1

If 3loga + 5loga - 6loga = log64, what is a?

A

4

B

6

C

8

D

16

CORRECT OPTION:
c

loga^{3} + loga^{5} - loga^{6}

log(

a^{3} * a^{5}/a^{6}) = loga^{64}

a^{2} = 64 a = 8

a

2

If the second and fourth term of a G.P are 8 and 32 respectively,what is the sum of the first four terms?

A

28

B

40

C

48

D

60

CORRECT OPTION:
d

ar = 8 .....(1)

ar^{3} = 32 .....(2)

divide (2) by (1)

r^{2} = 4 r = 2 ∴ a = 4

S =

a(r^{n} - 1)/r - 1

S =

4(2^{4} - 1)/2 - 1 = 60

3

In the diagram above, TPS is a straight line, PQRS is a parallelogram with base QR and height 8cm. |QR| = 6cm and the area of triangle QST is 52cm2. Find the area of ΔQPT

A

39cm^{2}

B

28cm^{2}

C

24cm^{2}

D

21cm^{2}

CORRECT OPTION:
b

Area of \(\Delta\)QST = 52cm\(^2\); height = 8cm

b=base length; but A = 1/2 b x h

=52=1/2 x b x 8cm = 104 =8b

b=104/8 = 13cm; ST= 13cm; PS = 6cm

TP = 13 - 6 = 7cm;

area of \(\Delta\)QST = 1/2 b x h

= 1/2 x 7 x 8/1 = 28cm\(^2\)

4

In the diagram O is the center of the circle, if ∠QRS = 62o, find the value of ∠SQR.

A

14^{o}

B

28^{o}

C

31^{o}

D

45^{o}

CORRECT OPTION:
b

< QSR = 90° (angle in a semi-circle)

\(\therefore\) < SQR = 180° - (90° + 62°)

= 28°

5

Evaluate, using logarithm tables \(\frac{5.34 \times 67.4}{2.7}\)

A

1.332

B

13.32

C

133.2

D

1332

CORRECT OPTION:
c

No | Log |

5.34 | 0.7275 + |

67.4 | 1.8287 |

2.5562 - | |

2.7 | 0.4314 |

Antilog = 133.2 | 2.1248 |

\(\therefore \frac{5.34 \times 67.4}{2.7} = 133.2\)

6

Factorize 35 - 2b - b^{2}

A

(35-2b)(b-1)

B

(7+b)(5-b)

C

(3+7b)(5-b)

D

(35-b)(3b+7)

CORRECT OPTION:
b

35 - 2b - b ^{2};

35 - 7b + 5b - b^{2}

7(5 - b) + 5(5 - b)

(7 + b)(5 - b)

35 - 7b + 5b - b

7(5 - b) + 5(5 - b)

(7 + b)(5 - b)

7

Evaluate \(\frac{0.009}{0.012}\), leaving your answer in standard form.

A

7.5 x 10^{2}

B

7.5 x 10^{1}

C

7.5 x 10^{-1}

D

7.5 x 10^{-2}

CORRECT OPTION:
c

\(\frac{0.009}{0.012}\)

=\(\frac{0.009}{0.012}\) = \(\frac{9}{12}\) = 0.75

=\(7.5 \times 10^{-1}\)

8

The graph above is that of a quadratic function y = 2x^{2} - x - 6

The roots of the equation are

The roots of the equation are

A

1.5, 2

B

-1.5, 2

C

1, -6

D

1, 6

CORRECT OPTION:
b

The roots are; x = -1.5 and 2

9

Factorize the following expression; 2x^{2} + x - 15

A

(2x+5)(x-3)

B

(2x-5)(x+3)

C

(2x-5)(x-3)

D

(2x-3)(x+5)

CORRECT OPTION:
b

2x ^{2} + x - 15; 2x ^{2} + 6x - 5x - 15

(2x^{2} + 6x) - ( 5x + 15)

2x(x + 3) - 5(x + 3)

(2x - 5)(x + 3)

(2x

2x(x + 3) - 5(x + 3)

(2x - 5)(x + 3)

10

The angle of elevation of X from Y is 30^{o}. If XY = 40m, how high is X above the level of Y?

A

10m

B

20m

C

20√3m

D

40m

CORRECT OPTION:
b

XZ = 40 x sin30^{o}

= 20m

= 20m

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