6 or - i) 7 or - j) ± k) ± l) ± m) ± n) ±8 o) ± p) or -7 q) or -6 r) or -0 ) b), f), g), j), l) Formule - Pge 8 A x ) ) L = b) C = πd c) = d) u = v t B y v u y y e) = f) x = g) b = h) r = t + b x l i) w = xy πd ) ) v = h πd b) v = 8 ) ) V = ( + b)d b) V = -- ) ) πr h b) V = πd c) -- xyh d) -- x Simultneous Eqution Problems - Pge 9 ) x + y = x = y = 6x + y = 8 8 ) x + y = 8 x = y = 8x + y = 0.7 ) x + y = 0 x = y = 0 x + y = 0 weights re g nd 0g ) h + e = e = h = h + e = points Equtions from Experimentl Dt - Pge 60 ) ) b) C = d + 0 c) 70 d) 7 dys ) ) b) D = t + 8 c) 7cm d) 0 minutes nd 0 seconds ) ) b) C = HA c) cm d).cm 000 Solving Equtions - Pge ) ) b) 9 c) 8 d) e) 6 f) 0 g) h) 7 i) j) 0 k) 0 l) 6 m) n) o) p) ) ) 8 b) c) d) e) f) 6 g) h) - i) -- j) k) l) m) n) -- o) p) q) - -- r) ) ) b) -- c) 7 d) 9 -- e) 8 f) g) h) 7 i) 6 j) k) 7 l) 0 m) 8 n) -- o) 9 Fctorising Expressions - Pge 6 ) ) (x y)(x + y) b) (m n)(m + n) c) (c d)(c + d) d) (x )(x + ) e) (m )(m + ) f) (c )(c + ) g) (x )(x + ) h) (m )(m + ) i) (c )(c + ) j) 0 k) 80 l) 80 m) (x y)(x + y) n) (m n)(m + n) o) (c d)(c + d) p) (x y)(x + y) q) (6m n)(6m + n) A π 89

90 Sumbooks 00 Key Stge r) (9c d)(9c + d) s) (b )(b + ) t) (b )(b + ) u) (b )(b + ) ) ) -- ( + b) b) -- (b + ) c) -- y(x ) d) -- x( + x) e) -- ( + b) f) -- b(b ) g) -- ( + b) h) -- b( b) i) -- y(y ) j) -- ( + b) k) -- b(8 + b) l) -- ( + ) m) -- b( + b) n) -- ( + ) o) -- x( + x) p) -- b( ) q) -- x(x y) r) -- b(7 b) 8 8 b b ) ) -- ( b) b) -- (c ) c) -- ( + ) d) -- ( + b) y e) -- (b + ) f) -- ( + b) g) -- ( b) h) -- (x ) 8 6 y x i) -- (y ) j) -- (b + ) k) -- ( + b) l) -- (x + y) 8 b xy m) -- (b + ) n) (b + ) o) ( + z) p) -- ( + b) c y q) -- ( + ) r) -- ( + ) s) -- ( c) t) -- (y + x) u) -- ( + b) Tringulr Numbers - Pge 6 ), 6 b), c) w = -- n(n ) d) n -- n(n ) = n n n = n n = -- (n + n) The Grph of y = x - Pge 6 ) A (,6) B (,-6) C) (-, -6) D) (-, 6) ) A (8,6) B) (0,6) ) ) A (0,6) B (-8,6) b) y = (x + ) ) ) (,9) nd (-, 9) b) y = 8 x ) ) A (-,0) B (,0) b) y = x Inequlity Questions - Pge 6 ) ), nd 6 b) 0 c), 0, 0,, ) ), b) 00,99 c) 0,, 7, 96, 0 Ares Bounded by Curves - Pge 66 ) y < 0 nd y > x ) y > 0 nd y < 7 x ) y < nd y > x ) y < 9, y > (x + ) nd x < 0 ) x > -, x <, y < 0 nd y > -(x + ) Pythgors etc - Pge 67 ) ) (i) c = + c = c ---- = c c = ---- = c (ii) ---- b) c or c ( + ) ) ) ( ) = + x = + x x = x = = b) c) or 9. cm ) cm Ares - Pge 68 ) ).6cm b) cm ) ) -- b).9cm c) 7.0cm d) 8.08cm 6 ) ) 7cm b) 6.9cm Ares nd Perimeters - Pge 69 ) π ( ) π ( -- ) = π 9 π -- = π 9 ( -- ) = π 6 9 ( ) = π or -- π ) ) -- π b) x = + x = x = c) π = π ( ) = -----(π ) π π π π ) π = -- ( 0) = π Volume - Pge 70 ) ) 6cm b) 8cm c) 80cm d)89.76% e) one solution is 0cm 0cm 60cm. There re others. ) ) 6.cm b).8cm c).8cm d) grms e).087kg Congruent Tringles - Pge 7 ), e nd g ) c, e nd g ) (iv) is true. The others re flse Similr Tringles - Pge 7 ) ) 7.6cm b).86cm ) ) bº b) º c) d) 0cm e) 80cm ) ) BCD b) BAE c).cm d) 9.cm Angles - Pge 7 ) x ) 8º ) ) 6º b) 8º, 90º, 90º, º ) 7º, 60º nd 8º Sine Cosine nd Tngent Rtios - Pge 7 ) ).cm b).9cm c).00cm d) 6.89cm e) 9.6cm f).cm g).6 ) ) 60.º b) 7.º c).º d) 6.º e).º f) 8.9º g) 7.7º ) 9.º Berings Pge 7 ) ) N.º E or 0.º b) S.º W or.º ) ) N 0.6º W or 9.º b) N 6.08º W or 0.9º 90

91 Sumbooks 00 Key Stge Clculting Lengths in Tringles Pge 76 ) ).6cm b) 0.90cm c).cm d).cm nd.8cm ) ).0º b).0º c).cm ) 7.6cm More Similrity - Pge 77 ) ) or 0.87 b) or.7 c) 9.cm d) : ) ) π b) c) 80cm nd 78cm --π d) Smll : Lrge π : π 7 π : 9π : 9 e) 7 : 6 The Cricket Scores - Pge 78 ) Cumultive Frequency - Pge 80 ) ) C b) A B D ) ) B b) 6kg nd 6.kg c).6 nd.60 d) The increse in the medin is 0.kg bove 6kg, which is 6.7% increse. It would help if the men ws lso checked. However this figure does indicte tht they re right to clim % increse Cumultive Frequency - Pge 8 ) b) 0,, 0,, 80, 00 c) b) > 0 nd 00 d) Approx. 9: ) b) 0, 7, 8, 8,, 6, 67, 70 c) About > 00 nd 0 > 0 nd 00 > 00 nd > 0 nd 00 > 00 nd c) Feldown d) Eggwold. Feldown. Cumultive Frequency - Pge 79 ) ) 7 b) c) ) ) b) About 6.0 c) % Probbility - Pge 8 ) ) -- b) c) d) e) ) ) -- b) c) d) = ) ) -- b) c) ) ) 0.8 b) 0. c) 0. d) 0.7 Probbility - Pge 8 7 ) ) b) c) d) e) ) ) 0. b) 7 ) ) 0. b) 0. ) ) -- b) c)