leave - longhill high school 11/exam papers... · web view9. a boy has a pen that is of length 10...

Centre Number Paper Reference Surname Other Names

Candidate Number Candidate Signature

1387For Examiner’s use only

Edexcel GCSEFor Team Leader’s use only

Mathematics APaper 5

HIGHER TIER

Specimen PaperTime: 2 hours N0000

Materials required for the examination Items included with these question papersRuler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser.Tracing paper may be used.

Formulae sheets

Instructions to Candidates

In the boxes above, write your centre number, candidate number, the paper reference, your surname and other names and your signature. The paper reference is shown in the top left hand corner.Answer all questions in the spaces provided in this book. Supplementary answer sheets may be used

Information for Candidates

The total mark for this paper is 100. The marks for the various parts of questions are shown in round brackets: e.g. (2).Tracing paper may be used.Calculators must not be used.This question paper has 20 questions. There are no blank pages.

Advice to Candidates

Work steadily through the paper.Do not spend too long on one question.Show all stages in any calculations.If you cannot answer a question, leave it and attempt the next one.Return at the end to those you have left out.

N0000© 2000 EdexcelThis publication may only be reproduced in accordance with Edexcel copyright policy.Edexcel Foundation is a registered charity.

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2

Answer ALL TWENTY THREE questions.

Write down your answers in the spaces provided.

Do NOT use a calculator. You must write down all stages in your working.

1. The exterior angle of a regular polygon is 30º.

Work out the number of sides in the regular polygon. SSM2dGrade C

……………………… sides (Total 2 marks)

2. Here are the equations of 5 straight lines.

They are labelled from A to E.

A y = 2x + 1

B y = 1 – 2x

C 2y = x – 1

D 2x – y = 1

E x + 2y = 1

(a) Put ticks in the table to show the two lines that are parallel. NA6cGrade C

(2)(b) Write down the two lines that are perpendicular to line E NA6c

Grade A

…………………………..(2)

(Total 4 marks)

30

3. The mass of an atom of Uranium is kg.

(a) Calculate the mass of 3 000 000 atoms of Uranium. NA3hGive your answer in standard form. Grade B

………………………………..(2)

(b) Evaluate NA2bGrade B

…………………..(1)

(Total 3 marks)

4.

Two rods are fastened together.The total length is inches.

The length of rod B is inches.

Find the length of rod A. NA3cGrade C

……………..…. inches(Total 3 marks)

A B

313

431

5. (a) (i) Express 72 and 96 as products of their prime factors. NA3aGrade C

72 = ……………………….……..

96 = ……………………….……..(4)

(ii) Use your answer to (i) to work out the Highest Common Factor of 72 and 96. NA2aGrade C

…………………(2)

(b) Change the decimal into a fraction in its lowest terms. NA3cGrade A

………………….(3)

(Total 5 marks)

6. Sybil weighed some pieces of cheese

The table gives information about her results.

Weight (w) grams Frequency

90 < w ≤ 94 1

94 < w ≤ 98 2

98 < w ≤ 102 6

102 < w ≤ 106 1

Work out an estimate of the mean weight. HD4eGrade C

………………. grams(Total 4 marks)

7. (a) Simplify

(i)

…………………..

(ii)

…………………..(2)

(b) Expand and simplify

(i) (2x + 3)(x – 2) NA5bGrade B

……………………………..(ii) (3x – 2)²

……………………………(4)

(c) Solve the equation

x² – 3x – 10 = 0 NA5kGrade B

…………………………………….(3)

(d) Solve the equation

NA5f

Grade B

h = ………………..(4)

(Total 13 marks)

8.

Find the size of the largest angle in the pentagon. SSM2dNA3eGrade C

…………………………………….. (Total 6 marks)

5x – 25

5x – 10

3x + 15

4x + 20

3x

9. A boy has a pen that is of length 10 cm, measured to the nearest centimetre.His pen case is of length 10.1 cm, measured to the nearest millimetre.

