GCE Mathematics S1 0983-01
WJEC 2014 Online Exam Review GCE Mathematics S1 0983-01 All Candidates' performance across questions
Question Title 1 2 3 4 5 6 7 8 9
N 3116 3017 3124 3061 3067 3093 3078 3041 2943
Mean 3.7 3.7 5.6 4.6 6.8 5.4 6.8 4.5 6.7
SD 1.9 1.9 2.1 1.8 3.5 2.8 3.8 2.3 4.2
Max Mark 6 5 7 6 11 9 12 7 12
FF 62.4 74.4 80.4 77.4 61.5 60.1 57 64.6 56
Attempt % 99.1 96 99.4 97.4 97.5 98.4 97.9 96.7 93.6
Question
GCE Mathematics S1 0983-01 9 8 7 6 5 4 3 2 1
56 64.6 57 60.1 61.5 77.4 80.4 74.4 62.4 0
10
20
30
40
50
60
Facility Factor %
70
80
90
100
3 5 6 9b
2 3.
A bag contains 9 coloured balls, of which 3 are red, 3 are blue and 3 are yellow. Huw selects 3 of these balls at random, without replacement. Calculate the probability that he selects (a) 1 ball of each colour,
[3]
(b) 2 balls of the same colour and 1 ball of a different colour.
[4]
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(0983-01)
Question number Rhify Cwestiwn
33-7
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2 5.
A zoologist is studying a certain breed of dog. (a) He knows from past experience that the probability of a newly born puppy being female is 0·55. He selects a random sample of 20 newly born puppies. Calculate the probability that the number of females in the sample is (i) exactly 12, (ii) between 8 and 16 (both inclusive).
[8]
(b) The probability of a newly born puppy being yellow is 0·05. Use an approximating distribution to find the probability that less than 5 out of a random sample of 60 newly born puppies are yellow. [3]
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(0983-01)
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3 6.
A purse contains three fair coins and one double-headed coin. A coin is selected at random from the purse and tossed. (a) Find the probability that a head is obtained.
[3]
(b) Given that a head is obtained, (i) determine the probability that the double-headed coin was selected, (ii) find the probability that a head will be obtained if the selected coin is tossed a second time. [6]
END OF PAPER © WJEC CBAC Ltd.
(0983-01)
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The continuous random variable X has cumulative distribution function F given by
F (x) = 0 F (x) = 2x3 – x6 F (x) = 1 (b)
for x < 0, for 0 X x X 1, for x > 1.
(i) Find an expression for f (x), valid for 0 X x X 1, where f denotes the probability density function of X. (ii) Calculate E(X 3).
[6]
END OF PAPER © WJEC CBAC Ltd.
(0983-01)
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Question Title 1 2 3 4 5 6 7 8 9
N 3116 3017 3124 3061 3067 3093 3078 3041 2943
Mean 3.7 3.7 5.6 4.6 6.8 5.4 6.8 4.5 6.7
SD 1.9 1.9 2.1 1.8 3.5 2.8 3.8 2.3 4.2
Max Mark 6 5 7 6 11 9 12 7 12
FF 62.4 74.4 80.4 77.4 61.5 60.1 57 64.6 56
Attempt % 99.1 96 99.4 97.4 97.5 98.4 97.9 96.7 93.6
Question
GCE Mathematics S1 0983-01 9 8 7 6 5 4 3 2 1
56 64.6 57 60.1 61.5 77.4 80.4 74.4 62.4 0
10
20
30
40
50
60
Facility Factor %
70
80
90
100
3 5 6 9b
2 3.
A bag contains 9 coloured balls, of which 3 are red, 3 are blue and 3 are yellow. Huw selects 3 of these balls at random, without replacement. Calculate the probability that he selects (a) 1 ball of each colour,
[3]
(b) 2 balls of the same colour and 1 ball of a different colour.
[4]
© WJEC CBAC Ltd.
(0983-01)
Question number Rhify Cwestiwn
33-7
^r
/
2 5.
A zoologist is studying a certain breed of dog. (a) He knows from past experience that the probability of a newly born puppy being female is 0·55. He selects a random sample of 20 newly born puppies. Calculate the probability that the number of females in the sample is (i) exactly 12, (ii) between 8 and 16 (both inclusive).
[8]
(b) The probability of a newly born puppy being yellow is 0·05. Use an approximating distribution to find the probability that less than 5 out of a random sample of 60 newly born puppies are yellow. [3]
© WJEC CBAC Ltd.
(0983-01)
Leave Blank Gadewch yn wag
- Q- us -
_
?0,Q;<SS
Ao
16-1 • -
0
feoxoos) Z) •
rr-
- >'
S ft.
n x-i? 20 ^A
-. % -i
3 6.
A purse contains three fair coins and one double-headed coin. A coin is selected at random from the purse and tossed. (a) Find the probability that a head is obtained.
[3]
(b) Given that a head is obtained, (i) determine the probability that the double-headed coin was selected, (ii) find the probability that a head will be obtained if the selected coin is tossed a second time. [6]
END OF PAPER © WJEC CBAC Ltd.
(0983-01)
Leave Blank Gadewch yn wag
Question number Rhify Cwestiwn
-L
C
nu-na.
-
fc.iQ
Os.vu
x
^\(^
Xi
3
t
X
3
9.
The continuous random variable X has cumulative distribution function F given by
F (x) = 0 F (x) = 2x3 – x6 F (x) = 1 (b)
for x < 0, for 0 X x X 1, for x > 1.
(i) Find an expression for f (x), valid for 0 X x X 1, where f denotes the probability density function of X. (ii) Calculate E(X 3).
[6]
END OF PAPER © WJEC CBAC Ltd.
(0983-01)
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number Rhify Cwestiwn
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4-: £4^U
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4^
o 9
Z. ca^
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