June 2009 Paper 3

June 2009Paper 3

1)a)

b)P(walk) = 37100

Walk Car Other Total

Boy 15 25 14 54

Girl 22 8 16 46

Total 37 33 30 100

2) a) 4x + 3y – 2x + 5y = 2x + 8y

b) 2c + 4r

Hint: make up values for c and r and work out what sum you would need to do

3)a) y = 4x – 3

b)Your graph should be a straight line through all the points with no

‘corners’

On this exam you only got 1 mark for plotting your points if they were wrong

x -2 -1 0 1 2 3y -11 -7 -3 1 5 9

4)a) P = 4k – 10 P = 50

50 = 4k – 10 (1 mark)60 = 4k k = 60 ÷ 4 k = 15 (1 mark)

b) y = 4n – 3d n=2 d=5

y = 4x2 – 3x5 (1 mark)y = 8 – 15y = -7 (1 mark)

5)a)

5)b)

Translation 3 right and 1 down 3 (1 mark) (1 mark) -1

6) a) Opposite sides of a rectangle are equal

b) 4x + 1 = 2x + 122x + 1 = 12 2x = 11

x = 5.5

c) Perimeter = 5.5 + 5.5 + 23 + 23 = 57cm

7) 322 x 48 = 15456

a) 3.22 x 4.8 = 15.456

b) 0.322 x 0.48 = 0.15456

c) 15456 ÷ 4.8 = 3220

8) a) 2x2 = 72 x2 = 36 x = 6

b)

72 = 2 x 2 x 2 x 3 x 3

= 23 x 32

72

36 2

6 6

2 3 2 3

9)

9)

10)There are 40 litres of water in a barrel.The water flows out of the barrel at a rate of 125 millilitres per second.1 litre = 1000 millilitres.Work out the time it takes for the barrel to empty completely.

40 litres = 40 000 millilitres40 000 ÷ 125 = 320 seconds

(40 000 ÷ 125 = 40 x 8)

11)a) 62.5

11)b) 63.5

12)

13) a) What type of magazines do you read?

Sport Music Fashion

One question 1 mark

Tick box options – at least two options 1 mark

13) b) How many magazines have you read in the last month?

0 1-2 3+

Time period e.g. month, week, year1 mark

Tick box options – at least three non-overlapping options 1 mark

14) 6.8 x 191 0.051

7 x 200 (1 mark for at least

0.05 two of these)

1400 (1 mark) 0.05

28000 (1 mark)

(Dividing by 0.05 is the same as multiplying by 20)

15)a) Write 64 000 in standard form

6.4 x 104

(b) Write 156 x 10-7 in standard form

1.56 x 10-5

16)a) Factorise fully 4x2 – 6xy

2x(2x – 3y)

b) Factorise x2 + 5x – 6

(x + 6)(x – 1)

17)

Use upperbounds

Join with a smoothcurve

17)b) Median is‘middle

one’

60th value

Mark given for any value

between 235 and 245

17)c) Men spent more money than women

18)a)

Work out the size of angle AOD54° (2 marks)

tangent is perpendicular to a radiusangles in a triangle add up to 180° (reasons not required)

18)b)

Work out the size of angle ABC. Give a reason for your answer.

27° (2 marks)

Angle at the centre is twice the angle at the circumference. (1 mark)

19)a)

x = 2, y = 3

19b) Find an equation of the straight line which is parallel to the

line y = ½x + 2 and passes through

the point (0, 4)

y = mx + c

y = ½x + c

y = ½x + 4

20)a) 3t + 1 < t + 12

2t + 1 < 12 2t < 11

t < 5.5

20)b) t is a whole number.Write down the largest value

of t that satisfies

3t + 1 < t + 12

t < 5.5

largest value of t is 5

21) M is directly proportional to L3.When L = 2, M = 160Find the value of M when L = 3

M = k x L3

160 = k x 23

160 = k x 8 160 = k 8

k = 20M = 20 x L3

M = 20 x 33

M = 20 x 27 = 540

22)

23)a)

0.2

0.2

0.2

0.2

0.30.5

0.50.3

0.50.3

23)b) Work out the probability that Vishi will win both games.

0.5 x 0.5 = 0.25

24)a) AB = AC (sides of an equilateral triangle)

AD = AD (common side)

ADC = ADB = 90°

Therefore ABD and ACD are congruent (RHS)

24)b) BD = DC (congruent triangles)

BC = AB (equilateral triangles)

Therefore BD = ½ AB

25) 1 + 1 = 1u v f

1 + 1 = 1 (1 mark)5/2 10/3 f 2 + 3 = 1 5 10 f 4 + 3 = 1 10 10 f

7 = 1 (1 mark) 10 f

f = 7 (1 mark)10

25) 1 + 1 = 1u v f

1 = 1 - 1u f v

1 = v - f u fv fv

1 = v - fu fv

u = fv v - f

26)

a) Find an equation of the translated curve.

y = f(x – 4)

26)

b) On the grid, sketch the graph of

y = 3 cos (2x°) for values of x from 0 to 540