# 2011 - WAEC Mathematics Past Questions and Answers - page 1

1

If N112.00 exchanges for D14.95, calculate the value of D1.00 in naira

A

0.13

B

7.49

C

8.00

D

13.00

**correct option:**b

D14.95 = N112.00

D1.00 = \(\frac{N112}{D14.95} \times\) D1.00

= 7.49

Users' Answers & CommentsD1.00 = \(\frac{N112}{D14.95} \times\) D1.00

= 7.49

2

Solve for x in the equation; \(\frac{3}{5}\)(2x - 1) = \(\frac{1}{4}\)(5x - 3)

A

zero

B

1

C

2

D

3

**correct option:**d

\(\frac{3}{5}\)(2x - 1) = \(\frac{1}{4}\)(5x - 3)

\(\frac{6x}{5} - \frac{3}{5} = \frac{5x}{4} - \frac{3}{4}\)

\(\frac{6x}{5} - \frac{5x}{4} = \frac{3}{5} - \frac{3}{4}\)

\(\frac{24x - 25x}{20} = \frac{12 - 15}{20}\)

\(\frac{-x}{20} = \frac{-3}{20}\)

-20x = -60

x = \(\frac{-60}{-20}\)

x = 3

Users' Answers & Comments\(\frac{6x}{5} - \frac{3}{5} = \frac{5x}{4} - \frac{3}{4}\)

\(\frac{6x}{5} - \frac{5x}{4} = \frac{3}{5} - \frac{3}{4}\)

\(\frac{24x - 25x}{20} = \frac{12 - 15}{20}\)

\(\frac{-x}{20} = \frac{-3}{20}\)

-20x = -60

x = \(\frac{-60}{-20}\)

x = 3

3

Given that cos x

^{o}= \(\frac{1}{r}\), express tan x^{}in terms of rA

\(\frac{1}{\sqrt{r}}\)

B

\(\sqrt{r}\)

C

\(\sqrt{r^2 + 1}\)

D

\(\sqrt{r^2 - 1}\)

**correct option:**d

cos x

By Pythagoras r

x = \(\sqrt{r^2 - 1}\)

tan x

= \(\sqrt{r^2 - 1}\)

Users' Answers & Comments^{o}= \(\frac{1}{r}\); \(\sqrt{r^2 - 1}\)By Pythagoras r

^{2}= 1^{2}+ x^{2}- 1x = \(\sqrt{r^2 - 1}\)

tan x

^{o}= \(\sqrt{r^2 - 1}\)= \(\sqrt{r^2 - 1}\)

4

Solve the equation; 3x - 2y = 7, x + 2y = -3

A

x = 1, y = -2

B

x = 1, y = 3

C

x = -2, y = -1

D

x = 4, y = -3

**correct option:**a

3x - 2y = 7; Solve by elimination method

x + 2y = -3

3x - 2y = 7.....(i)

-3x + 6y = -9.....(ii)

-8y = 16

y = \(\frac{16}{-8} = -2\)

Put y = -2 into equation (i); 3x - 2y = 7

3x - 2(-2) = 7

3x + 4 = 7

3x = 7 - 4

3x = 3

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

Users' Answers & Commentsx + 2y = -3

3x - 2y = 7.....(i)

-3x + 6y = -9.....(ii)

-8y = 16

y = \(\frac{16}{-8} = -2\)

Put y = -2 into equation (i); 3x - 2y = 7

3x - 2(-2) = 7

3x + 4 = 7

3x = 7 - 4

3x = 3

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

5

If a number is chosen at random from the set {x: 4 \(\leq x \leq 45\)}. Find the probability that it is a multiple of 3 or a multiple of 4

A

\(\frac{1}{12}\)

B

\(\frac{5}{12}\)

C

\(\frac{7}{2}\)

D

\(\frac{11}{12}\)

**correct option:**c

set = 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15

multiple of 3 = 6, 9, 12, 15

multiple of 4 = 4, 8, 12

Prob(multiple of 3 or 4) = Prob(multiple of 3) + pro(multiple of 4)

