6 y x 0 1 1 2 3 4 5 6 7 8 9 2 3 4 5 6 7 8

The line x y 7 +

is drawn on the grid.

(a) On the grid, draw the line y x 2 1

• . [2]

(b) Use your graph to solve these simultaneous equations.

x

y y x 7 2 1 +

= +

x = y = [1] , ,

7 Write the recurring decimal .0 26o as a fraction.

Give your answer in its simplest form [3]

4 Work out.

6 5 3 2 8 3

[3]

8

m n 11 5 8 3

= - e e o o

(a) Find 2m - n.

f p [2]

(b) The vector y 5 e o has a magnitude of 7.

Find the value of y.

y = [2]

9 The table shows some information about the marks scored by a group of students in a test. Test mark 4 5 8 Frequency 2 4 n

The mean mark is 6.

Work out the value of n.

n = [3]

10 NOT TO SCALE D E A B C O 35° 40°

A, B and C are three points on a circle, centre O.

DE is a tangent to the circle at A.

Angle ° ACO 35

and angle ° BCO 40

.

Find

(a) angle AOC

Angle AOC = [1]

(b) angle ABC

Angle ABC = [1]

(c) angle DAC

Angle DAC = [1]

(d) angle OAB.

Angle OAB = [1] , ,

1 Simplify.

c d c d 7 5 3

• [2]

11 The diagram shows the graph of ( ) f y x

and the point ( , ) P 2 11

. 0 1 5 – 5 – 10 10 15 2 3 – 2 – 1 y P x

The tangent from P touches the graph of ( ) f y x

at the point (a, b).

The values of a and b are integers.

(a) By drawing this tangent, find the value of a and the value of b.

a = , b = [2]

(b) Find the equation of the tangent.

Give your answer in the form y mx c

• .

y = [3] , ,

12 The time spent on the internet by each of 120 adults is recorded for one day.

The cumulative frequency diagram shows this information. 0 0 Cumulative frequency Time (hours) 20 40 60 80 100 120 2 4 6 8 10

(a) Use the cumulative frequency diagram to find an estimate of the interquartile range h [2]

(b) 70% of the adults spent less than k hours on the internet.

Use the cumulative frequency diagram to find an estimate of the value of k.

k = [2] , ,

13 10 cm 6 cm Solid A Solid B 4 cm h cm NOT TO SCALE

The diagram shows solid A and solid B.

Solid A is made from a hemisphere and a cone each with radius 6 cm.

The cone has sloping edge 10 cm.

Solid B is a cylinder with radius 4 cm and height h cm.

The total surface area of solid A is equal to the total surface area of solid B.

(a) Work out the value of h.

h = [5]

(b) Work out the height of solid A cm [3] , ,

2 158° 76° x° y° w° NOT TO SCALE

The diagram shows two parallel lines intersecting two straight lines.

Find the values of w, x and y.

w = x = y = [4]

14

( ) f x x 3 4

( ) g x x 4 1

(a) Find ( ) f 2

[1]

(b) Find ( ) f x 1

.

( ) f x 1

• [2]

(c) ( ) fg x ax b

Find the value of a, and the value of b.

a = b = [2]

(d) Simplify.

( ) ( ) f g x x 2 5

Give your answer as a single fraction in terms of x [3] , ,

3 Sally invests $1500 at 3% per year simple interest.

Work out the total value of her investment at the end of 6 years.

$ [3] , ,

15 (a) Expand and simplify.

( )( ) 2 5 1 3 5

[2]

(b) Rationalise the denominator.

Give your answer in its simplest form.

10 6

[2] 16 Expand and simplify.

( )( )( ) x x x 4 3 3 2 +

[3] , ,

5 The interior angle of a regular polygon is 150°.

Find the number of sides of this polygon [2]

17 (a) A bag contains 6 red marbles, 3 green marbles and 1 blue marble.

Two marbles are picked at random from the bag with replacement.

Find the probability that both marbles are green [2]

(b) Another bag contains 4 red counters and 2 yellow counters.

Two counters are picked at random from this bag without replacement.

(i) Complete the tree diagram. First counter Second counter Red Yellow Red Yellow Red Yellow 4 6 3 5 2 6

[2]

(ii) Find the probability that one of the two counters is yellow [3] , ,

18 One day, Anya runs 12 km at a speed of x km/h.

The next day she walks 10 km at a speed of ( ) x 4

km/h.

(a) Write down an expression, in terms of x, for the time she spends running h [1]

(b) Write down an expression, in terms of x, for the time she spends walking h [1]

(c) The time Anya spends walking is 1 hour more than the time she spends running.

Write an equation in terms of x and show that it simplifies to x x 2 48 0 2 -

= .

[4]

(d) Use factorisation to solve the equation x x 2 48 0 2 -

= .

x = or x = [3]

(e) Find the time Anya spends running h [1] , ,

19 Find the value of 27 3 2

• [2]

20 6 cm x cm NOT TO SCALE 30°

Find the exact value of x.

x = [4]

21 A B O C P NOT TO SCALE n 2m

OABC is a rhombus and O is the origin.

The diagonals of the rhombus intersect at P.

and m n 2 OP AP

= .

(a) Find, in terms of m and n, in its simplest form

(i) OA

OA = [1]

(ii) OC.

OC = [1]

(b) D is the point such that 10 3 AD m n

.

Show that OADC is a trapezium.

[3] , ,

22 A curve has equation y x qx x 9 n 2

.

x y x x 3 12 9 d d 2

(a) Find the value of n, and the value of q.

n = q = [2]

(b) Work out the coordinates of the turning points of the curve.

( , ) and ( , ) [4]