GCSE MATH Three Tier PP MayJune 2008 Higher Tier Paper 5 Non Calculator 4128 (1)

8/3/2019 GCSE MATH Three Tier PP MayJune 2008 Higher Tier Paper 5 Non Calculator 4128 (1)

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71

Centre Number

Candidate Number

General Certificate of Secondary Education

2008

Mathematics

Paper 5(Non-calculator)

Higher Tier

[G6005]

MONDAY 19 MAY, MORNING

G605H8 3472

TIME

2 hours.

INSTRUCTIONS TO CANDIDATES

Write your Centre Number and Candidate Number in the spaces

provided at the top of this page.

Write your answers in the spaces provided in this question paper.

Answer all twenty-one questions.

Any working should be clearly shown in the spaces provided since

marks may be awarded for partially correct solutions.

You must not use a calculator for this paper.

INFORMATION FOR CANDIDATES

The total mark for this paper is 100.

Figures in brackets printed down the right-hand side of pages indicate

the marks awarded to each question or part question.

You should have a ruler, compasses, set-square and protractor.

The Formula Sheet is on page 2.

G

6005

TotalMarks

For Examinersuse only

QuestionMarks Number

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21


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G605H8 3472 2 [Turn over

Formula Sheet

Area of trapezium =12 (a + b)h

Volume of prism = area of cross section length

In any triangle ABC

Area of triangle = 12 ab sin C

Cosine rule: a2 = b2 + c2 2bc cos A

Volume of sphere =43 r

3

Surface area of sphere = 4r2

Volume of cone =13r

2h

Curved surface area of cone = rl

Quadratic equation:

The solutions ofax2 + bx + c = 0, where a 0, are given by

a

h

b

Crosssection

length

B

c

A

b

Ca

r

h

r

l

Sine rule:

sin sin sin

a

A

b

B

c

C

= =

x b b aca

= 2

42


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BLANK PAGE

[Questions start overleaf]


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Examiner Only

Marks Remark

1 (a) Sam bought five pencils at x pence each, one pen which is twice the

price of a pencil and three rulers which are 10p cheaper than a pen.

He got 7.05 change from 10.

(i) Write down an equation in terms ofx.

Equation ___________________________ [1]

(ii) Solve your equation to find the value ofx.

Answer x = __________________ [3]

x (b) Solve 2 = 8

5

Answer ___________________________ [2]


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Examiner Only

Marks Remark

(c) Rearrange V= 30 10t to make t the subject.

Answer t= __________________ [2]


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Examiner Only

Marks Remark

2 (a) Write 60 as a product of prime factors.

Answer __________________ [2]

(b) Find the HCF (highest common factor) of 60 and 36

Answer __________________ [2]

(c) Find the LCM (lowest common multiple) of 60 and 36

Answer __________________ [1]


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Examiner Only

Marks Remark

3 Tins of fruit come in boxes. A record is kept of the number of damaged tins

in each box.

No. of

damaged tins No. of boxes

02 38

35 2668 10

911 3

1214 2

1517 1

1820 0

(a) Which class interval contains the median?

Answer _________ [1]

(b) Draw a frequency polygon for this data.

[2]

0

10

20

30

40

0 2 4 6 8 10 12 14 16 18 20No. of damaged tins

No. ofboxes


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Examiner Only

Marks Remark

4 Write down the nth term for each of the sequences.

(a) 4, 8, 12, 16, ......

Answer _____________ [1]

(b) 4, 9, 14, 19, ......

Answer _____________ [2]


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Examiner Only

Marks Remark

5 (a) P is the point (4, 2). Q is the point (6, 8). Find the co-ordinates of

the midpoint ofPQ.

Answer (_____, _____) [2]

(b) The interior angle of a regular polygon is 160

(i) How many sides has the polygon?

Answer _____________ [2]

(ii)

Two polygons, identical to each other, are joined to the regular

polygon as shown. Explain why these cannot be regular polygons.

[2]

Regular polygon

160

Polygon Polygon

Diagram notdrawn accurately


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Examiner Only

Marks Remark

6 (a) Expand y(y2 9)

Answer ___________________________ [2]

(b) Expand and simplify (x 4)(x + 3)

Answer ___________________________ [2]

7

A, N and B are points on a circle, centre O. MB is 12cm. OB is 13cm. Theangle OMB is 90

(a) Calculate the length of MO.

Answer _____________ cm [3]

(b) Hence find the length of MN.

Answer _____________ cm [1]

N

MA B

O



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Examiner Only

Marks Remark

4 593.628 (a) Estimate the value of

3 81.6

Show your working.

Answer _____________ [2]

(b) Calculate 318 12

3, giving your answer as a mixed number.

Answer __________________ [3]

(c) Evaluate (10)

2

Answer __________________ [1]

(d) Calculate (1.3 105) (8 103) giving your answer in standard form.

