71

Centre Number

Candidate Number

General Certificate of Secondary Education

2009

Mathematics

Module N6 Paper 1

(Non-calculator)Higher Tier

[GMN61]

MONDAY 1 JUNE

9.15 am – 10.30 am

4624

TIME

1 hour 15 minutes.

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 twelve 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 56.

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.

TotalMarks

GM

N61

For Examiner’s use only

Question Marks Number

1

2

3

4

5

6

7

8

9

10

11

12

4624 2 [Turn over

Formula Sheet

Area of trapezium = 1–2 (a + b)h

Volume of prism = area of cross section × length

In any triangle ABC

Area of triangle = 1–2 ab sin C

Cosine rule: a2= b2

+ c2– 2bc cos A

Volume of sphere = 4–3πr3

Surface area of sphere = 4πr2

Volume of cone = 1–3πr2h

Curved surface area of cone = πrl

Quadratic equation:

The solutions of ax2+ 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

aA

bB

cC

= =

x b b aca

=±– –2

4

2

4624 3 [Turn over

Examiner Only

Marks Remark1 A spinner can point to the colours Red, Green, Yellow, Blue or Black. The probabilities for some of these are given in the table.

Colour Red Green Yellow Blue Black

Probability 0.3 0.15 0.25 0.1

(a) What is the probability of getting the colour Yellow?

Answer ______________ [2]

(b) If the spinner is spun 600 times, estimate how many times you would expect the colour to be Green.

Answer ______________ [2]

2 Use the formula

to find the value of P when Q = 12 and S = –4

Answer ______________ [3]

PQ S= ( – )2

8

4624 4 [Turn over

Examiner Only

Marks Remark

3

The diagram shows the front and side views of a 3-D solid consisting of

6 cubes.

Draw

(a) the plan of the solid,

[2]

(b) the side elevation of the solid.

[2]

Front viewSide view

4624 5 [Turn over

Examiner Only

Marks Remark4 (a) Estimate the answer to

(i)

Answer _________________ [2]

(ii)

Answer _________________ [3]

(b)

Answer _________________ [1]

5 36 27 359 35 7 04. .. – .

×

90101

9 932

⋅( )

Given that

find 154840.98

98 158 15484× = ,

4624 6 [Turn over

–7 –6 –5 –4 –3 –2 –1 1 2 3 4 5 70

1

–1

–2

–3

–4

–5

–6

–7

–8

2

3

4

5

6

7

8

6

B

A

D

C

x

y5

(a) Describe fully the single transformation which takes Triangle A to

Triangle B.

______________________________________________________ [3]

(b) Describe fully the single transformation which takes Triangle A to

Triangle C.

______________________________________________________ [2]

(c) Describe fully the single transformation which takes Triangle A to

Triangle D.

______________________________________________________ [3]

Examiner Only

Marks Remark

4624 7 [Turn over

Examiner Only

Marks Remark

6 (a) Make g the subject of the formula v = u + gt.

Answer _________________ [2]

(b) Solve the inequality –6 < 3n + 1 � 10 for integer values of n.

Answer n = _________________ [4]

7

The triangles are congruent.

What is the size of angle x?

Answer x = _________________° [1]

93°

17°

xDiagrams not

drawn accurately

4624 8 [Turn over

Examiner Only

Marks Remark8 (a) Prove that the square of any even number is a multiple of 4

[2]

(b) If x < 1 then x2 < 1 Give a counter example to disprove this statement.

Answer _________________ [1]

(c) Prove that (n – 1)(n + 1) + 2n – 2(n – 1) – n2 ≡ 1

[2]

4624 9 [Turn over

Examiner Only

Marks Remark9 (a) Write 367 140 000 in standard form.

Answer ______________________ [1]

(b) Write 0.000 059 72 in standard form.

Answer ______________________ [1]

(c) Find, in standard form, the value of

(3 × 10–2) × (6 × 10–5)

Answer ______________________ [2]

4624 10 [Turn over

10 On her way to work Rebekah passes through two sets of traffic lights. The probability that the first set is green when she reaches them is 0.7 and the probability that the second set is green is 0.6

(a) Complete the tree diagram for these events.

0.7

Green

NotGreen

0.6

Green

NotGreen

Green

NotGreen

Examiner Only

Marks Remark

[1]

4624 11 [Turn over

Examiner Only

Marks Remark (b) Use the tree diagram to find the probability that, on a work day chosen

at random, Rebekah had to stop at only one set of traffic lights.

Answer ______________________ [2]

4624 12 [Turn over

Examiner Only

Marks Remark11 (a) Show that ( 8 + 3 2 )2 = 50

[2]

(b) Change 3.4̇ 5̇ into a fraction.

Answer ______________________ [3]

4624 13 [Turn over

Examiner Only

Marks Remark12 Mike takes cubes at random without replacement from a bag containing

7 red, 3 yellow and 2 white cubes.

What is the probability that

(a) the first two cubes he takes are both yellow,

Answer _________________ [3]

(b) the first two cubes are the same colour as each other but the third is a different colour?

Answer _________________ [4]

THIS IS THE END OF THE QUESTION PAPER

General Certificate of Secondary Education

2009

Mathematics

Module N6 Paper 2

(With calculator)Higher Tier

[GMN62]

MONDAY 1 JUNE

10.45 am – 12.00 noon

4625

TIME

1 hour 15 minutes.

