# FHS - Written Solutions ```November 2010
Paper 4
1)a)
5 x 8 &divide; 2 = 20cm2
2)
Colour
Red
Probability 0.58
P (Pink) = 0.12
Blue
0.30
Pink
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 &frac34; 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 = 10
2x = 7
x = 3.5
c)i)
c x c = c
c)ii)
e12 &divide; e4 = e8
7)
8 x 100 = 40%
20
8)
19
31
a) Modal class is 10-19
b) Median is 30th person so lies in the
class 20-29
8)
9)
2.42927(0474)
10)a) −2, −1, 0, 1, 2
b)
2x &lt; 10
3
2x &lt; 30
x &lt; 15
11)
A
B
C
D
and
and
and
and
3
2
4
1
12) T = 7x + 5y
13) Speed =
Speed
distance
time
=
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)
b)
3(x + 5) + 2(5x – 6)
= 3x + 15 + 10x – 12
= 13x + 3
2x + 4 = x + 2
2
c) 5x + 10 = 5(x + 2)
d) x2y + xy2 = xy(x + y)
17) a)
b)
8.25 x 107
1.456 x 10-15
18) 19.5 litres = 19500 millilitres (1 mark)
19500 &divide; 210 = 92.85714
(1 mark)
Therefore a maximum of 92 full cups
can be poured
(1 mark)
19)a)
Age (A years)
20 &lt; A &lt; 30
20 &lt; A &lt; 40
20 &lt; A &lt; 50
20 &lt; A &lt; 60
20 &lt; A &lt; 70
Cumulative
Frequency
26
61
82
94
100
19)b)
19)c)
2 marks
for 36-38
or for
correct
from your
graph if
lines are
drawn on
19)d)
2 marks
for 9-11
or for
correct
from your
graph if
lines are
drawn on
20)a)
56
28
4
2
2
7
2
56 = 2 x 2 x 2 x 7
= 23 x 7
20)b)
14
21)
hyp
cos 37 =
AB
8
(1 mark)
AB =
cos 37 x 8
(1 mark)
AB =
6.389
(1 mark)
22)a)
x
-2
-1
0
1
2
3
y
-15
-8
-7
-6
1
20
22)b)
23)
256&deg;
52&deg;
1 mark for 256&deg; or 52 seen in
working or on diagram
1 mark for x = 104&deg;
22)
b) OB2 = OA2 + AB2
OB2 = 82 + 62
OB2 = 100
OB = 10
BC = OB – 6 = 4cm
23) (x − 3)(x + 5)
x2 – 3x + 5x – 15
x2 + 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–5
x+2
25)d)
=
x2 + 6x − 2 = (x + p)2 + q
(x + 3)2 – 11
(x + 3)2 = x2 + 6x + 9
26)
6/
10
7/
11
4/
11
W
B
W
4/
10
B
7/
10
W
3/
10
B
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 = 40
2
P = 20
27)a)
27)b)
28)a)
Area = &frac12; 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
```