# Mathematics (2015) | Study Mode

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

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

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

= $$\frac{7}{15}$$

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)

Question 45
A

2 log5y + 5log5 y2-3

B

log5 y2 + 5log5 x + 3

C

25logy 5 + 3

D

2log5y + 5log5x - log5b - 3

##### Explanation

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

= $$6x^2 + 3x + 1$$

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

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

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

= $$x^2/2 - 4x - 1/x^2 + C$$

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)

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

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

Z = 2n = 24

= 16

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