Answer _____________ [2]


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[3]

160

140

120

100

80

60

40

20

00 50 100 150 200 250 300 350 400

marks

Cumulativefrequency()

9 The graph shows the cumulative frequency of marks obtained in a mathematics examination.

(a) From this graph draw a box plot.

Examiner Only

Marks Remark


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Examiner Only

Marks Remark

(b) Use the cumulative frequency graph to estimate how many candidates

scored more than 320 marks.

Answer _____________ [2]


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Examiner Only

Marks Remark

10

The diagram shows the side view of an ironing board standing on

horizontal ground. The top of the ironing board is parallel to the ground.

The legs AB and CD meet at X.

(a) Prove that the triangles AXD and BXC are similar.

[2]

(b) CX = 63cm, DX = 42cm and AD = 48cm. Find the distance

between the feet, CB.

Answer _____________ [4]

C B

A D

X Diagram notdrawn accurately


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Examiner Only

Marks Remark

11 Solve the simultaneous equations:

2x 3y = 7

3x + 5y = 1

Show your working.

Solution by trial and improvement will not be accepted.

Answer x = _________, y = _________ [4]


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Examiner Only

Marks Remark

12 (a)

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

The angle ADC is 106.

Calculate:

(i) the angle ABC

Answer _____________ [1]

(ii) the marked angle AOC

Answer _____________ [1]

(b)

BT is a tangent to the circle at B. Mark clearly an angle in the circle

equal to the angle CBT. [2]

A

DC

B

O

106


A

DC

B

O Diagram notdrawn accurately

T


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Examiner Only

Marks Remark

13 (a) Write the recurring decimal 0.318

as a fraction.

Answer _____________ [2]

(b) Evaluate:

(i) 110

Answer _____________ [1]

(ii) 253

2

Answer _____________ [2]

14 Each edge of a cube is enlarged by a scale factor of 32.

By what factor is

(a) the surface area enlarged,

Answer _____________ [1]

(b) the volume enlarged?

Answer _____________ [1]


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Examiner Only

Marks Remark

15 (a) Factorise x2 25

Answer ______________________ [1]

(b) Simplify

Answer ______________________ [3]

x2 25

3x2 + 11x 20


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BLANK PAGE

(Questions continue overleaf)


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Examiner Only

Marks Remark

16 (a)

On the grid above, sketch the graph ofy = cosx for 0 x 360 [1]

(b)

On the grid above, sketch the graph ofy = sinx for 0 x 360 [1]

2

1

0

1

2

90 180

y

xdegrees270 360

2

1

0

1

2

90 180

y

xdegrees270 360


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Examiner Only

Marks Remark

(c) Given that tan 45 = 1, work out the value of

(i) tan 135

Answer _____________ [1]

(ii) tan (135)

Answer _____________ [1]


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Examiner Only

Marks Remark

17 One side of a rectangle is (2x 3) metres.

The perimeter of the rectangle is 50 metres.

(a) Show that the area, A, of the rectangle is given by

A = 62x 84 4x2

[2]

The area of the rectangle is 126 m2.

(b) (i) Show that 2x2 31x + 105 = 0

[1]

(ii) Hence, solve the equation for x

Answer x = _________, _________ [3]


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BLANK PAGE

(Questions continue overleaf)


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(a) Draw a histogram on the graph paper.

[3]

(b) After the recording was completed a stratified sample of the

applications was taken. Two of the applications processed in 10 daysor less were selected.

(i) How many applications were in the stratified sample?

Answer _____________ [2]

(ii) How many applications processed in more than 15 days were in

the sample?

Answer _____________ [1]

Number of days (D) 0 D 10 10 D 15 15 D 20 20 D 35

Frequency 30 45 33 12

Examiner Only

Marks Remark

18 The numbers of days spent processing applications for passports were recorded:


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Examiner Only

Marks Remark

19 The midpoints of the sides of a square of side 12cm are joined to form

another square. The process is repeated so that a nest of 4 squares is

formed as shown.

Is the length of the side of the shaded square rational or irrational?

Show your working.

Answer _____________ [3]

Y Z

W X

12cm

12cm


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Examiner Only

Marks Remark

V

U T

R Sa

b

20

RSTU is a parallelogram. U is the mid-point of the line RV. RS = a and

RU = b.

Explain by using vectors and giving reasons, why VT is parallel to US.

[3]


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THIS IS THE END OF THE QUESTION PAPER

21 Solve

A solution by trial and improvement will not be accepted.

Answer x = _____________ [7]


1 3 1 = x 1 x + 2 4

Examiner Only

Marks Remark


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GCSE MATH Three Tier PP MayJune 2008 Higher Tier Paper 5 Non Calculator 4128 (1)

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