5 The pie chart shows some information about the way 600 students travel to school. Walk Bicycle 60°

(a) Work out the number of students that walk to school [2]

(b) 120 of the students travel to school by car.

The remaining students travel by bus.

Complete the pie chart.

[3] , ,

6 NOT TO SCALE C E D B A 80° 75°

ABCD is a quadrilateral.

E lies on CD and AE is parallel to BC.

EA = ED.

Find

(a) angle ABC

Angle ABC = [1]

(b) angle AED

Angle AED = [1]

(c) angle DAB.

Angle DAB = [2] , ,

1 The temperature at 4 am is -12 °C.

The temperature at 4 pm is 21 °C.

Find the increase in temperature from 4 am to 4 pm °C [1]

2 Find all the common factors of 8 and 12 [1]

7 Represent the inequality x 4 3 1 G

on the number line. x – 6 – 5 – 4 – 3 – 2 – 1 1 0 2 3 4 5 6

[2]

8 Kemi buys p pens that each cost 40 cents.

She pays with $20.

Write an expression, in terms of p, for the change, in cents, Kemi receives from the $20 cents [2] , ,

9 Rajid has a full bottle of juice.

He drinks 3 1 of the full bottle on Monday.

He drinks 7 3 of the full bottle on Tuesday.

Find the fraction of the bottle of juice remaining [3]

3 A cuboid has length 6 cm, width 5 cm and height 2.5 cm.

Work out the volume of the cuboid cm3 [2]

10

b dm mk 2

(a) . d 3 14

, . m 7 92

and . k 1 10 6

.

By rounding each value correct to 1 significant figure, work out an estimate for b [3]

(b) Rearrange the formula to make m the subject.

m = [2]

11 NOT TO SCALE S P Q T R

In the diagram, S lies on PQ and T lies on PR.

ST is parallel to QR.

(a) Explain why triangle PQR is mathematically similar to triangle PST.

Give a geometrical reason for each statement you make [3]

(b) ST = 3 cm, QR = 9 cm and PS = 5 cm.

Work out PQ.

PQ = cm [2]

(c) The area of triangle PST is 2k cm2.

Find, in terms of k, the area of quadrilateral QRTS cm2 [2] , ,

12 A fitness club has 100 members.

60 swim (S ).

70 cycle (C ).

25 do not swim or cycle. C S %

(a) Complete the Venn diagram.

[3]

(b) One member of the fitness club is chosen at random.

For this member, find

(i) P(C )

[1]

(ii) P(S C + )

[1]

(iii) P(S C , l) [1] , ,

13

M 2 3 5 7 3 2

=

(a) Write 14M as a product of its prime factors.

Give your answer in index form [2]

(b) R is an integer.

R M is a cube number.

Find the smallest possible value of R.

R = [2] 14 Find the value of

(a) 3 3 2 2 '

[2]

(b) 16 2 3

• [2]

15 Factorise.

(a) x 64 2 -

[1]

(b) ( ) ( ) x x y x y 5 2 6 2 2

[2] , ,

16 NOT TO SCALE D C B A 14°

AB and BD are two sides of a regular 15-sided polygon.

AB and BC are two sides of a regular n-sided polygon.

Angle DBC = 14°.

Work out the value of n.

n = [4]

17 B is the point (-3, 1) and D is the point (-5, 9).

BD is a diagonal of the kite ABCD.

(a) The ratio of the lengths of the diagonals BD : AC = 2 : 3.

Work out the length of AC.

Give your answer as a surd in its simplest form [5]

(b) Find the coordinates of the midpoint of BD.

( , ) [2]

(c) The diagonal AC of the kite passes through the midpoint of BD.

Find an equation of AC.

Give your answer in the form y mx c

• .

y = [4]

18 Rationalise the denominator and simplify. 4 6 20 +

[3] , ,

19 NOT TO SCALE 7 cm 5 cm 5 cm

The diagram shows a box in the shape of a cuboid.

Mala has a straight rod of length 10 cm.

Show that this rod does not fit completely inside the box.

[3]

20

( )x x 2 1 21 f

• , x 2 1 !

( )x x 3 4 g

(a) Find

(i) g(2)

[1]

(ii) gf(-1)

[2]

(iii) ( )x f 1

.

( )x f 1

• [3]

(b) Solve ( ) ( ) x x f g

.

x = or x = [5]

4 A computer costs $560.

In a sale, this cost is reduced by 20%.

Find the cost of the computer in the sale.

$ [2]

21 (a) y x 1 – 1 360° O 180°

On the diagram, sketch the graph of cos y x

for ° ° x 0 360 G G . [2]

(b) Solve the equation cosx 2 3 0 +

for ° ° x 0 360 G G .

x = or x = [3] 22 A graph with equation y x bx c 2

• has a minimum point at (-5, 12).

Find the value of b and the value of c.

b = c = [3] , ,

23 NOT TO SCALE B A 240° 12 cm O

The diagram shows a major sector, AOB, of a circle.

The sector angle is 240° and the radius is 12 cm.

(a) Show that the length of the major arc AB is rcm 16 .

[1]

(b) OA is joined to OB to form a cone.

Work out the volume of the cone.

Give your answer in the form r a b 3 ` j where a is an integer and b is a prime number cm3 [6] Question 24 is printed on the next page. , ,