Mathematics (2015) | Study Mode

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Question 31
A

21cm2

B

21cm2

C

15cm2

D

17cm2

Explanation

The external radius = 11cm

The internal radius = 10cm

The area of cross section = (2 - 102)

= (11 + 10)(11 - 10)

(21)(1)

= 21cm2


Correct option: B
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Question 32
A

x = 2 or 1

B

x = 3 or -1

C

x = 1 or 0

D

x = 1 or 2

Explanation

x2 - 2x - 3 = 0

-3x + x = - 2x

- 3x \(\times\) x = - 3x2

(x2 - 3x)(x - 3) = 0

(x - 3)(x + 1) = 0

Either (x - 3) = 0 or (x + 1) = 0

x = 3 or - 1


Correct option: B
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Question 33
A

3.13cm2

B

145cm2

C

314cm2

D

214cm2

Explanation

Explanation

V = r2h

V = ?, h = 4cm, r = 5cm

V = 3.14(5)2 (4)

V = 3.14(25)(4)

V = 3.14 \(\times\) 1200

= 314cm2


Correct option: C
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Question 34
A

-Cos x + 2xSin x + C

B

-Cos x + 2

C

x2Cos x + 2xSin x + 2Cos x+ C

D

-x2Cos x + 2xSinx + 2Cos x + C

Explanation

Let u= x2

du = 2xdx

Let v = sinx

-dv = - sin x i.e. v = cos x

- udv = uv - - vdu

- x2 Sin xdx = - x2 Cos x - - (- Cos x)2 \(\times\) dx

x2 Cos x + 2 - x cos x1 dx

= - x2 Cos x + 2 - x Cos x2 dx

2 - u Cos xdx

Let u = x

du = dx

dv = Cos x

-dv = - Cos x

- x2 Sin x1 dx = - x2 Cos x + 2Sin x - 2Cos x + C

- x2 Sin xdx

= - x2 Cos x + 2xSin + 2Cos x + C


Correct option: D
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Question 35
A

\( \frac{2}{15} \)

B

\( \frac{3}{4} \)

C

\( \frac{7}{15} \)

D

\( \frac{1}{15} \)

Explanation

Prob(A) = \( \frac{1}{5} \) , Prob(B) = \( \frac{1}{4} \), Prob (A B) = \( \frac{1}{15} \), Prob (A B) = ?

Note:

I. the probability is either event of A or B or both.

The formula using is prob (A \(\cup\) B) = -prob(A) + prob(A) \(\cup\) prob(A B)

II. But if the probability of both outcomes A and B

The formula using is Prob(A B) \(\cup\) prob(A) + prob(B) + prob (A \(\cup\) B)

In this question, A or B, Prob (A \(\cup\) B): A and B, Prob (A \(\cup\) B)

prob (A \(\cup\) B) = prob(A) + prob(B) \(\cup\) Prob (A B) is used.

prob (A \(\cup\) B) = \( \frac{1}{15} \) + \( \frac{1}{3} \) + \( \frac{1}{15} \)

= (3 + 5 + 1) 15

= \( \frac{7}{15} \)


Correct option: C
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Question 36
A

1/T

B

2T

C

5/T

D

T/5

Explanation

4-(390625T - 8)
[(390625T - 8)]

[((390625) \(\times\) T - 8)]

(- 390625 \(\times\) T - 4 )

(625 \(\times\) T -)

(54 \(\times\) T -4)

= (54) \(\times\) (T - 4 )

= 5 \(\times\) T - 1

= 5 \(\times\) 1/T

= 5/T


Correct option: C
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Question 37
A
x6 = 123.346
B
x6 = 424.56
C
x6 = 122.436
D
x6 = 124.456
Explanation
(159.75)10 = (y)6

\( \begin{array}{c|c}
6 & 159 \\
\hline
6 & 26 \text{ rem 3} \\
6 & 4 \text{ rem 2} \\
& 0 \text{ rem 4} \\
\end{array}\uparrow \)

15910 = 4236

Then Convert 0.75 to base 6

0.75 x 6 =4.5 i.e 4.5 - 3.00 = 1.5
0.5 x 6 = 3.00 423 + 1.5 =424.5

159.75 = (424.5)6

(159)10 = (424.5)6

Correct option: B
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Question 38
A

15%

B

25%

C

35%

D

10%

Explanation

Percentage Loss = (actual loss ) (Cost price) \(\times\) 100

Actual loss = Cost Price - Selling Price (sold price)

= N800 - N520 = N280

Percentage loss = (280 800) \(\times\) 100 = 35%

His loss percent = 35%


Correct option: C
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Question 39
A

\( 3 \frac{5}{6}\)

B

\( 4 \frac{5}{6}\)

C

\( 2 \frac{1}{6}\)

D

\( \frac{1}{3} \)

Explanation

6 - 2 + 1

73/12 - 11/4 + 3/2

[(73 - 33 + 18) (12)]

58/12

29/6

\( 4\frac{5}{6}\)


Correct option: B
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Question 40
A
3m
B
2.4m
C
3.2m
D
5.1m
Explanation

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


Correct option: D

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