## Mathematics | Study Mode

Question 1
A
B
C
15
D
18
Explanation.

No official Explanation yet!

Question 2
A
m = 0, n = 0
B
m = 1, n = 0
C
m = 0, n = 1
D
m = 1, n = 1
Explanation.

No official Explanation yet!

Question 3
A
N250,000.00
B
N200,000.00
C
N150,000.00
D
N100,000.00
Explanation.
N1.00 = $0.075 NX =$15,000

X = $$\frac{1.00 \times 15000}{0.075}$$

= N200,000.00

Question 4
A
B
$$\frac{1}{2}$$
C
-$$\frac{1}{2}$$
D
-1
Explanation.
$$\frac{27^x \times 3^{1 - x}}{9^{2x}} = 1$$

$$\frac{3^{3x} \times 3^{1 - x}}{3^{2(2 - x)}} = 3^0$$

$$3^{3x} \times 3^{1 - x} \div 3^{4x} = 3^0$$

$$3^{(3x + 1 - x - 4x)} = 3^0$$

$$3^{(1 - 2x)} = 3^0$$

since the bases are equal,

1 - 2x = 0

- 2x = -1

x = $$\frac{1}{2}$$

Question 5
A
37
B
48
C
50
D
63
Explanation.

No official Explanation yet!

Question 6
A
B
C
12
D
24
Explanation.
If logx 64 = 3, then 64 = x3

43 = x3

Since the indices are equal,

x = 4

Hence, x log28 = log28x

= log284

= log2(23)4

= log2212

= 1 log2 = 1(1)

= 12

Question 7
A
4y$$^\frac{1}{3}$$
B
4y$$^-3$$
C
2y$$^\frac{1}{3}$$
D
2y$$^-3$$
Explanation.
If 2n = y,

then, 2$$^{(2 + \frac{n}{3})}$$ = 22 x 2$$^\frac{n}{3}$$

= 4 x (2n)$$^{\frac{1}{3}}$$

But y = 2n, hence

2$$^{(2 + \frac{n}{3})}$$ = 4 x y$$^{\frac{1}{3}}$$

= 4y$$^\frac{1}{3}$$

Question 8
A
(2a - 3b)(4x + 3y)
B
(3a + 4b)(2x - 3y)
C
(3a - 4b)(2x + 3y)
D
(2a + 3b)(4x -3y)
Explanation.
6ax - 12by - 9ay + 8bx

= 6ax - 9ay + 8bx - 12by

= 3a(2x - 3y) + 4b(2x - 3y)

= (3a + 4b)(2x - 3y)

Question 9
A
4x2 - 13x + 12 = 0
B
4x2 - 13x - 12 = 0
C
4x2 + 13x - 12 = 0
D
4x2 + 13x + 12 = 0
Explanation.
Let x = $$\frac{3}{4}$$ or x = -4

i.e. 4x = 3 or x = -4

(4x - 3)(x + 4) = 0

therefore, 4x2 + 13x - 12 = 0

Question 10
A
1$$\frac{5}{16}$$
B
1$$\frac{1}{16}$$
C
$$\frac{5}{16}$$
D
- 1$$\frac{37}{48}$$
Explanation.
If m = 4, n = 9, r = 16,

then $$\frac{m}{n}$$ - 1$$\frac{7}{9}$$ + $$\frac{n}{r}$$

= $$\frac{4}{9}$$ - $$\frac{16}{9}$$ + $$\frac{9}{16}$$

= $$\frac{64 - 258 + 81}{144}$$

= $$\frac{-111}{144}$$

= - 1$$\frac{37}{48}$$

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