Explain why it might not be possible for him to fit the pen in the pen case. SSM4aGrade B

………………………………………………………………………………………………..

………………………………………………………………………………………………..

………………………………………………………………………………………………..

………………………………………………………………………………………………..(Total 3 marks)

10. There are 12 boys and 15 girls in a class.

In a test the mean mark for the boys was n.

In the same test the mean mark for the girls was m.

Work out an expression for the mean mark of the whole class of 27 students. HD4eGrade B

……………………………… (Total 3 marks)

11.

(a) Work out the length of AD. SSM2gGrade B

…………….. cm(2)

(b) Work out the length of BC. SSM2gGrade B

………… cm(2)

(Total 4 marks)

B

D

A C E

4.5 cm

6 cm 4 cm

5 cm

Diagram NOTaccurately drawn

12. A wax statue of a spaceman is on display in a museum..Wax models are to be sold in the museum shop. The statue and the wax models are similar.

The height of the statue is 1.8 mThe height of the model is 15 cm.The area of the flag in the model is 10 cm²

(a) Calculate the area of the statue’s flag. SSM3dGrade A

………………………. cm²(3)

The volume of the wax of the original statue is 172.8 litres.

(b) Calculate the volume of wax used to make the model. SSM3dGive your answer in ml. Grade A

………………………. ml(2)

(Total 5 marks)

13. K is an integer.

Find the value of K. NA4aGrade A

K = ………………..(Total 3 marks)

123

K3

14. The probability that a team will win a game is always 0.5.The team plays n games.The probability that the team will win all of the n games is less than 0.05.

Find the smallest value of n. HD4gGrade A

……………………(Total 3 marks)

15. The intensity of light L, measured in lumens, varies inversely as the square of the distance d m from the light.

When the distance is 2 m the light intensity is 250 lumens.

(a) Calculate the value of L when d is 2.5 m. NA5hGrade A

…………… lumens(3)

(b) Calculate the value of d when L is 90 lumens. NA5hGrade A

……………. m(2)

(Total 5 marks)

16.

ABCD is a parallelogram. Prove that triangles ABD and BCD are congruent. SSM2e

Grade A

(Total 3 marks)

Diagram NOT accurately drawn

A B

D C

17. The equation of a curve is

y = f(x)

where f(x) = x² – 10x + 32.

(a) Complete the square for f(x). NA5kGrade A*

………………………………..(2)

(b) Hence, sketch the graph of

(i) y = f(x)

(ii) y = f(x + 5) NA6gGrade A*

(4)

y = f(x) wheref(x) = sin x where 0 ≤ x ≤ 180

(c) By considering the function f(ax), sketch the graph of y = sin 2x. NA5kGrade A*

(2)(Total 8 marks)

18.

OA = a OB = b AC = 2a OD = 3b

Prove that AB is parallel to CD. SSM3fGrade A*

(Total 3 marks)

B

O

A

DC

ba

19. The diagram represents a right pyramid. The base is a square of side 2x.

The length of each of the slant edges is 8√3 cm.

The height of the pyramid is x cm.

Calculate the value of x.

SSM2fGrade A*

x

2x

8 3 2x

83


………………….. cm(Total 6 marks)

20. Solve the equation

NA6e

Grade A*

x = ………………………….(Total 6 marks)

21. Leon recorded the lengths, in minutes, of the films shown on television in one week.His results are shown in the histogram.

20 films had length from 60 minutes up to, but not including, 80 minutes.

(a) Use the information in the histogram to complete the table. HD4aGrade A

Length in minutes (m) Frequency

60 ≤ m < 80 20

80 ≤ m < 90

90 ≤ m < 100

100 ≤ m ≤ 120(2)

Leon also recorded the lengths, in minutes, of all the films shown on television the following week. His results are given in the table below.

