1

Evaluate (0.13)\(^3\)correct to three significant figures

A

0.00219

B

0.00220

C

0.00300

D

0.00390

CORRECT OPTION:
b

(0.13)\(^3\) = 0.13 x 0.13 x 0.13 = 0.002197

= 0.00220 (3 s.f)

= 0.00220 (3 s.f)

2

Simplify: 11011\(_2\) - 1101\(_2\)

A

101000\(_2\)

B

1100\(_2\)

C

1110\(_2\)

D

1011\(_2\)

CORRECT OPTION:
c

11011\(_2\) - 1101\(_2\) = 1110\(_2\)

3

Simplify \(\frac{25 \frac{2}{3} \div 25 \frac{1}{6}}{( \frac{1}{5})^{-\frac{7}{6}} \times ( \frac{1}{5})^{\frac{1}{6}}}\)

A

25

B

\(\frac{1}{5}\)

C

1

D

\(\frac{1}{25}\)

CORRECT OPTION:
c

\(\frac{25 \frac{2}{3} \div 25 \frac{1}{6}}{( \frac{1}{5})^{-\frac{7}{6}} \times ( \frac{1}{5})^{\frac{1}{6}}}\) = \(\frac{25^{4 - \frac{1}{6}}}{(\frac{1}{5})^{-7 + \frac{1}{6}}}\)

= \(\frac{25^{\frac{1}{2}}}{(\frac{1}{5})^{-1}}\)

= \(\frac{(5^2)^{\frac{1}{2}}}{(5^{-1})^{-1}}\)

= \(\frac{5}{5}\)

= 1

= \(\frac{25^{\frac{1}{2}}}{(\frac{1}{5})^{-1}}\)

= \(\frac{(5^2)^{\frac{1}{2}}}{(5^{-1})^{-1}}\)

= \(\frac{5}{5}\)

= 1

4

Simplify \(\frac{x - 4}{4} - \frac{x - 3}{6}\)

A

\(\frac{x - 18}{12}\)

B

\(\frac{x - 6}{12}\)

C

\(\frac{x - 18}{24}\)

D

\(\frac{x - 6}{24}\)

CORRECT OPTION:
b

\(\frac{x - 4}{4} - \frac{x - 3}{6}\) = \(\frac{3(x - 4) - 2(x - 3)}{12}\)

= \(\frac{3x -12 - 2x + 6}{12}\)

= \(\frac{3x - 2x - 12 + 6}{12}\)

= \(\frac{x - 6}{12}\)

= \(\frac{3x -12 - 2x + 6}{12}\)

= \(\frac{3x - 2x - 12 + 6}{12}\)

= \(\frac{x - 6}{12}\)

5

Given that y = 1 - \(\frac{2x}{4x - 3}\), find the value of x for which y is undefined

A

3

B

\(\frac{3}{4}\)

C

\(\frac{-3}{4}\)

D

-3

CORRECT OPTION:
b

for undefined expression, the denomination is zero 4x - 3 = 0

4x = 3; x = \(\frac{3}{4}\)

4x = 3; x = \(\frac{3}{4}\)

6

P is a point on the same plane with a fixed point A. If P moves such that it is always equidistant from A, the locus of P is

A

a straight line joining A and P

B

the perpendicular bisector of AP

C

a circle with centre A

D

the triangle with centre P

CORRECT OPTION:
c

7

A fair coin is tossed three times. Find the probability of getting two heads and one tail.

A

\(\frac{1}{2}\)

B

\(\frac{3}{8}\)

C

\(\frac{1}{4}\)

D

\(\frac{1}{8}\)

CORRECT OPTION:
b

Pr(head) = \(\frac{1}{2}\), Pr(tail) = \(\frac{1}{2}\):Pr(2 heads)

= \(\frac{1}{2}\) x \(\frac{1}{2}\) = \(\frac{1}{4}\)

Pr(2 heads and tail) 3 times

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

= \(\frac{3}{8}\)

= \(\frac{1}{2}\) x \(\frac{1}{2}\) = \(\frac{1}{4}\)

Pr(2 heads and tail) 3 times

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

= \(\frac{3}{8}\)

8

If 30% of y is equal to x, what in terms of x, is 30% of 3y?

A

\(\frac{x}{9}\)

B

\(\frac{x}{3}\)

C

x

D

3x

CORRECT OPTION:
d

If 30% of y = x, then 30% of 3y = 3x

9

A baker used 40% of a 50kg bag of flour. If \(\frac{1}{8}\) of the amount used was for the cake, how many kilogram of flour was used for the cake?

A

2\(\frac{1}{2}\)

B

6\(\frac{1}{2}\)

C

15\(\frac{3}{8}\)

D

17\(\frac{1}{2}\)

CORRECT OPTION:
a

\(\frac{40}{100} \times 50\)kg = 20kg

\(\frac{1}{8}\) of 20kg for cake; \(\frac{1}{8}\) x \(\frac{20}{1}\)

= 2\(\frac{1}{2}\)kg

\(\frac{1}{8}\) of 20kg for cake; \(\frac{1}{8}\) x \(\frac{20}{1}\)

= 2\(\frac{1}{2}\)kg

10

If tan y = 0.404, where y is acute, find cos 2y

A

0.035

B

0.719

C

0.808

D

0.927

CORRECT OPTION:
b

tan y = 0.404; y = tan^{-1} 0.0404(tables);y = 22^{o}

cos 2y = cos 2(22^{o}); cos 44^{o}

= 0.719

cos 2y = cos 2(22

= 0.719

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