# Mathematics (2015) | Study Mode

Question 21
A

(x + 3)2

B

(x + 5)(x -3)

C

(x -5)2

D

(x -5)(x + 3)

##### Explanation

x2 - 2x - 15

(x2 - 5x) + (3x - 15)

x(x - 5)+ 3(x - 5)

(x - 5)(x + 3)

Question 22
A

2,

B

, 2

C

1,

D

0, 2

Question 23
A
N48.75K
B
N50.10K
C
N75.50K
D
N15.75K
##### Explanation
I =[ PRT 100]

[(325 $$\times$$ 5 $$\times$$ 3) (100)]

N(195 4)

N48.75K

Question 24
A
0.81
B
0.081
C
0.0081
D
8.0001
##### Explanation
(0.09)2 = 0.09 $$\times$$ 0.09

= 0.0081

= 0.008100 to 4 significant figures

Please, start counting first from the non-zero digits i.e. 8

Question 25
A
$$\frac{2}{(x + 1)^2}$$
B
$$\frac{2}{(x + 1)(x + 2}$$
C
$$\frac{2}{(x + 1)(x + 2}$$
D
$$\frac{2}{(x + 1)(x + 3}$$
##### Explanation
$$[1 (x^2 + 3x + 2)] + [1 (x^2 + 5x + 6)]$$

= $$1 (x^2 + 3x + 2) + [1 (x^2 +5x + 6)]$$

= $$[1 ((x^2 + x) + (2x + 2) )] + [1 ((x^2 + 3x) + (2x + 6) )]$$

= [1 (x(x + 2) + 2(x +1))] + [1 (x(x + 3) +2(x + 3) )]

= [1 (x + 1)(x + 2)] + [1 ((x + 3) + (x + 2))]

=((x + 3) + (x + 1)) (x + 1)(x + 2)(x + 3)

Using the L.C.M

=((x + x + 3 + 1)) (x + 1)(x + 2)(x + 3)

=(2x+4)/(x+1)(x+2)(x+3) =2(x+2)/(x+1)(x+2)(x+3)

= $$\frac{2 }{(x + 1)(x + 3)}$$

Question 26
A

$$\frac{2}{15}$$

B

$$\frac{3}{24}$$

C

$$\frac{3}{21}$$

D

$$\frac{3}{28}$$

##### Explanation

One bag with 3 blue and 5 red

Pr (H) = 3/8Pr (r) 5/8

Another bag with 2 blue and 4 red (note one ball is drawn from each bag)

i.e. prob.=8 - 1 = 7

prob. (2 ball both are blue=pr (1st blue and 2nd blue)

prob. 2 balls both blue = 3/8 $$\times$$ 2/7

= $$\frac{3}{28}$$

Question 27
A

{}

B

{?, 1, 2}

C

{3, 4, ?}

D

{1, 3, ?}

A B = {3, 4, ?}

Question 28
A

5

B

3

C

6

D

1

##### Explanation

132x = 708

$$1 \times x^2 + 3 \times x^1 + 2 \times x^0$$

$$7 \times 8^1 + 0 \times 8^0$$

$$x^2 + 3x + 2 - 56 = 0$$

$$x^2 + 3x - 54 = 0$$

x(x + 9)-6(x + 9) = 0

(x + 9)(x - 6) = 0

Either (x + 9) = 0 or (x - 6) = 0

x = - 9 or +6

The positive values for x = 6

The base number for 132x = 1326

Question 29
A

N410,000

B

N365, 217

C

N157, 250

D

N257,000

##### Explanation

Cost Price:

Selling price = 100 : (100 + 15)

= 100 : 115

Cost Price

= 100 115 of selling price (i.e N420,000)

= 100 15 $$\times$$ N420,000

= N365,217.4

Cost Price = N365, 217

Question 30
A

$$\frac{3}{2}$$

B

$$\frac{2}{3}$$

C

$$\frac{1}{3}$$

D

$$-\frac{3}{2}$$

##### Explanation

$$[ 1 64^{(x + 2)}]= [4^{(x - 3)} 16^x ]$$

$$64^{-(x + 2)} = [4^{(x - 3)}] [16^x]$$

breakdown 4,16,64 into a small index no

$$2^{-6(x + 2)} = 2^{2(x - 3)} 2^{4(x)}$$

$$2^{-6x- 12} = 2^{2x - 4x - 6}$$

$$2^{-6x -12} = 2^{-2x - 6}$$

- 6x - 12 = - 2x - 6

Collect the like term

-6x + 2x = -6 + 12

-4x =6

x = $$\frac{6}{4}$$

x = $$\frac{-3}{2}$$

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