November 2010Paper 4

1)a) 5 x 8 ÷ 2 = 20cm2

2)

P (Pink) = 0.12

Colour Red Blue PinkProbability

0.58 0.30

3)a) There are 20 beads in box A. In box B there are twice as many beads as in box A. Box B = 40

In box C there are ¾ of the number of beads as in box A. Box C = 15 In box D there are 10% more beads than in box A. Box D = 22

Total = 20 + 40 + 15 + 22 = 97

4)a)

3 x 100 = 300g

4)b)

4 x 6 = 24 people

5)a)

5)b)

6)a) 7x + 2y – x + y = 6x + 3y

b) 2x + 3 = 102x = 7 x = 3.5

c)i) c5 x c6 = c11

c)ii) e12 ÷ e4 = e8

7) 8 x 100 = 40% 20

8)

a) Modal class is 10-19b) Median is 30th person so lies in

the class 20-29

19

31

8)

9) 2.42927(0474)

10)a) −2, −1, 0, 1, 2

b) 2x < 10 3

2x < 30

x < 15

11) A and 3B and 2C and 4D and 1

12) T = 7x + 5y

13) Speed = distance time

Speed = 7120 8

= 890 km/h

14)a)

14)b)

15)a) She only asks the best students

or The sample is too small

or The sample is biased

15)b) All the choices are positive

There is no box for someone who doesn’t like maths

15)c) How many hours do you spend on

your maths homework in a day?

0 hours 1-2 hours 3+ hours

1 mark for question with time frame

1 mark for three non-overlapping response boxes(no marks for inequalities)

16) a) (0, 3, 2)

b) (5, 3, 0)

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) 8.25 x 107

b) 1.456 x 10-15

18) 19.5 litres = 19500 millilitres (1 mark)

19500 ÷ 210 = 92.85714 (1 mark)

Therefore a maximum of 92 full cups can be poured (1 mark)

19)a)

Age (A years)

Cumulative Frequency

20 < A < 30 2620 < A < 40 6120 < A < 50 8220 < A < 60 9420 < A < 70 100

19)b)

19)c)2 marks for 36-38

or for correct reading

from your graph if reading

lines are drawn on

19)d)2 marks for 9-11

or for correct reading

from your graph if reading

lines are drawn on

20)a)

56 = 2 x 2 x 2 x 7 = 23 x 7

56

28 2

4 7

2 2

20)b) 14

21)

cos 37 = AB (1 mark)

8

AB = cos 37 x 8 (1 mark)

AB = 6.389 (1 mark)

hyp

adj

22)a)

x -2 -1 0 1 2 3

y -15 -8 -7 -6 1 20

22)b)

23)

1 mark for 256° or 52 seen in working or on diagram

1 mark for x = 104°

256°52°

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) 35.5 x 26.5 = 940.75

1 mark for 35.5 or 26.5

1 mark for 35.5 x 26.5

1 mark for 940.75

25)a) (2x + 4y)(4x – 5y)

8x2 + 16xy – 10xy – 20y2

= 8x2 + 6xy – 20y2

25)b) (x + 10)5

(x + 10)4

= x + 10

25)c) x2 – 25 x2 + 7x + 10

= (x – 5)(x + 5) (x +2)(x + 5)

= x – 5x + 2

25)d) x2 + 6x − 2 = (x + p)2 + q

= (x + 3)2

(x + 3)2 = x2 + 6x + 9

– 11

26)

W

B

W

B

W

B

7/11

4/11

6/10

4/10

7/10

3/10

White then black= 7/11 x 4/10

= 28/110

Black then white= 4/11 x 7/10

= 28/110

One of each = 56/110

(or equivalent)

26)b) P = 40 V

P = 402

P = 20

27)a)

27)b)

28)a)

Area = ½ x 10.5 x 8.3 x sin 62

= 38.474... cm2

28)b)

QR2 = 10.52 + 8.32 – 2x10.5x8.3xcos62

QR2 = 97.311111

QR = 9.8646... cm