1

Find (101\(_2\))\(^2\), expressing the answer in base 2.

A

10101

B

11001

C

10010

D

11101

CORRECT OPTION:
b

You can convert it to base 10 and square, then re-convert it after the operation.

OR

You can multiply it straight applying the rules of binary multiplication.

2

If three children shares N10.50 among themselves in ratio 6:7:8, how much is the largest share?

A

N3.00

B

N3.50

C

N4.00

D

N4.50

CORRECT OPTION:
c

Ratio = 6 + 7 + 8 = 21

21 = N10.50

1 = 1050K/21 = 50K

6 = 6 x 50K = N3.00

7 = 7 x 50K = N3.50

8 = 8 x 50K = N4.00

the Largest share = N4.00

21 = N10.50

1 = 1050K/21 = 50K

6 = 6 x 50K = N3.00

7 = 7 x 50K = N3.50

8 = 8 x 50K = N4.00

the Largest share = N4.00

3

Express 0.000834 in standard form

A

8.34 x 10^{-4}

B

8.34 x 10^{-3}

C

8.34 x 10^{3}

D

8.34 x 10^{4}

CORRECT OPTION:
a

4

Given that log_{2}a = log_{8}4, find a

A

2^{1/3}

B

4^{2/3}

C

4^{2/3}

D

2^{2/3}

CORRECT OPTION:
d

Log_{2}a = Log_{8}4

Log_{2}a = Log_{8}8^{2/3} → 2/3Log_{8}8 → 2/3 x 1

Log_{2}a = 2/3

Recall; If Log_{a}x = y ∴ ay = x

Log_{2}a = 2/3

2^{2/3} = a

Log

Log

Recall; If Log

Log

2

5

By selling some crates of soft drinks for N600.00, a dealer makes a profit of 50%. How much did the dealer pay for the drinks?

A

N1,200.00

B

N900.00

C

N450.00

D

N400.00

CORRECT OPTION:
d

S.P = N600.00

(100 + 50)% = N600

150% = N600

1% = \(\frac{600}{150}\)

100% = \(\frac{600}{150} \times 100%\)

= N400

6

Find the nth term Un of the A.P., 11, 4, -3,....... .

A

Un=19+7n

B

Un=19-7n

C

Un=18+7n

D

Un= 18-7n

CORRECT OPTION:
d

A.P 11, 4, -3

1st term = 11

A.P = a, a + d, a + 2d ...... a + (n - 1)d

If a = 11

a + d = 4

d = 4 - 11 = -7

nth term = a + (n-1)d

= 11 + (n-1)(-7)

= 11 - 7n + 7

= 18 - 7n

1st term = 11

A.P = a, a + d, a + 2d ...... a + (n - 1)d

If a = 11

a + d = 4

d = 4 - 11 = -7

nth term = a + (n-1)d

= 11 + (n-1)(-7)

= 11 - 7n + 7

= 18 - 7n

7

lf 16/9 , x, 1, y are in Geometric Progression (GP), find the product of x and y.

A

9/16

B

3/4

C

1

D

4/3

CORRECT OPTION:
c

16/9, x, 1, y => a, ar, ar^{2}, ar^{3}

ar^{2} = 1 => 16r^{2}/9 = 1 => 16r^{2}

9 => r^{2} = 9/16 => r = 3/4

ar^{2} = y = ar^{2} x r = 1 x 3/4 = 3/4

x xy = 4/3 x 3/4 = 1

ar

9 => r

ar

x xy = 4/3 x 3/4 = 1

8

If R = [2, 4, 6, 7] and S = [1, 2, 4, 8], then R∪S equal

A

[1,2,4,6,7,8]

B

[1,2,4,7,8]

C

[1,4.7,8]

D

[2.6.7]

CORRECT OPTION:
a

R = {2, 4, 6, 7}; S = {1, 2, 4, 8}

R \(\cup\) S = {1, 2, 4, 6, 7, 8}

9

Find the value(s) of x for which the expression is undefined: \(\frac{6x - 1}{x^2 + 4x - 5}\)

A

+4 or+1

B

-5 or +1

C

-5 or -1

D

+5 or -1

CORRECT OPTION:
b

\(\frac{6x - 1}{x^2 + 4x - 5}\)

The expression is undefined when \(x^2 + 4x - 5 = 0\)

\(x^2 + 5x - x - 5 = 0\)

\(x(x + 5) - 1(x + 5) = 0\)

\((x - 1)(x + 5) = 0\)

The expression is undefined when x = 1 or -5.

10

Which of the following could be the inequality illustrated in the sketch graph above?

A

y≥2x+3

B

y≤-3x+3

C

y < 3x+2

D

y≤x +3

CORRECT OPTION:
b

Gradient of the line = \(\frac{3 - 0}{0 - 1}\)

= -3

y = -3x + b.

Using (1,0), we have

0 = -3(1) + b

0 = -3 + b

b = 3

y = -3x + 3

\(\therefore\) The graph illustrates y \(\leq\) -3x + 3.

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