5 P T y x 4 2 3 1 0 – 2 – 1 – 2 – 3 – 1 2 1 3 4 – 4

(a) Describe fully the single transformation that maps triangle T onto triangle P [2]

(b) Draw the image of triangle T after an enlargement of scale factor 2, centre (3, 3). [2]

6 Find the value of

(a) 5 5 5 5

[1]

(b) 125 3 2. [2]

7 Simplify.

(a) t p t 2 '

[2]

(b) x x 4 3 2 1

[2]

10 ℰ = {n: n is an integer and n 1 8 G G }

A = {factors of 12}

B = {odd numbers}

Find

(a) A B +

A B + = { } [1]

(b) ( ) A B n , l [1]

14 D E NOT TO SCALE 88° 55° X B A C

A, B, C, D and E lie on the circle.

AC and BD intersect at X.

Angle ACD = 55° and angle CXD = 88°.

(a) Complete the statements, giving a geometrical reason in each part. Angle CDB = because Angle ABD = because Angle AED = because [6]

(b) Triangle CXD is mathematically similar to triangle BXA.

DX = 8.0 cm, BX = 2.7 cm and AX = 4.0 cm.

(i) Work out the length of CX.

CX = cm [2]

(ii) Complete the statement.

Area of triangle CXD : area of triangle BXA = : [1] 15 (a) Write 66 000 in standard form [1]

(b) Work out . . 3 7 10 3 7 10 8 7

j j.

Give your answer in standard form [2]

17 ( I M k2 2

) c +

(a) Find the value of I when M = 7, k = 3 and c = 2.

I = [2]

(b) Rearrange the formula to write k in terms of I, M and c. k = [3]

20 Bag A Bag B

Bag A contains 5 white balls and 3 black balls.

Bag B contains 3 white balls and 1 black ball.

(a) Two balls are picked at random from bag B without replacement.

Find the probability that both balls are black [1]

(b) The balls are replaced into bag B.

Kyle picks a ball at random from each bag.

(i) Complete the tree diagram. Bag A Bag B 8 5 white black white black white black

[2]

(ii) Find the probability that the two balls are the same colour [3]

(c) The balls are replaced into their bags.

Jo picks a ball at random from bag A and places it into bag B.

She then picks a ball at random from bag B.

Find the probability that she picks a black ball from bag B [3]

21 (a) a b 3 5 3 5 2 5

= + j j

Find the value of a and the value of b.

a = b = [2]

(b) Rationalise the denominator.

Write your answer in its simplest form.

2 6

[2]