### FHS - Written Solutions

```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
Mark the position of C
B 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 105
(b) Write in standard form 0.00123
1.23 x 10-3
14) (a) Write down the value of 50
anything to the power 0 = 1
(b) Write down the value of 2–1
a negative power means ‘one over’
2-1 = 1 = ½
21
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
5q + 5p = 4 + 8p
5p = 4 + 3p
p = 4 + 3p
5
(one mark for
expanding the
bracket)
(one mark for putting
the ps together)
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
18) (a) Find the size of angle ABD. Give a
55° (1 mark)
tangent is perpendicular to a radius (1 mark)
(b) Find the size of angle DEB. Give a reason for
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/
2/ = 10/
x
7
7
49
or
Red and blue
2/
5/ = 10/
x
7
7
49
10/
10/ = 20/
+
49
49
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
16x = 4
x = 4/16 = ¼
Make the ys the
same
Same signs subtract
(our signs are
different
in (1)
1 + y = -1
21) Work out (2 + 3)(2 – 3)
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.
OA + 2/3AB
= a + 2/3(-a + b)
= a - 2/3 a + 2/3 b
= 1/3 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
=
+
2n + 1
(n + 1)
(1 mark)
(1 mark)
Therefore it is always an odd number
(1 mark)
```