Teacher s Notes. GCSE Maths Homework Pack 3: Higher Tier

Transcription

1 Teacher s Notes This pack is intended to cover all of the topics required y candidates in the GCSE Higher Tier eamination. The pack can e used in a variety of ways: As a homework pack The pack provides 90 homeworks for Years 0 and. The homework sheets can e attempted in any order to fit in with the school s scheme of work. If two homeworks are completed each week this will allow the pack to e completed efore the mock GCSE eaminations. The pack can then e used again for revision in Year either for homework or in class. As a classroom resource The pack can e used: To provide class tests at the end of the topic. For class revision in Year. As a attery of tests in preparation for the mock eamination or GCSE eamination. The tests will highlight any weaknesses. As a worksheet resource ank. As supplementary material The pack can e used y students after school or in lessons. Worksheets can e supplied to students who wish to do etra work. As a pupil profiling pack The pack contains a series of recording sheets which can e used to provide a profile of each student. This can e etremely useful at Key Stages and. At Key Stage teachers are epected to e ale to identify the students weaknesses and strengths. Profile Sheet (page ) simplifies the process and worksheets provide evidence. At Key Stage it is even more important to identify students weaknesses so that a student can e directed to revise the correct material for the GCSE eamination. The worksheets correspond to the GCSE Mathematics Revision Guides*. If a student has difficulties with, say, Worksheet 7, they can e directed to revise page 7 of the Higher Tier Revision Guide. Profile Sheet Individual assessment (page ). This can e used to record the marks of each student on each homework sheet. Marks for each topic can e totalled, eg graphs, total the marks for worksheets to and use the mark/grade converter on the profile sheet to produce a grade, ie 0 or aove = A, 9 or aove = B, etc. An A or B grade would indicate a strength, a D or E would indicate a weakness. This will produce a complete profile of each pupil. Profile Sheets to Class assessment (pages to 9) A simpler alternative is to use the profile sheets for class assessment. These can e used in the same way as a normal mark ook. A vertical column of poor marks would alert the teacher to a difficult topic for the whole class. A horizontal line of poor marks would alert the teacher to a particular student s difficulties. Profile Sheet 7 Class assessment (page 0) A lank class assessment profile sheet has een provided for teachers who wish their students to attempt the worksheets in a different order to the one given in this pack. Simply fill in the topic, worksheet numers and possile marks for the areas you want to cover. Strengths and weaknesses for a particular student can easily e identified. This makes it easy to advise a student aout areas requiring careful revision. * GCSE Mathematics Higher Tier Revision Guide can e otained from Pearson Pulishing, Chesterton Mill, French s Road, Camridge, CB NP, telephone 0 0, fa 0, for less than per copy for class sets. Pearson Pulishing, Chesterton Mill, French s Road, Camridge CB NP

2 In the event of a parental enquiry or an OFSTED inspection it is a simple task to transfer marks from the class assessment sheets to Profile Sheet. Using the homework pack in conjunction with the Revision Guides The worksheet pages in this pack correspond with the pages in Pearson Pulishing s GCSE Mathematics Higher Tier Revision Guide. If students have oth, it etends the ways in which this pack can e used: Students can revise from the Revision Guide in preparation for using a worksheet as a test in class. Worksheets can e used for revision homework. If students have forgotten the topic they can use the Revision Guide to refresh their memory. If a few students in a foundation eamination class wish to attempt the Intermediate eamination the Revision Guide can e used to support their learning and the homework worksheets used to provide additional work. If the students have difficulties with questions they can e directed to revise the appropriate pages in the Revision Guides. This is particularly useful as the GCSE eamination approaches. Using the speed marking system First photocopy the answer pages. Cut out the answers for the page to e marked. (You may find it quicker to fold the answer page for most worksheets.) Place the answers in the marked section of the student worksheet Use and 0 or and Minimum mark Circle grade 9 7 A B C D E Use this o to convert the mark to a grade if you wish (In general A = 0% B = % C = 0% D = %) Unlike most answer pages the answer will e net to the student s answer to allow marking to e carried out more quickly. The system is designed to allow the student to answer on the worksheet itself. However, in the majority of worksheets, it is possile for the student to answer on lank A paper. This will allow the worksheet to e re-used. Pearson Pulishing, Chesterton Mill, French s Road, Camridge CB NP