= \(\frac{4}{12} + \frac{3}{12} = \frac{7}{2}\)

Users' Answers & Commentsmultiple of 3 = 6, 9, 12, 15

multiple of 4 = 4, 8, 12

Prob(multiple of 3 or 4) = Prob(multiple of 3) + pro(multiple of 4)

= \(\frac{4}{12} + \frac{3}{12} = \frac{7}{2}\)

6

One of the factors of (mn - nq - n2 + mq) is (m - n). The other factor is

A

(n - q)

B

(q - n)

C

(n + q)

D

(q - m)

**correct option:**a

mn - nq - n

mn - n

(mn - n

n(m - n) - q(n - m)

= n - q

Users' Answers & Comments^{2}+ mqmn - n

^{2}- nq + mq(mn - n

^{}) - (nq - mq)n(m - n) - q(n - m)

= n - q

7

A cylindrical container has a base radius of 14cm and height 18cm. How many litres of liquid can it hold? correct to the nearest litre [Take \(\pi = \frac{22}{7}\)]

A

11

B

14

C

16

D

18

**correct option:**a

Volume of cylinder = \(\pi r^2 h\)

= \(\frac{22}{7} \times 14^2\) x 14 x 18 = 22 x 28 x 18

= 11088cm

1000cm

= 11.088

= 11

Users' Answers & Comments= \(\frac{22}{7} \times 14^2\) x 14 x 18 = 22 x 28 x 18

= 11088cm

^{3}1000cm

^{3}= \(\frac{1}{1000}\) x 11088cm^{3}= 11.088

= 11

8

A regular polygon of n sides has each exterior angle to 45

^{o}. Find the value of nA

6

B

8

C

12

D

15

**correct option:**b

Each interior angle = \(\frac{360^o}{n}\)

45

45

n = \(\frac{360^o}{45}\)

= 8

Users' Answers & Comments45

^{o}= \(\frac{360^o}{n}\)45

^{o}n = 360^{o}n = \(\frac{360^o}{45}\)

= 8

9

Esther was facing S 20

^{o}W. She turned 90^{o}in the clock wise direction. What direction is she facing?A

N 70

^{o}WB

S 70

^{o}WC

N 20

^{o}WD

S 20

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

10

The cross section section of a uniform prism is a right-angled triangle with sides 3cm. 4cm and 5cm. If its length is 10cm. Calculate the total surface area

A

142cm

^{2}B

132cm

^{2}C

122cm

^{2}D

112cm

^{2}**correct option:**b

A prism has 3 rectangular faces and 2 triangular faces and 2 rectangular faces = 10(3 + 4 + 5) = 120

Area of triangular faces = \(\sqrt{s(s - a) (s - b) (s - c)}\)

where s = \(\frac{a + b + c}{2}\)

= \(\frac{3 + 4 + 5}{2}\)

= \(\frac{12}{2}\)

= 6

Area of \(\bigtriangleup\) = \(\sqrt{6(6 - 30(6 - 4)(6 - 5)}\)

= \(\sqrt{6 \times 3 \times 2 \times 1}\) = 6

Area of triangle faces = 2 x 6 = 12cm

Total surface area = Area of rectangular face + Area of \(\bigtriangleup\) = 120 + 12

= 132cm

Users' Answers & CommentsArea of triangular faces = \(\sqrt{s(s - a) (s - b) (s - c)}\)

where s = \(\frac{a + b + c}{2}\)

= \(\frac{3 + 4 + 5}{2}\)

= \(\frac{12}{2}\)

= 6

Area of \(\bigtriangleup\) = \(\sqrt{6(6 - 30(6 - 4)(6 - 5)}\)

= \(\sqrt{6 \times 3 \times 2 \times 1}\) = 6

Area of triangle faces = 2 x 6 = 12cm

^{2}Total surface area = Area of rectangular face + Area of \(\bigtriangleup\) = 120 + 12

= 132cm

^{2}