# 2013 - WAEC Mathematics Past Questions and Answers - page 2

11

If x = 64 and y = 27, evaluate: \(\frac{x^{\frac{1}{2}} - y^{\frac{1}{3}}}{y - x^{\frac{2}{3}}}\)

A

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

B

1

C

\(\frac{5}{11}\)

D

\(\frac{11}{43}\)

**correct option:**c

\(\frac{x^{\frac{1}{2}} - y^{\frac{1}{3}}}{y - x^{\frac{2}{3}}}\)

substitute x = 64 and y = 27

\(\frac{64^{\frac{1}{2}} - 27^{\frac{1}{3}}}{27 - 64^{\frac{2}{3}}} = \frac{\sqrt{64} - 3\sqrt{27}}{27 - (3\sqrt{64})^2}\)

= \(\frac{8 - 3}{27 - 16}\)

= \(\frac{5}{11}\)

Users' Answers & Commentssubstitute x = 64 and y = 27

\(\frac{64^{\frac{1}{2}} - 27^{\frac{1}{3}}}{27 - 64^{\frac{2}{3}}} = \frac{\sqrt{64} - 3\sqrt{27}}{27 - (3\sqrt{64})^2}\)

= \(\frac{8 - 3}{27 - 16}\)

= \(\frac{5}{11}\)

12

If \(\frac{1}{2}\)x + 2y = 3 and \(\frac{3}{2}\)x and \(\frac{3}{2}\)x - 2y = 1, find (x + y)

A

3

B

2

C

1

D

5

**correct option:**a

\(\frac{1}{2}\)x + 2y = 3......(i)(multiply by 2)

\(\frac{3}{2}\)x - 2y = 1......(ii)(multiply by 2)

x + 4y = 6......(iii)

3x - 4y = 2.....(iv) add (iii) and (iv)

4x = 8, x = \(\frac{8}{4}\) = 2

substitute x = 2 into equation (iii)

x + 4y = 6

2 + 4y = 6

4y = 6 - 2

4y = 4

y = \(\frac{4}{4}\)

= 1(x + y)

2 + 1 = 3

Users' Answers & Comments\(\frac{3}{2}\)x - 2y = 1......(ii)(multiply by 2)

x + 4y = 6......(iii)

3x - 4y = 2.....(iv) add (iii) and (iv)

4x = 8, x = \(\frac{8}{4}\) = 2

substitute x = 2 into equation (iii)

x + 4y = 6

2 + 4y = 6

4y = 6 - 2

4y = 4

y = \(\frac{4}{4}\)

= 1(x + y)

2 + 1 = 3

13

Given that p

^{\(\frac{1}{3}\)}= \(\frac{3\sqrt{q}}{r}\), make q the subject of the equationA

q = p\(\sqrt{r}\)

B

q = p

^{3}rC

q = pr

^{3}D

q = pr

^{\(\frac{1}{3}\)}**correct option:**d

p

3\(\sqrt{q}\) = r x 3\(\frac{\sqrt{q}}{r}\)(cross multiply)

3\(\sqrt{q}\) = r x 3\(\sqrt{p}\) cube root both side

q = 3\(\sqrt{r}\) x p

q = r

Users' Answers & Comments^{\(\frac{1}{3}\)}= \(\frac{3\sqrt{q}}{r}\)(cross multiply)3\(\sqrt{q}\) = r x 3\(\frac{\sqrt{q}}{r}\)(cross multiply)

3\(\sqrt{q}\) = r x 3\(\sqrt{p}\) cube root both side

q = 3\(\sqrt{r}\) x p

q = r

^{\(\frac{1}{3}\)}p = pr^{\(\frac{1}{3}\)}14

A chord is 2cm from the centre of a circle. If the radius of the circle is 5cm, find the length of the chord

A

2\(\sqrt{21}\)cm

B

\(\sqrt{42}\)cm

C

2\(\sqrt{19}\)cm

D

\(\sqrt{21}\)cm

**correct option:**a

From \(\bigtriangleup\) OMQ find /MQ/ by Pythagoras OQ

5

25 = 4 + MQ

25 - 4 = MQ

21 - MQ

MQ

MQ

Length of chord = 2 x \(\sqrt{21}\) = 2\(\sqrt{21}\)cm

Users' Answers & Comments^{2}= OM^{2}+ MQ^{2}5

^{2}= 2^{2}+ MQ^{2}25 = 4 + MQ

^{2}25 - 4 = MQ

^{2}21 - MQ

^{2}MQ

^{2}= 21MQ

^{2}= \(\sqrt{21}\)Length of chord = 2 x \(\sqrt{21}\) = 2\(\sqrt{21}\)cm

15

A cube and cuboid have the same base area. The volume of the cube is 64cm

^{3}while that of the cuboid is 80cm^{3}. Find the height of the cuboidA

1cm

B

3cm

C

5cm

D

6cm

**correct option:**a

16

If sin x = \(\frac{5}{13}\) and 0

^{o}\(\leq\) x \(\leq\) 90^{o}, find the value of (cos x - tan x)A

\(\frac{7}{13}\)