3 Eplain the method to pupils as shown elow: Worksheet Blank A Factorise: 0a +... a - c... 0a - c... Pupils should use a ruler to draw answer lines a - 0c +... a + a... Draw mark oes or leave a space Minimum mark Circle grade 9 7 A B C D E The pack can also e used as traditional worksheets with the teacher reading the answers and students marking their own or each other s work. Pearson Pulishing, Chesterton Mill, French s Road, Camridge CB NP

4 Worksheet Worksheet Worksheet Worksheet Worksheet / () Irrational / / (7) / ( / 00) Irrational /99 Irrational 9 Irrational / (.) / (.) 0 Irrational / (.) / /000 7a.7 0 0a 9 7 / a /00 7 / ( / 9) a a a a Pearson Pulishing, Chesterton Mill, French s Road, Camridge CB NP 9

5 Worksheet Worksheet 7 Worksheet Worksheet 9 Worksheet 0 a a 9, 9 0 Square numers c 0 a,. 0. Fionacci sequence..7. d 99 a,, a.. Triangle numers a, Cue numers. a a, c 0,,, 9 d c, 9, 7, d,, 9 a e e, Accept rounded answers. 7a / (0.0) a i 99 ii 797 iii 9 a,, c 7, 90 / 7 (.7 ) d,, 9 c - / (-0.). 999 e, Pearson Pulishing, Chesterton Mill, French s Road, Camridge CB NP 9

6 Worksheet Worksheet Worksheet Worksheet Worksheet A = C a a A = D A = B A = E D + a i Converges ii 0.70 i Converges a c 7 a = kc (k = ) a 7 c a - d a - e a f a A = 0C ii.7 g a a = ky 9. h a 9 A = -C c i Diverges (k = ) i a -7 7 A =.Y ii No answer 7 c 0.90 j a - k a A = 7C + D.9 9 A = C B 0 A = CD BE A = C (D 7) A = CE D Solutions shown in any order. a i n + = - n + ii - i n + = - n ii - a p = q k (k = ) 0. c a 0 7 c d e 0. A = B CD i n + = 0 n a a A = B + C D F A = Y C D ii - i n + = 0 + n ii a M = k R (k = 000) a / c a / d a / c Pearson Pulishing, Chesterton Mill, French s Road, Camridge CB NP 9

7 Worksheet Worksheet 7 Worksheet Worksheet 9 Worksheet 0 (y + 7)(y 7) a (a ) ( + )( + ) in any order a 7 c ( + y) = -.79 or = 0.79 (a 9)(a + 9) a d ( + )( + 7) 9(a ) a 9(a c + y) ( )( 7) =.7 or = -0. = - y y(y 7) or = - a + ay y(y ) ( + )( ) a = -. or a =.7 7 a (a + ) = 7 a + a (a + )(a ) or = ac(a c ) y =. -a + ac or y = a a 0 9 a cy(c a y ) 0 ad(c a) (y )(y ) = or = -7 =.7 0 0y y + a (a c + ay) 7 (y + )(y + 7) or = -.7 a + a + 0 a (a a + ) (a + )(a - ) = - or = 7 = 0.70 y y + 9 or =. Pearson Pulishing, Chesterton Mill, French s Road, Camridge CB NP 97

8 GCSE Maths Homework Pack : Higher Tier Worksheet Worksheet Worksheet Worksheet = y = a a + 7 9a + H B y 0 G = D y = - + c + E A = - 7 -c 7 F y = - a c C C a =. c =. a c 7 a y a 7 7a (a + )(a ) a = y = c d a a (a + )(a + ) Pearson Pulishing, Chesterton Mill, French s Road, Camridge CB NP 9

9 Worksheet Worksheet Worksheet 7 Worksheet / 0 / y 0 - / 0 / = / 0 / y 0 / / y = a - / y = - / + a y = a - y = - + a / y = / are approimate a / y = / = y = - a 0. or -. y Accept anything close.. or -. a c -0. d -. Pearson Pulishing, Chesterton Mill, French s Road, Camridge CB NP 99

10 Worksheet 9 Worksheet 0 Worksheet Worksheet y a Assume the graph is correct if - it goes through (0, ) and (00, 9). f y c a / m - o y h e - y 7 a P = (0.N + ) c a / g d 7 / 9 n - c. Pearson Pulishing, Chesterton Mill, French s Road, Camridge CB NP 00

