Mathematics (2015) | Study Mode

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Question 41
A

N14,950.50K

B

N25,150.30K

C

N15,000.00K

D

N38,888.90K

Explanation

[Return Investment] as a ratio ;

i.e The Ratio is Return : Investmen

[(Return1 Investment1 ) = (Return2 Investment2)]

R1 = N 25000

R2 =?

I1 = N450,000,

I1 = N 700000

(25000 450000) = (R2 700000)

R2 = [(25000 \(\times\) 700000 ) 450000]

= N38,888.90K

The return on a investment of Y = N38888.90K


Correct option: D
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Question 42
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 43
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 44
A
1.35
B
1.353
C
1.455
D
0.455
Explanation
log717

= [log 17 log7]

= [1.2304 0.8451]

[100.0899 101.9270]

= 1.455(antilog)

Correct option: C
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Question 45
A

2 log5y + 5log5 y2-3

B

log5 y2 + 5log5 x + 3

C

25logy 5 + 3

D

2log5y + 5log5x - log5b - 3

Explanation

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


Correct option: D
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Question 46
A

\( (3x^2 + 8x + 7) (3x + 4)^2 \)

B

\( x^2 + 2x + (1 (x + 1)^2) \)

C

\( 2x^2 + 4x + (1 (2x + 4)^2) \)

D

\( x^2 + 3x + (2 (x + 3)^2) \)

Explanation

dy/dx \( (4x^3 + 3x^2 + 2x + 1) \)

= \( 12x^2 + 6x + 2 \)

= \( 12x^2 + 6 + 2 \)

Divide both sides by 2

\( \frac{12x^2}{2} +\frac{6x}2 +\frac{2}{2} \)

= \( 6x^2 + 3x + 1 \)

dy/dx

= \( 6x^2 + 3x + 1 \)


Correct option: A
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Question 47
A

\( \frac{5x^4}{4} + \frac{7x^3}{3} + 2x + C \)

B

\( \frac{5x}{4} + \frac{7x^3}{3} - x^2 + 5x + C \)

C

\( \frac{5x^3}{3} + \frac{7x^2}{x} - x + C \)

D

\( \frac{2x^2}{3} + \frac{x}{5} - C \)

Explanation

\(- [(x^2 + 4x^2 + 1 ) x^2]dx = - (x^3/x^2)dx + -(1/x^2)dx \)

-\( - xdx + - 4^{-1} or + - (1/x^2)dx\)

= \( x^2/2 - 4x - 1/x^2 + C \)


Correct option: B
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Question 48
A

\(\frac{2x}{(x + 1)(x-3)} \)

B

\(\frac{2}{(x + 1)(x-1)} \)

C

\(\frac{2x}{(x + 1)2}\)

D

2x(x+1)2

Explanation

[1 (x+1)] + [1 (x - 1)]

= ((x - 1) + [(x + 1)) (x+1)(x - 1)]

Using the L.C.M.

= (x - 1 + x + 1) (x + 1)(x - 1)

= (x + 2 - 1 + 1) (x + 1)(x - 1)

= 2x (x + 1)(x - 1) =2x (x + 1)(x - 1)


Correct option: B
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Question 49
A

157cm3

B

155cm3

C

175cm3

D

145cm3

Explanation

V = 1/3r2 h

Volume of a cone (Vc) = 1/3 \(\times\) 3.14 \(\times\) (5)2 \(\times\) 6

= 156.9cm3

157cm3


Correct option: A
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Question 50
A
16
B
8
C
10
D
12
Explanation
Z has 4 elements, power = number of subset = 2p

Z = 2n = 24

= 16

Correct option: A

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