Length in minutes (m) Frequency Height

60 ≤ m < 100 72 36

100 ≤ m < 160 x

(b) Complete the table giving your answers in terms of x. HD4aGrade A*

(2)(Total 4 marks)

TOTAL FOR PAPER: 100 MARKS

60 80 100 120 140

Frequency density per unit interval

Time in minutes

Centre Number Paper Reference Surname Other Names

Candidate Number Candidate Signature

1387For Examiner’s use only

Edexcel GCSEFor Team Leader’s use only

Mathematics APaper 6

HIGHER TIER

Specimen PaperTime: 2 hours N0000

Materials required for the examination Items included with these question papersRuler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator.Tracing paper may be used.

Formulae sheets

Instructions to Candidates

In the boxes above, write your centre number, candidate number, the paper reference, your surname and other names and your signature. The paper reference is shown in the top left hand corner.Answer all questions in the spaces provided in this book. Supplementary answer sheets may be used

Information for Candidates

The total mark for this paper is 100. The marks for the various parts of questions are shown in round brackets: e.g. (2).Tracing paper may be used.Calculators may be used.This question paper has 20 questions. There are no blank pages.

Advice to Candidates

Work steadily through the paper.Do not spend too long on one question.Show all stages in any calculations.If you cannot answer a question, leave it and attempt the next one.Return at the end to those you have left out.

N0000© 2000 EdexcelThis publication may only be reproduced in accordance with Edexcel copyright policy.Edexcel Foundation is a registered charity.

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Answer ALL NINETEEN questions.

Write your answers in the spaces provided.

You must write down all stages in your working.

1. Calculate

NA3o

Grade C

………………………(Total 3 marks)

24

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2. Tony carries out a survey about the words in a book.He chooses a page at random.He then counts the number of letters in each of the first hundred words on the page.The table shows Tony’s results.

Number of letters in a word 1 2 3 4 5 6 7 8

Frequency 6 9 31 24 16 9 4 1

The book has 25000 words.Estimate the number of 5 letter words in the book. HD4b

Grade C

……………………….(Total 3 marks)

25Turn over

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3.

The diagram shows a field which a farmer wants to fence.The field is in the shape of an isosceles trapezium in which AB is parallel to DC and AD = BC.

AB = 80 m and CD = 60 m.

The distance between the parallel sides is 30 m.

Calculate the length of fencing the farmer will need. SSM2fGrade C

……………………… m(Total 5 marks)

26

A

D C

B80 m

60 m

30 m


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4. Wayne shares £360 between his children, Sharon and Liam, in the ratio of their ages. Sharon is 13 years old and Liam is 7 years old.

(a) Work out how much Sharon receives. NA3f Grade C

Sharon £ ………… (2)

(b) What percentage of the £360 does Sharon receive? NA3fGrade C

………………………. %(2)

(Total 4 marks)

27Turn over

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5. (a) Solve the equation Grade CNA5f

7p + 3 = 3(p –1)

p = …………….(2)

q is an integer such that 0 < 3q 16

(b) List all the possible values of q. Grade CNA5j

…………………………….(2)

(c) Solve the inequality Grade BNA5j

…………….……….(3)

(Total 7 marks)

28

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6. The Andromeda Galaxy is 21 900 000 000 000 000 000 km from the Earth.

(a) Write 21 900 000 000 000 000 000 in standard form. Grade BNA3h

………………………(1)

Light travels km in one year.

(b) Calculate the number of years that light takes to travel from the Andromeda Galaxy to Grade BEarth. NA3mGive your answer in standard form correct to 2 significant figures.

………………………(2)

(Total 3 marks)

29Turn over

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7.

A, B and C are points on the circumference of a circle, with centre O.

(i) Find angle AOC. Grade BSSM2h

……………………….(ii) Give a reason for your answer.

…………………………………………………………………………………………………...

…………………………………………………………………………………………………...(Total 2 marks)

30


58

C

B

A

O

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8. (a) Expand Grade CNA5b

………………………..(2)

(b) Factorise completely Grade BNA5b

ax + ay – by – bx..