11 Worksheet Worksheet Worksheet Worksheet y a = 70 = c = 0 d = 70 y e = f = 0 g = 0 y - Any answer etween: -0 m h = km/h 0 km a and 09.0 Steepest part c 0 km/h i = 7 j = 0 k = 7 l = 9 m = - y a - km/h (appro) n = 9 0 km/h c 0 km/h 0 7 o = 0 p = / hours Cyclist B overtook cyclist A Any answer etween: a 0- m Less = 7 = 0 - Pearson Pulishing, Chesterton Mill, French s Road, Camridge CB NP 0

12 Worksheet 7 Worksheet Worksheet 9 Worksheet 0 Worksheet Translation - SSS Reflection in the line y = + Not a. cm. cm a 7 AAS or ASA. cm a Rotation 0 anticlockwise, centre of c cm rotation (, ) Rotation 00 AAS or ASA clockwise, centre of rotation (, ) RHS (use Allow ± o 07 o 0 o a cm. cm Pythagoras theorem) Enlargement, scale factor - /, centre of enlargement (, ) 00 o a DEC 7 o SAS o DCB Enlargement, scale o 7 0 o c CDB or BDC factor /, centre of enlargement (-, ) o 9 o 7 AAS d CDE or EDC 0 o Rotation 0, o o a Not e ACB or BCA centre of rotation (0, 0) Pearson Pulishing, Chesterton Mill, French s Road, Camridge CB NP 0

13 Worksheet Worksheet Worksheet Worksheet Worksheet. km/h. Accept.9 instead of for maimum values,. eg.9.. a. kg. kg. km/h h min a. cl 7. cl a.... km a.7 m.7 m a h min a. t. t 0. km h min 7 sec a. cm. cm 7a. ml A (-, -). g/cm.7 ml A (0, ) B (, ) C (, ) B (-, -) C (-, -) D (-, -) a min min sec a 7. l 7. l D (, ) E (, ) F (, 0) G (, 0) D (7, 9) E (9, 9) F (9, 7) G (7, 7) E (, -) F (, -) G (, -) H (, -).9 g 7.0 km/h a h min h min sec 9a.00 cm.99 cm 0a 0.0 kg 9.9 kg a 790 g 770 g H (, ) I (0, ) J (0, ) a (7, ) - / a. ml 7. ml Pearson Pulishing, Chesterton Mill, French s Road, Camridge CB NP 0

14 Worksheet 7 Worksheet Worksheet 9 Worksheet 0 Worksheet a ml a.7 cm. cm a 0 7 ml 0 a 00 0 a c 0 d 0 c 7 c 0 a.7 cm e 0 d. cm f 0 c 0 0 d 70 e a.0 cm g 0 cm f 0 a 90 h 70 g 0 90 a.0. c 0 d 0 i 0. h 0 TOB.9 a cm 90 cm i 0 j 0 c k 70 j 0 k 0 d.0 a 7.7 cm l 0.0 cm l 0. cm m 0 c 7. cm m 90 n 0 Pearson Pulishing, Chesterton Mill, French s Road, Camridge CB NP 0

15 Worksheet Worksheet Worksheet Worksheet Worksheet a cm cm 0 cm a. cm a 0 cm. cm Length 0 cm a :7 None None :9 cm a m Area c : m None 7:. cm Length a cm 7 Area 77. cm or m Area. km 000 cm or 0. m 9 Volume cm 0 None a 0 cm 70.9 cm Length. m a 90 m Volume. m c. kg. cm Pearson Pulishing, Chesterton Mill, French s Road, Camridge CB NP 0

16 Worksheet 7 Worksheet Worksheet 9 Worksheet 0 Worksheet 9.0 m a =. a =. cm a sec = 9. =. cm. m m c =. c =.0 cm a. m. cm d =. d =. cm. c 7 m. cm e =.0 f =.0 e =. cm a 0. m g =. f =. cm h = 7..9 cm 7 i = 7 g =. cm h =. cm.7 m a 7.07 cm. cm j =. i =.7 cm k =. c. Pearson Pulishing, Chesterton Mill, French s Road, Camridge CB NP 0

