November 2009
Paper 3

11) Bearings – identify where you are starting from, draw north line, measure clockwise
N Measure the bearing of B from A 60°
N
A
B
Mark the position of C with a cross:
160 ° angle from B (1 mark)
Point 4cm from B (1 mark)

12) Batteries are sold in packets and boxes.
Each packet contains 4 batteries.
Each box contains 20 batteries.
Bill buys p packets of batteries and b boxes of batteries.
Bill buys a total of N batteries.
Write down a formula for N in terms of p and b N = 4p + 20b
Hint: make up values for p and b and work out what sum you would need to do

13) (a) Write in standard form 213 000
2.13 x 10 5
(b) Write in standard form 0.00123
1.23 x 10 -3

14) (a) Write down the value of 5 0 anything to the power 0 = 1
(b) Write down the value of 2 –1 a negative power means ‘one over’
2 -1 = 1 = ½
2 1

15) k is an integer such that –1 < k < 3
(a) List all the possible values of k.
-1, 0, 1, 2 (not 3)
(b) Solve the inequality 6y > y + 10
5y > 10 y > 2 solve it like an equation but keep the symbol the same

16) Make q the subject of the formula
5(q + p) = 4 + 8p
Give your answer in its simplest form.
5q + 5p = 4 + 8p (one mark for expanding the
5p = 4 + 3p bracket)
(one mark for putting the ps together) p = 4 + 3p
5 final mark for isolating p

17) (a) What is the highest mark in the
English test?
50
(b) Compare the distributions of the marks in the English test and marks in the Maths test.
One comment must relate to the medians e.g. the median was higher for English so students did better in English.
One comment must relate to the inter-quartile range e.g. the IQR is smaller for maths so the results weren’t as spread out

18) (a) Find the size of angle ABD. Give a reason for your answer.
55° (1 mark) tangent is perpendicular to a radius (1 mark)
(b) Find the size of angle DEB. Give a reason for your answer.
55° (1 mark) either alternate segment theorem or angle in a semicircle and angles in a triangle (1 mark)

19) Emma has 7 pens in a box. 5 of the pens are blue. 2 of the pens are red. Emma takes at random a pen from the box and writes down its colour. Emma puts the pen back in the box.

19b) Work out the probability that Emma takes exactly one pen of each colour from the box.
Blue and red 5 /
7 x 2 /
7
= 10 /
49 or
Red and blue 2 /
7 x 5 /
7
= 10 /
49
10 /
49
+ 10 /
49
= 20 /
49
‘and’ means ‘x’, ‘or’ means ‘+’

20) Solve the simultaneous equations
4x + y = -1 (1)
4x – 3y = 7 (2)
(1)x3 12x + 3y = -3
4x – 3y = 7
Make the ys the same different
16x = 4 x = 4 /
16
Same signs subtract
= ¼ (our signs are so we add) in (1) 1 + y = -1 y = -2

21) Work out (2 +

3)(2 –

3)
Give your answer in its simplest form.
Use bird face/smiley face/FOIL
4 – 2

3 + 2

3 – 3 = 1

22) (a) Find the vector AB in terms of a and b.
-a + b
P is the point on AB so that AP : PB = 2 : 1
(b) Find the vector OP in terms of a and b.
Give your answer in its simplest form.
OA + 2 /
3
AB
= a +
= 1 /
3
2 /
= a 2 /
3
3
(-a + b) a + 2 /
3 b a + 2 /
3 b

23) Prove that the recurring decimal
0.36 = 4 /
11 x = 0.36363636….
100x = 36.36363636…
99x = 36 x = 36 = 4
99 11

24) (a) Write down the coordinates of the minimum point of the curve with the equation y = f(x – 2)
(5, -4)
(b) Write down the coordinates of the minimum point of the curve with the equation y = f(x + 5) + 6
(-2, 2)

25) Prove, using algebra, that the sum of two consecutive whole numbers is always an odd number.
n + (n + 1) (1 mark)
= 2n + 1 (1 mark)
Therefore it is always an odd number
(1 mark)