………………………..(2)

(c) Expand Grade ANA5d

………………………..(2)

(d) Solve the simultaneous equations Grade BNA5i

x = …………

y = ………… (4)

(Total 10 marks)

31Turn over

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9.

On the grid, triangle Q is the image of triangle P after a reflection.

(a) Rotate triangle Q through 90 clockwise about (2, 1). Grade CLabel this image R. SSM3b

(2)

(b) Describe fully the single transformation which maps triangle P onto triangle R. Grade B SSM3a

…………………………………….………………………………………………………...

…………………………………….………………………………………………………...

(2) (Total 4 marks)

32

-6 -4 -2 2 4 6 8

-4

-2

2

4

6

O x

y

PP Q

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10. The cumulative frequency graph gives information about the examination marks of a group of students.(a) How many students were in the group? Grade B

HD5d …………

(1)

(b) Use the graph to estimate the inter-quartile range. Grade BHD5d

………... (2)

The pass mark for the examination was 56.

(c) Use the graph to estimate the number of students who passed the examination. Grade BHD5d

………...(2)

(Total 5 marks)

11.

33Turn over

0 20 806040 100

40

60

30

20

10

50

Cumulative frequency

Mark

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The diagram shows a triangle ABC.The line CD is perpendicular to the line AB.AC = 7.3 cm, BD = 6.4 cm and angle BAC = 51.

Calculate the size of the angle marked x. Grade BGive your answer correct to 1 decimal place. SSM2g

……………….…

(Total 5 marks)

12. The population of the world is increasing at an annual rate of 1.6%.In 1990, it was 5250 million.Calculate an estimate for the population of the world in 2010. Grade A

NA3e

…………..……million (Total 3 marks)

13. Prove algebraically that the sum of the squares of any two consecutive integers is an odd Grade A

34

6.4 cm

D

51

7.3 cm

A B

C


x

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number. NA5b

(Total 3 marks)

35Turn over

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14.

The arc length of a sector of a circle is 15 cm.The radius of the circle is 12 cm.Work out size of the angle, θ°, of the sector. SSM4d

Grade A

…………………… (Total 3 marks)

36

θ

12 cm

15 cm


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15. The length of a rectangle is a centimetres.Correct to 2 decimal places, a = 6.37.

(a) For this value of a, write down Grade ANA3q

(i) the upper bound,

…………..……

(ii)the lower bound.

………..……… (1)

Correct to 1 significant figure, the area of the same rectangle is 20 cm².(b) Calculate the upper bound for the width of the rectangle. Grade A*

Write down all the figures on your calculator display. NA3q

………………………… (4)

A diagonal of the rectangle makes an angle of θ with one of the sides of length a centimetres.

(c) Calculate the upper bound for the value of tan θ. Grade A*Write down all the figures on your calculator display. NA3q

………………………… (2)

(Total 7 marks)

37Turn over

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16.

The diagram shows a rectangle with length x + 4 and width x 1.All measurements are given in centimetres.

The area of the rectangle is A square centimetres.

(a) Show that . Grade CNA5b

(2)

When A = 10, x satisfies the equation .

(b) Find the length of the rectangle. Grade AGive your answer correct to 2 decimal places. NA5k

………………cm (4)

(Total 6 marks)

38

x – 1

x + 4

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17.Year 10 Group Year 11 Group

Boys 75 50Girls 60 30

The table shows the number of boys and the number of girls in Year 10 and Year 11 of a school.The headteacher wants to find out what pupils think about a new Year 11 common room.A stratified sample of size 50 is to be taken from Year 10 and Year 11.

(a) Calculate the number of pupils to be sampled from Year 10. Grade AHD2d

………… (2)

Two pupils are to be chosen at random to speak to the headteacher.

One pupil is to be chosen from Year 10.One pupil is to be chosen from Year 11.