17 Worksheet Worksheet Worksheet Worksheet Worksheet a 7.0 y 0 0. cm a. km 0 o 0 o 0. 0 o o 0 0 o o o - 0 o o o 0 00 o 0. 0 o 0. 0 o a y 0 o 0 o 0 o.7 90 o 0 o.7 0 o 0 o 0 o 0 0 o o - 00 o o 0. cm 09 If tale is correct assume graph is correct. Accept values etween: a 0 0 o If tale is correct assume graph is. a 7. a 0-0 correct. None 0 c None d 0-0 e a m f 70-0 g None h 0-0 a 07 Accept 0 - Accept 0-0 i 0-0 j None k c Accept - Accept cm l 0-90 Pearson Pulishing, Chesterton Mill, French s Road, Camridge CB NP 07

18 Worksheet 7 Worksheet Worksheet 9 Worksheet 70 a. km/h a N 0 a / ~ 7 y ~ ~ ( - ) 0 ( - ) c / y ~ d - / + / y e -y + / f - / y + a = y = = - y = c = - y = a m c 0 min secs a 00. km/h Pearson Pulishing, Chesterton Mill, French s Road, Camridge CB NP 0

19 Worksheet 7 Worksheet 7 Worksheet 7 Accept any sensile answers. Do not ask personal questions or should have an age range. 0 9 cm Which o would a person aged 0 tick? Do not accept decimals, eg. a 7 or Which o would a person aged 0, or 0 c 9 or A 0, 0 or 0 tick? or 0, 0, 0 and 0 are shown twice. d or Total 0 B C What does young, middle aged and old mean? or different meanings to different people: a child might think 0 is old; a senior citizen might think 0 is young. Bad children should e asked ut they are not on the electoral roll. Good Pearson Pulishing, Chesterton Mill, French s Road, Camridge CB NP 09

20 Worksheet 7 Worksheet 7 Worksheet 7 Questionnaire Eperiment Assume graph is correct if tale is correct. Oservation or questionnaire Questionnaire Eperiment a Boys Girls 7 Eperiment Frequency 7 Oservation Oservation or questionnaire or eperiment Time (seconds) 9 Questionnaire The frequency polygon shows that oys generally take longer to thread a needle 0 Questionnaire than girls. Pearson Pulishing, Chesterton Mill, French s Road, Camridge CB NP 0

21 Worksheet 77 Worksheet 7 Worksheet 79 Worksheet 0 Worksheet a 7 a. a a a 00 a 0 under Accept any answers in the range: - a 0. c % c -.00 a.7 a 00 Check point (0,70). If correct give graph a mark. Check point (70, ). If correct give graph a mark. 700 a -0 Accept any answers in the range: - Accept any answers in the range: c 7-7 d - e 7-9 d 7-7 e - f -0 a Adam..9 Barry.. c 7 c -0 e -9 f -9 g 7- g Any valid comparison, eg oys are taller than girls; any comparison should mention oth medians and oth interquartile ranges. c Adam Any valid eplanation, eg Adam has a lower sd and therefore is more consistent. d Pearson Pulishing, Chesterton Mill, French s Road, Camridge CB NP

22 Worksheet Worksheet Worksheet Worksheet Worksheet a 0. a Check points (0, ) and (90, ). If correct award mark. Accept any reasonale line. a a c 0. c 0.07 d 0.0 a / c 0. d 7 / d 0.7 c /0 e 0. d 9 /0 a 0.0 c Positive correlation f a /0 di ii 9 cm (appro) 90 cm (appro) a Mrs Jarvis asked more people. Accept rounded answers. g 0. h 0. c 0.07 /0 c / iii iv v. cm (appro) 7 cm (appro). cm (appro) Size 00 Size 0 00 Size 000 Size 7 00 i 0. j 0. d 0.9 Size 00 Pearson Pulishing, Chesterton Mill, French s Road, Camridge CB NP

23 Worksheet 7 Worksheet Worksheet 9 Worksheet 90 > a 0.0 ( / ) or ( / ) > < ( / ) right, up or 0 00 or 0 right, up or a 0. ( / ) 9 left or -9 0 left, up or - y < ( / ) right, down or or in any order.. c 0. ( / ) R (, ) 7 R (-, -) R (-, ) 9 y - y - 9 R (, -) Pearson Pulishing, Chesterton Mill, French s Road, Camridge CB NP

