## Mathematics (2015) Study Mode

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1.
In a town of 6250 inhabitants, there were 62 births during 1984. Find the percentage birth rate
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A.
3%
B.
1.00%
C.
2.50%
D.
5.40%
Explanation. Give a better Explanation
Percentage birthrate = 1.0%

2.

Simplify 1¼ ÷ (2 ÷ ¼) of 28

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A.

1 $$\frac{3}{8}$$

B.

2 $$\frac{3}{4}$$

C.

4 $$\frac{3}{8}$$

D.

3 $$\frac{1}{5}$$

Explanation. Give a better Explanation

1¼ ÷ [ 2 ÷ ¼] of 28

Apply BODMAS rules

$$\frac{5}{4}$$ ÷ [ 2 ÷ ¼ $$\times$$ 28 ]

$$\frac{5}{4} ÷ \frac{2}{7}$$

$$\frac{5}{4} \times \frac{7}{2}$$

$$\frac{35}{8}$$

= $$4 \frac{3}{8}$$

A.

(x - 5) 2

B.

(x + 5)(x + 4)

C.

(x + 5)(x + 3)

D.

(x + 3) 2

Explanation. Give a better Explanation

$$x^2 + 9x + 20$$

Find the two numbers whose product is 20 and its sum is 9}

$$5x \times 4x = 20x^2$$

$$5x + 4x = 9x$$

$$(x^2 + 5x) + (4x + 20)$$
$$x(x + 5)+ 4(x + 5) = (x + 5)(x + 4)$$

4.

If three staff of QuizzerWeb Inc. agreed to share their salary arrears in the ration of their ages, which are 18 years, 20 years, 22 years respectively. If the sum of the money collected is N120,000.00K, How much does the second staff received?

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A.

N36,000

B.

N44,000

C.

N40,000

D.

N15,000

5.

X and Y are two sets such that nX = 15, nY = 12 and n{- Y} = 7. Find -{X - Y}

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A.

21

B.

225

C.

15

D.

20

Explanation. Give a better Explanation

n(X - Y) = nx + ny - n(xX - Y)

= 15 + 12 - 7

- n(X - Y) = 20

6.

Find the x and y intercepts of the graph of 3x - z $$\leq$$ 9

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A.

(3, -9)

B.

(-3, 9)

C.

(-3, -9)

D.

(-3, 0)

Explanation. Give a better Explanation

Starting from 3x - z $$\leq$$ 9

x = 0, substitute the value of x (i.e. x = 0) into the equation 3x - z $$\leq$$ 9

3(0) - z $$\leq$$ - 9

z $$\leq$$ - 9

If z = 0

Then, 3x - 0 $$\leq$$ 9

3x $$\leq$$ 9

x $$\leq$$ 3

Intercept of x and z i.e (x,z)

= (3, -9)

7.

Simplify log101.5 + 3 log102 - log100.3

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A.

log104

B.

log1040

C.

log10-40

D.

log104-

Explanation. Give a better Explanation

log101.5 + 3 log102 - log100.3

log101.5 + log1023 - log100.3

[log10(1.5 $$\times$$ 23) ÷ log100.3]

[log10(15/10 $$\times$$ 8 ) ÷ log10( 3/10)]

log10(15/10 $$\times$$ 8 $$\times$$ 10/3 )

log1040

8.

Find the total surface area of a cylinder of base radius 5cm and length 7cm ( π = 3.14)

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A.

17.8cm2

B.

15.8cm2

C.

75.4cm2

D.

54.7cm2

Explanation. Give a better Explanation

The total surface area of a cylinder = 2πrl + 2πr2

= 2πr(l + r)

= 2 $$\times$$ 3.14(7+%=5)

2 $$\times$$ 3.14 $$\times$$ 12

= 75.4cm (1DP)

9.

If x + y = 90 simplify (sinx + siny)2 - 2sinxsiny

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A.

1

B.

$$0$$

C.

2

D.

-1

10.

A man with an annual salary of N2000, has allowances of N600. If Income Tax is 5%. How much tax does he pay each year?

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A.

15

B.

20

C.

30

D.

25

Explanation. Give a better Explanation

His annual salary = N2000

His allowances = N600

So his taxable income = Annual salary - allowance

= N2000 - N600

= N1400

He pay at 5%

Then, his allowance income tax 5/100 $$\times$$ 600 = N30