Mathematics 2014 | Study Mode

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Question 41
A
\(\frac{1}{5}\)
B
\(\frac{1}{2}\)
C
\(\frac{2}{5}\)
D
\(\frac{3}{4}\)
Explanation
Let E demote the event of obtaining at least a 4
Then n(E) = 16 + 10 + 14 = 40

Hence, prob (E) = \(\frac{n(E)}{n(S)}\)

\( = \frac{40}{100}\)

\( = \frac{2}{5}\)

Correct option: C
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Question 42
A
\(\frac{2}{15}\)
B
\(\frac{1}{10}\)
C
\(\frac{1}{3}\)
D
\(\frac{2}{5}\)
Explanation
Sample space S = {10, 11, 12, ... 30}

Let E denote the event of choosing a number divisible by 3

Then E = {12, 15, 18, 21, 24, 27, 30} and n(E) = 7

Prob (E) = \(\frac{n(E)}{n(E)}\)

Prob (E) = \(\frac{7}{21}\)

Prob (E) = \(\frac{1}{3}\)

Correct option: C
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Question 43
A
(P\(\cap\)Q)\(\cup\)(P\(\cap\)R)
B
(P\(\cup\)Q)\(\cap\)(P\(\cap\)R)
C
(P\(\cup\)Q)\(\cup\)(P\(\cup\)R)
D
(P\(\cap\)Q)\(\cup\)(P\(\cup\)R)
Explanation

Explanation not provided, please join discuss, your contributions are welcomed


Correct option: A
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Question 44
A
91o
B
89o
C
37o
D
19o
Explanation
In the diagram above, \(\alpha\) = 54o(alternate angles; KL||MN) < KNM = 2\(\alpha\) (LN is bisector of < KNM) = 108o

35o + < KMN + 108o = 180o(sum of angles of \(\bigtriangleup\))

< KMN + 143o = 180o

< KMN = 180o - 143o

= 37o

Correct option: C
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Question 45
A
135o
B
90o
C
60o
D
45o
Explanation
In the figure above, qo = 30o (vertically opposite angles)

(P + 2q)o + 30o = 180o(angles on a straight line)

p + 2 x 30o + 30o = 180o

p + 60o + 30o = 180o

p + 90o = 180o

p = 180o - 90o

= 90oMaths-explained-image

Correct option: B
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Question 46
A
20\(\sqrt{3}\)cm
B
10\(\sqrt{3}\)cm
C
5\(\sqrt{3}\)cm
D
4\(\sqrt{3}\)cm
Explanation
In the figure above, \(\frac{x}{\sin 60^o} = \frac{10}{\sin 30^o}\) (Sine rule)

x = \(\frac{10 \sin 60^o}{\sin 30^o}\)

= 10 x \(\frac{\sqrt{3}}{2} \times \frac{1}{2}\)

= 10 x \(\frac{\sqrt{3}}{2} \times \frac{2}{1}\)

= 10\(\sqrt{3}\)cmMaths-explained-image

Correct option: B
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Question 47
A
y = x + 5
B
y = -x + 5
C
y = x - 5
D
y = -x - 5
Explanation
(x1, y1) = (0,5)

(x2, y2) = (5, 0)

Using \(\frac{y - y_1}{y_1 - y_1} = \frac{x - x_1}{x_1 - x_1}\)

\(\frac{y - 5}{0 - 5} = \frac{x - 0}{5 - 0}\)

\(\frac{y - 5}{-5} = \frac{x}{5}\)

5(y - 5) = -5x

y - 5 = -x

x + y = 5

y = -x + 5

Correct option: B
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Question 48
A
N42,000
B
N18,000
C
N16,000
D
N12,000
Explanation
Angle of sector subtended by yam

= 360o - (70 + 80 + 50)o

= 360o - 200o

= 160o

But \(\frac{80^o}{360^o}\) x T = 8000

T = \(\frac{8000 \times 360^o}{80^o}\)

= N36,000

Hence the amount spent on yam = \(\frac{160^o}{260} \times N36,000\)

= N16,000

Correct option: C

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