24 Pearson Pulishing, Chesterton Mill, French s Road, Camridge CB NP Name Class General topic Worksheet numer Mark Out of Grade (A to E) General topic Worksheet numer Mark Out of Grade (A to E) General topic Worksheet numer Mark Out of Grade (A to E) General topic Worksheet numer Mark Out of Grade (A to E) Numer Skills Calculator Skills Questionnaires Perimeter, Area and Volume 0 NUMBER 9 Tales and Graphs Graphs Fractions, Decimals and Percentages Teacher Total A = 70 B = 7 C = D = Numer Patterns Angles Pythagoras Theorem and Trigonometry SHAPE, SPACE AND MEASURES HANDLING DATA Cumulative Standard Frequency Deviation Simi- larity 79 Scatter Diagrams Equations 0 7 ALGEBRA Varia- Algeraic Skills tion Congruence Proaility 7 Vectors Locus Transformations Total A = 09 B = 9 C = D = 7 Total A = B = 9 C = 07 D = Profile Sheet Individual Assessment 0 Additional Topics Total A = B = C = 7 D = Measurement Higher levels Total A = B = C = 9 D = 7 Circles Overall Total: A = 9 B = C = D = 0 0 GCSE Maths Homework Pack : Higher Tier Main strengths Main weaknesses

25 Class Teacher Profile Sheet Class Assessment Higher levels 7-0: Numer Numer Skills 7 Calculator Skills Total Numer Grade General topic Fractions, Decimals and Percentages A = 70 B = 7 C = D = 0 Mark out of Worksheet numer Name Pearson Pulishing, Chesterton Mill, French s Road, Camridge CB NP

26 Class Teacher Profile Sheet Class Assessment Higher levels 7-0: Algera Numer Patterns Equations Variation Algeraic Skills Total Algera Grade General topic A = B = C = 9 D = 7 Mark out of Worksheet numer Name Pearson Pulishing, Chesterton Mill, French s Road, Camridge CB NP

27 Class Teacher Profile Sheet Class Assessment Higher levels 7-0: Shape, Space and Measures Graphs Angles Similarity Congruence Transformations Measurement Total General topic Shape, Space and Measures Grade A = B = 7 C = 0 D = 7 Mark out of Worksheet numer Name Pearson Pulishing, Chesterton Mill, French s Road, Camridge CB NP 7

28 Class Teacher Profile Sheet Class Assessment Higher levels 7-0: Shape, Space and Measures 9 Perimeter, Area Circles and Volume Pythagoras Theorem and Trigonometry Vectors Locus Total General topic Shape, Space and Measures Grade A = B = C = 0 D = 7 Mark out of Worksheet numer Name Pearson Pulishing, Chesterton Mill, French s Road, Camridge CB NP

29 Class Teacher Profile Sheet Class Assessment Higher levels 7-0: Handling Data Pearson Pulishing, Chesterton Mill, French s Road, Camridge CB NP 9 General topic Worksheet numer Name Mark out of Questionnaires Tales and Graphs Cumulative Frequency 7 79 Standard Deviation 0 7 Scatter Diagrams Proaility Total Handling Data Grade A = 09 B = 9 Additional Topics C = D = 7 Total Additional Topics Grade A = B = C = 7 D = GCSE Maths Homework Pack : Higher Tier

30 Class Teacher Profile Sheet 7 Class Assessment General topic Mark out of Worksheet numer Name Pearson Pulishing, Chesterton Mill, French s Road, Camridge CB NP 0

31 Contents Teacher s Notes... Numer Numer Skills... Calculator Skills... Fractions, Decimals and Percentages... Algera Numer Patterns... 0 Equations... Variation... Algeraic Skills... 7 Shape, Space and Measures Graphs... 7 Angles... 9 Similarity... Congruence... Transformations... Measurement... 7 Circles... Perimeter, Area and Volume... Pythagoras Theorem and Trigonometry... 0 Vectors Locus... 7 Handling Data Questionnaires... 7 Tales and Graphs... 7 Cumulative Frequency... Standard Deviation... Scatter Diagrams... Proaility... Additional Topics Profile Sheets... Pearson Pulishing, Chesterton Mill, French s Road, Camridge CB NP