(b) Calculate the probability that both pupils will be boys. Grade AHD4g

…………(2)

However, the headteacher decides to choose one boy at random from all the boys in year 10 and 11 together and one girl at random from all the girls in year 10 and 11 together

(c) Calculate the probability that exactly one of the pupils will be from year 10. Grade A*HD4g

………… (3)

(Total 7 marks)

39Turn over

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18.

The diagram shows a quadrilateral ABCD.AB = 8.3 cm, BC = 7.8 cm, CD = 5.4 cm and AD = 6.1 cm.Angle BAD = 71.

(a) Calculate the area of triangle ABD. Grade AGive your answer correct to 3 significant figures. SSM2g

………….………… (3)

(b) Calculate the size of angle BCD. Grade A*Give your answer correct to 1 decimal place. SSM2g

……………..

(6)(Total 9 marks)

40

5.4 cm Diagram NOT accurately drawn

71

D

A B

C

8.3 cm

7.8 cm6.1 cm

A

C

B

D

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19. This is a sketch of the curve with equation y = f(x).

The maximum point of the curve is A (3, 8).Write down the co-ordinates of the maximum point for each of the curves having the following equations.

(i) y = f(x) + 2 Grade A*NA6g

(………, ………) (ii) y = f(x – 3)

(………, ………) (iii) y = f(–x)

(………, ………) (iv)y = f(3x)

(………, ………) (Total 4 marks)

41Turn over

y = f(x)

A (3, 8)

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20. Solve the simultaneous equations

Grade A*NA5l

………………………..

………………………..(Total 7 marks)

TOTAL FOR PAPER: 100

42

GCSE MATHEMATICS MARK SCHEME – PAPER 5

No NC Ref

Grade Working Answer Mark Notes

1 SSM2d C 360 30 = 12 12 sides 2 M1 for 360 30A1 cao

2 (a)

(b)

NA6c

NA6c

C

A

A and D selected

A and D selected

A and D

A and D

2

2

M1 for rearranging into y = mx + cA1 caoB1 for AB1 for D

3 (a) NA3h B 2 M1 for multiplying numbersA1 for

(b) NA2b B 4 1 B1 cao4 (a) NA3c C 3 M1 for using 12 as denominator

M1 for decomposing 2 wholesA1 cao

5 (a)(i) NA3a C 72 = 2 2 2 3 3 or

96 = 2 2 2 2 2 3 or

4 M1 for dividing through by 2 then 3A1 caoM1 for dividing through by 2 then 3A1 cao

(ii) NA2a C 2 2 2 3 = 24 2 M1 for selecting 2 and 3 as common prime factorsA1 cao

(b) NA3c A

Subtract

3 M1 for 0.454545 100M1 for 99x = 45A1 cao

6 HD4e C 92 1 = 9296 2 = 192

100 6 = 600104 1 = 104

98.8 4 M1 for f x; x within interval (accept both ends), at least 3 consistentM1 (dep) for use of all correct mid-interval values

43


No NC Ref


988 10 = M1 (dep on 1st M1) for numerical (candidate’s numerical )A1 cao

7 (i) NA5d C 2 B1 cao(ii) NA5d C B1 cao

(b)(i) NA5b B 2x² – x – 6 2 B1 for 2x² – 6B1 for –x

(ii) NA5b B (3x – 2)(3x – 2)9x² – 12x + 4

2 B1 for 9x² + 4B1 for –12x

(c) NA5k B (x – 5)(x + 2) x = 5x = –2

3 M1 for factorisationA1 for correct factorsB1

(d) NA5f B – or 4 M1 for any multiple of 6M1 for multiplying out brackets correctlyM1 for 7h + 16 = 5A1 cao

