November 2010 Paper 4
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Transcript of November 2010 Paper 4
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November 2010Paper 4
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1)a) 5 x 8 ÷ 2 = 20cm2
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2)
P (Pink) = 0.12
Colour Red Blue PinkProbability
0.58 0.30
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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 ¾ 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
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4)a)
3 x 100 = 300g
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4)b)
4 x 6 = 24 people
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5)a)
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5)b)
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6)a) 7x + 2y – x + y = 6x + 3y
b) 2x + 3 = 102x = 7 x = 3.5
c)i) c5 x c6 = c11
c)ii) e12 ÷ e4 = e8
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7) 8 x 100 = 40% 20
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8)
a) Modal class is 10-19b) Median is 30th person so lies in
the class 20-29
19
31
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8)
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9) 2.42927(0474)
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10)a) −2, −1, 0, 1, 2
b) 2x < 10 3
2x < 30
x < 15
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11) A and 3B and 2C and 4D and 1
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12) T = 7x + 5y
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13) Speed = distance time
Speed = 7120 8
= 890 km/h
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14)a)
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14)b)
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15)a) She only asks the best students
or The sample is too small
or The sample is biased
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15)b) All the choices are positive
There is no box for someone who doesn’t like maths
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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)
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16) a) (0, 3, 2)
b) (5, 3, 0)
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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)
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17) a) 8.25 x 107
b) 1.456 x 10-15
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18) 19.5 litres = 19500 millilitres (1 mark)
19500 ÷ 210 = 92.85714 (1 mark)
Therefore a maximum of 92 full cups can be poured (1 mark)
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19)a)
Age (A years)
Cumulative Frequency
20 < A < 30 2620 < A < 40 6120 < A < 50 8220 < A < 60 9420 < A < 70 100
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19)b)
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19)c)2 marks for 36-38
or for correct reading
from your graph if reading
lines are drawn on
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19)d)2 marks for 9-11
or for correct reading
from your graph if reading
lines are drawn on
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20)a)
56 = 2 x 2 x 2 x 7 = 23 x 7
56
28 2
4 7
2 2
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20)b) 14
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21)
cos 37 = AB (1 mark)
8
AB = cos 37 x 8 (1 mark)
AB = 6.389 (1 mark)
hyp
adj
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22)a)
x -2 -1 0 1 2 3
y -15 -8 -7 -6 1 20
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22)b)
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23)
1 mark for 256° or 52 seen in working or on diagram
1 mark for x = 104°
256°52°
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22)
b) OB2 = OA2 + AB2
OB2 = 82 + 62
OB2 = 100OB = 10
BC = OB – 6 = 4cm
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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
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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
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25)a) (2x + 4y)(4x – 5y)
8x2 + 16xy – 10xy – 20y2
= 8x2 + 6xy – 20y2
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25)b) (x + 10)5
(x + 10)4
= x + 10
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25)c) x2 – 25 x2 + 7x + 10
= (x – 5)(x + 5) (x +2)(x + 5)
= x – 5x + 2
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25)d) x2 + 6x − 2 = (x + p)2 + q
= (x + 3)2
(x + 3)2 = x2 + 6x + 9
– 11
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26)
W
B
W
B
W
B
7/11
4/11
6/10
4/10
7/10
3/10
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)
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26)b) P = 40 V
P = 402
P = 20
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27)a)
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27)b)
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28)a)
Area = ½ x 10.5 x 8.3 x sin 62
= 38.474... cm2
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28)b)
QR2 = 10.52 + 8.32 – 2x10.5x8.3xcos62
QR2 = 97.311111
QR = 9.8646... cm