November 2010Paper 3

1)a) Milk : Dark 2 : 1 24 : 12

There are 36 chocolates in total

2) a) p x p x p x p = p4

b) 2c x 3d = 6cd

3)a)

b) (2, 9) (4, 7) (6, 5) (8, 3)

c) P(less than 6) = 3/20

+ 2 4 6 81 3 5 7 93 5 7 9 115 7 9 11 137 9 11 13 159 11 13 15 17

4)a) 2 6 10 14 18

4n – 2

b) 10 – n2

i) 3rd term = 10 – 32 = 1ii) 5th term = 10 – 52 = -15

5) Area of circle = π x radius2

Area = π x 102

= 314cm2

6) 3870236 x 4.85

4000 (1 mark for any 200 x 5 one of these)

40001000

4 (1 mark for any answer between 3 and 4)

7) 175 x 37 = 6475

£64.75

8) Line drawn through

(−2, 6) (−1, 5) (0, 4) (1, 3) (2, 2) (3, 1) (4, 0), (5, − 1)

9)

Equilateral triangle so all angles are 60°

x = 120°

Angles on a straight line add up to 180 °

10)a)

Key 9|1 = 91

b) Mode = 77

6 97 2 4 7 7 7 88 0 1 2 3 3 69 1 2

11) 17.5% of 6000 = 1050 (1 mark)

6000 + 1050 (1 mark)

= 7050 (1 mark)

7050 – 3000 (1 mark)

4050 ÷ 10 (1 mark)

= 405 (1 mark)

12)

a)Rotation (1 mark)180° (1

mark)Centre (0,0) (1

mark)

12)b)

13) t =v + 25

t – 2 = v 5

(t – 2) x 5 = v

5(t – 2) = v

14) Midpoint of PQ is (7, 5)

15) B and E

16) a) 3(x + 5) + 2(5x – 6) = 3x + 15 + 10x – 12= 13x + 3

b) 2x + 4 = x + 2 2

c) 5x + 10 = 5(x + 2)

d) x2y + xy2 = xy(x + y)

17)

A B

18)a) 2 17/20 – 1 2/5

17 _ 2 or20 5

17 _ 8 20 20

9 20

Answer = 19/20 or 29/20

57 _ 720 5

57 _ 2820 20

2920

18)b) 2 2/3 x 1 3/4

8 x 73 4

5612

(or equivalent...e.g. 14/3 or 42/3

19)a)

10cm

5cm8cm

A

E

D C

B

10cm

8cm

15cm

x 1.5

or ÷ 2 then x 3

DC = 12cm

19)b)

10cm

5cm8cm

A

E

D C

B

Area of trapezium= ½ (a + b) x height

Parallel sides

5cm

8cm

12cm

Area of trapezium= ½ (8 + 12) x 5= 50cm2

20) a) 13.2

b) 13.8 – 12.6 = 1.2

c) IQR ignores extreme values/outliers

21) 6x + 2y = − 3 (1)4x − 3y = 11 (2)

Make the ys the same(1)x 3 18x + 6y = -9(2)x 2 8x – 6y = 22 (1 mark)Signs Same Subtract

26x = 13 (1 mark)

x = ½ (1 mark)Now find y 6x + 2y = -3

3 + 2y = -3 2y = -6

y = -3 (1 mark)

22)

a) A tangent is at right angles to a radius

22)

b) OB2 = OA2 + AB2

OB2 = 82 + 62

OB2 = 100OB = 10

BC = OB – 6 = 4cm

23) (x − 3)(x + 5)

x2 – 3x + 5x – 15x2 + 2x – 15

b) x2 + 8x − 9 = 0(x + 9)(x – 1) = 0

either x + 9 = 0 or x – 1 = 0 x = -9 x = 1

24)a)

24)b)

6 + 8 + 6 + 5 = 25

25) 180 x 50 = 9 1000

26) P is inversely proportional to V.When V = 8, P = 5

a)P = kV

5 = k8

k = 40

P = 40 V

26)b) P = 40 V

P = 402

P = 20

27)a)

OP = a + b

OM = ½a + ½b

27)b)

TM = -a + ½a + ½b

TM = -½a + ½b

28)

(-1.6,2.6)

(2.6,-1.6)