8 SSM2dNA3e

C 3 180 = 5403x + 5x – 10 + 4x + 20 + 5x – 25 + 3x + 15 = 540

128 6 M1 for 3 180 oeA1 for 540B1 for full equation

20x = 540x = 27Max angle is 4x + 20

M1 for simplifyingA1 for x = 27B1 ft angle = 128

9 SSM4a B 3 M1 for realising 10 cm to 1 cm = 10.5 cmM1 for realising 10.1 cm to 1 mm = 10.05 cm to 10.15 cmA1 therefore pen might be too big

10 HD4e B Total of boys marks = 12nTotal of girls marks = 15mTotal marks for whole class = 12 n + 15m

3 B1 for 12n or 15mM1 for 12 n + 15mA1 cao

44


No NC Ref


11 (a)

(b)

NA2g

NA2g

B

B

3 : 5 = 4.5 : 7.5

5 : 3

7.5

3

2

2

M1 for realising ratio is 3 : 5 oeA1 for 7.5 cmM1 for realising ratio is 3 : 5 oeA1 for 3

12 (a)

(b)

SSM3d

SSM3d

A

A

Linear ratio 1 : 12Area ratio 1 : 144Flag area 1440 cm ²Volume ratio 1 : 1728

1440

100

3

2

B1 for linear ratioB1 for area ratioB1 for 1440 cm²B1 for volume ratioB1 for 100 ml

13 NA4a A 6 3 B1 for 3 as result of √3² = 3 and 12 from √12² = 12B1 for √3 √12 = 6B1 cao

14 HD4g A 0.5 0.5 = 0.250.25 0.5 = 0.1250.125 0.5 = 0.06250.0625 0.5 = 0.03125

n = 5 3 B1 for 0.5 0.5 = 0.25B1 for 0.03125B1 cao

15 (a)

(b)

NA5h

NA5h

A

A

160 lumens 3

2

M1 for

M1 for k = 1000A1 cao

M1 for

A1 cao

45


No NC Ref


16 SSM2e A

BD is commonTherefore triangles are congruent ASAOr equivalent method (other sides, angle)

3 B1 for with reasonB1 for with reasonB1 with reason and conclusion

17 (a) NA5k A* 2 B1 for B1 (dep) for

(b) NA6g A* (i) (ii) 4 B1 for parabolaB1 (ft) for (0, 32) or (5, 7)B1 for parabolaB1 (ft) for (0, 7)

(c) NA6g A* 2 B1 for sine curve (between 1 and –1)B1 cao

46

(0, 32)(5, 7) (0, 7)


No NC Ref


18 (a) SSM3f A* AB = b – aCD = 3b – 3aCD = 3(b – a)Therefore AB is parallel to CD

3 B1 for AB = b – aB1 for CD = 3b – 3aB1 for identifying CD = 3(b – a) and saying

19 SSM2f A* 4x² + 4x² = 8x² or x² + x² = 2x²Diagonal = √8x or half diagonal = √2x

x = 8 6 M1 for 4x² + 4x² = 8x² or x² + x² = 2x²M1 for Diagonal = √8x

M1 for oe

M1 for

M1 for or A1 cao

20 NA6e A* x = 3x = –1

6 M1 for M1 for multiplying outM1 for 2x² – 4x –6 = 0M1 for (x – 3)(x + 1) = 0A1 for x = 3A1 for x = –1

21 (a)

(b)

HD4a

HD4a

A

A*

1 cm² = 10 films 70, 58, 60 2

2

B2 for all 3(B1 for any two or B1 for 1 cm² = 10 films and 1 correct result)

M1 for

A1 cao

47


No NC Ref


48


No NC Ref


1 NA3o C 10.2 3 M1 for 4.33 or 29.57 or better seenM1 for 2.90 or better seenA1 cao

2 HD4b C 4000 3M1 for

M1 for A1 cao

3 SSM2f C 203 5M1 for

M1 for squaring and adding

M1 (dep) for square rootA1 for 31.6B1 for 203 or better

4 (a) NA3f C 360 20 234 2 M1 for 360 20A1 cao

(b) NA3f C or 0.65

65 2M1 for

A1 ft from “234”5 (a) NA5f C 3p – 3 seen

7p – 3p = 3 32 M1 for 7p – 3p or –3 – 3

A1 cao(b) NA5j C 1,2,3,4,5 2 B1 for 1 and 5

B1 for 2, 3, 4(c) NA5j B 3r – 6 seen

1 +6 3r – r3 M1 for 3r – 6 seen

M1 for 1 +6 3r – rA1cao

6 (a)(b)

