November 2010
Paper 3
1)a)
Milk : Dark
2 : 1
24 : 12
There are 36 chocolates in total
2)
a)
p x p x p x p = p4
b)
2c x 3d = 6cd
3)a)
+
1
3
5
7
9
2
3
5
7
9
11
4
5
7
9
11
13
6
7
9
11
13
15
8
9
11
13
15
17
b) (2, 9) (4, 7) (6, 5) (8, 3)
c) P(less than 6) = 3/20
4)a)
2
6
10
14
18
4n – 2
b) 10 – n2
i) 3rd term = 10 – 32 = 1
ii) 5th term = 10 – 52 = -15
5) Area of circle = π x radius2
Area = π x 102
= 314cm2
6)
3870
236 x 4.85
4000
200 x 5
(1 mark for any
one of these)
4000
1000
4
(1 mark for any
answer between 3
and 4)
7) 175 x 37 = 6475
£64.75
8) Line drawn through
(−2, 6) (−1, 5) (0, 4) (1, 3) (2, 2)
(3, 1) (4, 0), (5, − 1)
9)
Equilateral triangle so all angles are
60°
x = 120°
Angles on a straight line add up to
180 °
10)a)
6
7
8
9
9
2
0
1
4
1
2
Key 9|1 = 91
b)
Mode = 77
7
2
7
3
7
3
8
6
11)17.5% of 6000 = 1050
(1 mark)
6000 + 1050
(1 mark)
= 7050
(1 mark)
7050 – 3000
(1 mark)
4050 ÷ 10
(1 mark)
= 405
(1 mark)
12)
a) Rotation
180°
Centre (0,0)
(1 mark)
(1 mark)
(1 mark)
12)b)
13) t = v + 2
5
t–2
=
v
5
(t – 2) x 5 = v
5(t – 2) = v
14) Midpoint of PQ is (7, 5)
15) B and E
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
18)a) 2
17/
2/
–
1
20
5
17 _ 2
20
5
or
57 _ 7
20
5
17 _ 8
20
20
57 _ 28
20
20
9
20
29
20
Answer = 19/20 or 29/20
18)b) 2 2/3 x 1 3/4
8 x 7
3
4
56
12
(or equivalent...e.g.
14/
2/
or
4
3
3
19)a)
A
10cm
10cm
x 1.5
E
B
8cm
8cm
or ÷ 2 then x 3
5cm
D
C
15cm
DC = 12cm
19)b)
A
10cm
Area of trapezium
= ½ (a + b) x height
Parallel sides
E
B
8cm
5cm
D
C
8cm
5cm
12cm
Area of trapezium
= ½ (8 + 12) x 5
= 50cm2
20) a)
13.2
b) 13.8 – 12.6 = 1.2
c) IQR ignores extreme values/outliers
21) 6x + 2y = − 3
(1)
4x − 3y = 11
(2)
Make the ys the same
(1) x 3
18x + 6y = -9
(2) x 2
8x – 6y = 22
(1 mark)
Signs Same Subtract
26x = 13
(1 mark)
x=½
(1 mark)
Now find y 6x + 2y = -3
3 + 2y = -3
2y = -6
y = -3 (1 mark)
22)
a) A tangent is at right angles to a
radius
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)a)
24)b)
6 + 8 + 6 + 5 = 25
25)
180 x 50
1000
=
9
26) P is inversely proportional to V.
When V = 8, P = 5
a) P = k
V
5 = k
8
k = 40
P = 40
V
26)b)
P = 40
V
P = 40
2
P = 20
27)a)
OP = a + b
OM = ½a + ½b
27)b)
TM = -a + ½a + ½b
TM = -½a + ½b
28)
(-1.6,2.6)
(2.6,-1.6)