November 2010 Paper 4. 1)a) 5 x 8 ÷ 2 = 20cm 2 2) P (Pink) = 0.12 ColourRedBluePink...
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Transcript of November 2010 Paper 4. 1)a) 5 x 8 ÷ 2 = 20cm 2 2) P (Pink) = 0.12 ColourRedBluePink...
November 2010Paper 4
1)a) 5 x 8 ÷ 2 = 20cm2
2)
P (Pink) = 0.12
Colour Red Blue PinkProbability
0.58 0.30
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
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 = 102x = 7 x = 3.5
c)i) c5 x c6 = c11
c)ii) e12 ÷ e4 = e8
7) 8 x 100 = 40% 20
8)
a) Modal class is 10-19b) Median is 30th person so lies in
the class 20-29
19
31
8)
9) 2.42927(0474)
10)a) −2, −1, 0, 1, 2
b) 2x < 10 3
2x < 30
x < 15
11) A and 3B and 2C and 4D and 1
12) T = 7x + 5y
13) Speed = distance time
Speed = 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) 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) 8.25 x 107
b) 1.456 x 10-15
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)
19)a)
Age (A years)
Cumulative Frequency
20 < A < 30 2620 < A < 40 6120 < A < 50 8220 < A < 60 9420 < A < 70 100
19)b)
19)c)2 marks for 36-38
or for correct reading
from your graph if reading
lines are drawn on
19)d)2 marks for 9-11
or for correct reading
from your graph if reading
lines are drawn on
20)a)
56 = 2 x 2 x 2 x 7 = 23 x 7
56
28 2
4 7
2 2
20)b) 14
21)
cos 37 = AB (1 mark)
8
AB = cos 37 x 8 (1 mark)
AB = 6.389 (1 mark)
hyp
adj
22)a)
x -2 -1 0 1 2 3
y -15 -8 -7 -6 1 20
22)b)
23)
1 mark for 256° or 52 seen in working or on diagram
1 mark for x = 104°
256°52°
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) 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 – 5x + 2
25)d) x2 + 6x − 2 = (x + p)2 + q
= (x + 3)2
(x + 3)2 = x2 + 6x + 9
– 11
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)
26)b) P = 40 V
P = 402
P = 20
27)a)
27)b)
28)a)
Area = ½ 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