november 2010 paper 3
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November 2010Paper 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)
b) (2, 9) (4, 7) (6, 5) (8, 3)
c) P(less than 6) = 3/20
+ 2 4 6 81 3 5 7 93 5 7 9 115 7 9 11 137 9 11 13 159 11 13 15 17
4)a) 2 6 10 14 18
4n – 2
b) 10 – n2
i) 3rd term = 10 – 32 = 1ii) 5th term = 10 – 52 = -15
5) Area of circle = π x radius2
Area = π x 102
= 314cm2
6) 3870236 x 4.85
4000 (1 mark for any 200 x 5 one of these)
40001000
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)
Key 9|1 = 91
b) Mode = 77
6 97 2 4 7 7 7 88 0 1 2 3 3 69 1 2
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 (1 mark)180° (1
mark)Centre (0,0) (1
mark)
12)b)
13) t =v + 25
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) 3(x + 5) + 2(5x – 6) = 3x + 15 + 10x – 12= 13x + 3
b) 2x + 4 = x + 2 2
c) 5x + 10 = 5(x + 2)
d) x2y + xy2 = xy(x + y)
17)
A B
18)a) 2 17/20 – 1 2/5
17 _ 2 or20 5
17 _ 8 20 20
9 20
Answer = 19/20 or 29/20
57 _ 720 5
57 _ 2820 20
2920
18)b) 2 2/3 x 1 3/4
8 x 73 4
5612
(or equivalent...e.g. 14/3 or 42/3
19)a)
10cm
5cm8cm
A
E
D C
B
10cm
8cm
15cm
x 1.5
or ÷ 2 then x 3
DC = 12cm
19)b)
10cm
5cm8cm
A
E
D C
B
Area of trapezium= ½ (a + b) x height
Parallel sides
5cm
8cm
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 = 100OB = 10
BC = OB – 6 = 4cm
23) (x − 3)(x + 5)
x2 – 3x + 5x – 15x2 + 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 = 9 1000
26) P is inversely proportional to V.When V = 8, P = 5
a)P = kV
5 = k8
k = 40
P = 40 V
26)b) P = 40 V
P = 402
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)
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