B

\(\frac{12}{13}\)

C

\(\frac{79}{156}\)

D

\(\frac{209}{156}\)

**correct option:**c

Sin x = \(\frac{5}{13}\)

0

AC

13

169 - 25 + BC

169 - 25 = BC

144 = BC

Cos x = \(\frac{Adj}{Hyp}\) = \(\frac{12}{13}\)

BC = \(\sqrt{144}\)

BC = 12

tan x = \(\frac{opp}{adj} = \frac{5}{12}\)

BC = 12

cos x - tan x = \(\frac{12}{13} - \frac{5}{12}\)

\(\frac{144 - 65}{156} = \frac{79}{156}\)

Users' Answers & Comments0

^{o}\(\leq\) x \(\leq\) 90^{o}, (cos x - tan x)AC

^{2}= AB^{2}+ BC^{2}13

^{2}= 5^{2}+ BC^{2}169 - 25 + BC

^{2}169 - 25 = BC

^{2}144 = BC

^{2}Cos x = \(\frac{Adj}{Hyp}\) = \(\frac{12}{13}\)

BC = \(\sqrt{144}\)

BC = 12

tan x = \(\frac{opp}{adj} = \frac{5}{12}\)

BC = 12

cos x - tan x = \(\frac{12}{13} - \frac{5}{12}\)

\(\frac{144 - 65}{156} = \frac{79}{156}\)

17

An object is 6m away from the base of a mast. The angle of depression of the object from the top pf the mast is 50

^{o}, Find, correct to 2 decimal places, the height of the mastA

8.60m

B

7.51m

C

7.15m

D

1.19m

**correct option:**c

Tan 50

h = 6 tan 50

= 6 x 1.1917

= 7.1505

= 7.15

Users' Answers & Comments^{o}= \(\frac{h}{6}\)h = 6 tan 50

= 6 x 1.1917

= 7.1505

= 7.15

18

The bearing of Y from X is 060

^{o}and the bearing of Z from Y = 060^{o}. Find the bearing of X from ZA

300

^{o}B

240

^{o}C

180

^{o}D

120

^{o}**correct option:**b

19

Which of the following is not a probability of Mary scoring 85% in a mathematics test?

A

0.15

B

0.57

C

0.94

D

1.01

**correct option:**d

The probability not scoring 85% is = 1 - pro(scoring 85%)

= 1 - \(\frac{85}{100}\) = 1 - 0.85

= 0.15

not scoring would be less than 1

Users' Answers & Comments= 1 - \(\frac{85}{100}\) = 1 - 0.85

= 0.15

not scoring would be less than 1

20

If 2 log x (3\(\frac{3}{8}\)) = 6, find the value of x

A

\(\frac{3}{2}\)

B

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

C

\(\frac{2}{3}\)

D

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

**correct option:**a

2 log x (3\(\frac{3}{8}\)) = 6(divide both sides by 2)

\(\frac{2 log_x(3 \frac{3}{8})}{2} = \frac{6}{2}\)

\(\log_x \frac{27}{8} = 3\)

\(\frac{27}{8} = x^3\)

\(x^3 = \frac{27}{8}\)

x = \(\sqrt{\frac{27}{8}}\)

= (\(\frac{27}{8}\))

= \(\frac{(3^3)^{\frac{1}{3}}}{(2^3)^{\frac{1}{3}}}\)

= \(\frac{3}{2}\)

Users' Answers & Comments\(\frac{2 log_x(3 \frac{3}{8})}{2} = \frac{6}{2}\)

\(\log_x \frac{27}{8} = 3\)

\(\frac{27}{8} = x^3\)

\(x^3 = \frac{27}{8}\)

x = \(\sqrt{\frac{27}{8}}\)

= (\(\frac{27}{8}\))

^{\(\frac{1}{3}\)}= \(\frac{(3^3)^{\frac{1}{3}}}{(2^3)^{\frac{1}{3}}}\)

= \(\frac{3}{2}\)