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 sixteen questions.

Any working should be clearly shown in the spaces provided since

marks may be awarded for partially correct solutions.

INFORMATION FOR CANDIDATES

The total mark for this paper is 56.

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 calculator, ruler, compasses, set-square and

protractor.

The Formula Sheet is on page 2.

GMN62

TotalMarks

71

Centre Number

Candidate Number

For Examiner’s use only

Question Marks

Number

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

4625 2 [Turn over

Formula Sheet

Area of trapezium = 1–2 (a + b)h

Volume of prism = area of cross section × length

In any triangle ABC

Area of triangle = 1–2 ab sin C

Cosine rule: a2= b2

+ c2– 2bc cos A

Volume of sphere = 4–3πr3

Surface area of sphere = 4πr2

Volume of cone = 1–3πr2h

Curved surface area of cone = πrl

Quadratic equation:

The solutions of ax2+ 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

aA

bB

cC

= =

x b b aca

=±– –

24

2

4625 3 [Turn over

Examiner Only

Marks Remark

1 A bag of 25 potatoes selected at random in a store has 4 bad potatoes. How

many potatoes are expected to be bad out of a bag of 200 potatoes?

Answer __________________ [2]

2 WXYZ is a trapezium.

Calculate the area of the trapezium.

Give your answer to an appropriate degree of accuracy.

Answer ___________________ cm2 [3]

6.1 cm

12.6 cm

8.5 cm

W

YZ

X

4625 4 [Turn over

Examiner Only

Marks Remark

3 (a) To feed 30 people John makes

20 beef sandwiches

36 cheese sandwiches

52 ham sandwiches

How many of each would he need to make for 45 people?

Answer _____________ beef

Answer _____________ cheese

Answer _____________ ham

[3]

(b) £1 = $2 and $5 = €3

Which is cheaper, a camera bought for £36 or another bought for €42?

Show your working.

Answer: The camera bought for _________ [2]

4625 5 [Turn over

Examiner Only

Marks Remark

4 (a) Complete the table of values for y = x2 – 3

x –3 –2 –1 0 1 2

y 6 –2 –3 1

[2]

(b) Hence draw the graph of y = x2 – 3

[2]

y

x

6

6

4

4

2

2

– 2

– 2

– 4

– 4

– 6

– 6 0

4625 6 [Turn over

Examiner Only

Marks Remark

5 A piece of metal has a volume of 600 cm3 and weighs 2700 g. Calculate its

density.

Answer ________________ g/cm3 [2]

4625 7 [Turn over

Examiner Only

Marks Remark

6 An athlete goes for a run from Newtown to Oldtown and back. His journey

is illustrated on the graph.

(a) What is the athlete’s speed on the return journey from Oldtown to

Newtown?

Answer __________________ km/hr [2]

(b) A second athlete leaves Oldtown at 1030 and runs towards Newtown,

at a speed of 7 km/hr.

(i) Illustrate his journey on the graph above. [3]

(ii) At what time do the two athletes pass each other?

Answer ______________________ [1]

10

12Oldtown

Newtown

8

dis

tance

fro

m N

ewto

wn (

km

)

6

4

2

0

1000

Time

1100 1200 1300 1400

4625 8 [Turn over

Examiner Only

Marks Remark

7 In Westwood School there are 550 girls and 450 boys. The probability that

a girl plays the piano is 0.3 and the probability that a boy plays the piano is

0.18

How many pupils at Westwood School play the piano?

Answer ___________ [4]

8 £180 is divided between Lisa, Mikey and Richard in the ratio 8:1:6

How much does each get?

Answer £ ______________ Lisa

Answer £ ______________ Mikey

Answer £ ______________ Richard [3]

9 Simplify

(a) t 3 × t 3

Answer ______________________ [1]

(b) r 6 ÷ r 2

Answer ______________________ [1]

(c) 4x–1y 3 × 2x2y

Answer ______________________ [2]

4625 10 [Turn over

Examiner Only

Marks Remark12 h, l and r represent lengths. Complete the table below indicating whether the expressions could

represent

length area volume none of these

32

2πr hrl

πrlh

r3 4πr2(l + h) (l + r)(h – r)

[3]

13 Make r the subject of the formula .

Answer r = ______________________ [4]

pq rr

= +50( )

4625 11 [Turn over

Examiner Only

Marks Remark

14 The diagram shows a sector of a circle, radius 20 cm. Angle AOB = 144 °

Diagram not drawn

accurately

(a) Find, in terms of π, the arc length of the sector.

Answer ___________ cm [3]

The straight edges of the sector are joined together to form a cone with

slant height 20 cm as shown below.

(b) Find the radius, r, of the base of the cone.

Answer ___________ cm [2]

O

A

B

20 cm

20 cm

r

Examiner Only

Marks Remark

4625 13

(b) Sketch the function y = f(3x)

[1]

(c) Sketch the function y = f(x) – 3

[1]

3

3

2

2

1

1

0

–1

–1

–2

–2

–3

–3

y

x

3

3

2

2

1

1

0

–1

–1

–2

–2

–3

–3

y

x

THIS IS THE END OF THE QUESTION PAPER