NA3hNA3m

BB

12

B1 caoM1 for 5.673A1 for or better

7 SSM2h B 116 2 B1 for 116B1 for angle at centre

49


No NC Ref


8 (a) NA5b C 3x³ + 4x 2 B1 for 3x³B1 for 4xB2

(b) NA5b B (a – b)(x + y) 2 B2 (B1 for a(x + y) – b(y + x) or y(a – b) + x(a – b) oe)

(c) NA5d A 2 B2 (B1 if one error)(d) NA5d B e.g. x = 2½ , y = 6 4 M1 for attempt to multiply

both eqns by appropriate nosM1 for attempt to add or subtract as appropriateA1, A1

9 (a)

(b)

SSM3b

SSM3a

C

B

R correct

Reflectiony = x – 1

2

2

B2 (B1 for 90o clockwise rotation of Q)B1 description: “reflection”B1 for y = x – 1

10 (a)(b)

(c)

HD5dHD5d

HD5d

BB

B

Lower 29, upper 58

38 stated or indicated on diagram

5229

14

12

2

B1 cao M1 for either upper or lower quartile found (1)A1 accept 28, 29, 30 as the IQRM1 evidence eg line on graphA1 cao

11 SSM2g B 7.3 sin 51o

5.673 …tan xo =

41.6 5 M1 for 7.3 sin 51o

A1 for 5.673M1 for use of tan

M1 for

A1 cao for 41.6 or better12 NA3e A 1.016 seen

or 1.3736 …7200 million 3 B1 for 1.016 seen

M1 for or 1.3736 …A1 cao (accept 7000 million)

50


No NC Ref


13 NA5b A 3 M1 for M1 for A1cao

14 SSM4d A 71.6 3 M1 for M1 for A1 cao

15 (a)(i)(ii)

(b)

(c)

NA3qNA3qNA3q

NA3q

AAA*

A*

25 seen“25” “6.365”

(b) 6.365

6.3756.365

3.927729772

0.617082446

1

4

2

B1 cao for both

B1 ft from (ii)B1 for 25 seenM1 for “25” “6.365”A1 cao 5 dp neededM1 for (b) 6.365A1 5 dp needed ft from (b)

16 (a) NA5b C (x + 4)(x – 1)x² – x + 4x – 4

2 B1 for (x + 4)(x – 1)B1 for x² – x + 4x – 4

(b) NA5k A

= 2.53 and –5.53

6.53 4 M1 subs in formula

M1 for

A1 for both solutionsB1 cao

17 (a) HD2d Aor 31.39 …

31 2M1 for or 31.39 …

A1 cao

51


No NC Ref


(b) HD4g Aoe

2M1 for

A1 cao(c) HD4g A*

or

Sum of both

oe3

M1 for or

M1 for sum of bothA1 cao

18 (a) SSM2g A 23.9 cm² 3M1 for

A1 for 23.9 or betterB1 (indep) for cm² (units)

(b) SSM2g A*

73.132 …8.55 …

0.200 …

78.4 6 B1 for use of cosine ruleB1 for 73.132B1 for DB = 8.55

B1 for use of sine ruleB1 for 0.200B1 for 78.4 or better

19 (a)(b)(c)(d)

NA6gNA6gNA6gNA6g

A*A*A*A*

(3,10)(6,8)(3,8)(1,8)

1111

B1 caoB1 caoB1 caoB1 cao

20 NA51 A*

or

7 M1 for M1 for M1 for M1 for

A1 + 1

A1 for both

52


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