1

Find the root of the equation 2x\(^2\) - 3x - 2 = 0

A

x = -2 or 1/2

B

x = -2 or1

C

x = -2 or 2

D

x = -1 or 2

CORRECT OPTION:
e

2x\(^2\) - 3x - 2 = 0

2x\(^2\) - 4x + x - 2 = 0

2x(x - 2) + 1(x - 2) = 0

(2x + 1)(x - 2) = 0

x = \(\frac{-1}{2}\) or x = 2

2

What value of k makes the given expression a perfect square ? m\(^2\) - 8m + k = 0

A

2

B

4

C

8

D

16

CORRECT OPTION:
d

Take half the coefficient of m and square it

=> (-8/2)2 = k = 16

3

If log\(_{10}\) q = 2.7078, what is q?

A

5102

B

849.9

C

510.2

D

84.99

CORRECT OPTION:
c

q = 10\(^{2.7078}\)

Antilog of 2.7078 = 510.2

4

Cos x is negative and sin x is negative.Which of the following is true of x?

A

0^{o} < x < 90^{o}

B

90^{o} < x <180^{o}

C

180^{o} < x < 270^{o}

D

270^{o} < x <360^{o}

CORRECT OPTION:
c

In the 3rd quadrant, only the tan of angles are positive.

The 3rd quadrant = 180° < x < 270°

5

Simplify 0.63954 ÷ 0.003 giving your answer correct to two significant figures

A

213.18

B

213.00

C

213

D

210

CORRECT OPTION:
d

= \(\frac{0.63954}{0.003}\)

moving the decimal places, we have

= \(\frac{639.54}{3}\)

= 213.18

\(\approxeq\) 210 (to 2 s.f.)

6

If log\(_{10}\) a = 4; what is a?

A

0.4

B

40

C

400

D

1000

CORRECT OPTION:
e

log\(_{10}\) a = 4

a = 10\(^4\)

= 10000

7

A student measured the length of a room and obtained the measurement of 3.99m. If the percentage error of is measurement was 5% and his own measurement was smaller than the length , what is the length of the room?

A

3.78m

B

3.80m

C

4.18m

D

4.20m

CORRECT OPTION:
d

Let the actual length of the room = y m

\(\therefore \frac{y - 3.99}{y} \times 100% = 5%\)

\(100(y - 3.99) = 5y \implies 100y - 399 = 5y\)

\(100y - 5y = 399 \implies y = \frac{399}{95}\)

y = 4.2 m

8

When an aeroplane is 800m above the ground, its angle of elevation from a point P on the ground is 30o. How far is the plane from P by line of sight?

A

400m

B

800m

C

1500m

D

1600m

CORRECT OPTION:
d

From the diagram, \(\sin 30 = \frac{800}{x}\)

\(x = \frac{800}{\sin 30} \)

= \(\frac{800}{0.5} \)

= 1600 m

9

Convert 35 to a number in base two

A

1011_{two}

B

10011_{two}

C

100011_{two}

D

110010_{two}

CORRECT OPTION:
c

10

The nth term of a sequence is represented by 3 x 2^{(2-n)}. Write down the first three terms of the sequence

A

B

6, 3, ^{3}/_{2}

C

D

CORRECT OPTION:
b

When n = 1, n = 2, n = 3

3 x 2^{2 - 1} = 6

3 x 2^{2 - 2} = 3

3 x 2^{2 - 3} = ^{3}/_{2}

3 x 2

3 x 2

3 x 2

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