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.