Mathematics Past Questions | West African Examinations Council (WAEC)

Question 41

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

Options

A) 0.15

B) 0.57

C) 0.94

D) 1.01

The correct answer is D.

Explanation:

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

Question 42

If 2 log_x (3$\frac{3}{8}$

) = 6, find the value of x

Options

A) $\frac{3}{2}$

B) $\frac{4}{3}$

C) $\frac{2}{3}$

D) $\frac{1}{2}$

The correct answer is A.

Explanation:

2 log_x (3$\frac{3}{8}$

) = 6(divide both sides by 2)
$\frac{2lo{g}_x\left(3\frac{3}{8}\right)}{2}=\frac{6}{2}$
${\log }_x\frac{27}{8}=3$
$\frac{27}{8}=x^3$
$x^3=\frac{27}{8}$
x = $\sqrt{\frac{27}{8}}$
= ($\frac{27}{8}$)$\frac{1}{3}$
= $\frac{(3^3{)}^{\frac{1}{3}}}{(2^3{)}^{\frac{1}{3}}}$
= $\frac{3}{2}$

Question 43

If p = (y : 2y $\ge$

6) and Q = (y : y -3 $\ge$ 4), where y is an integer, find p$\cap$

Q

Options

A) {3, 4}

B) {3, 7}

C) {3, 4, 5, 6, 7}

D) {4, 5, 6}

The correct answer is C.

Explanation:

p = (y : 2y $\ge$

6)
2y $\le$ 6
y $\le \frac{6}{2}$
y = $\le$ 3
and Q = (y : y -3 $\ge$ 4)
y - 3 $\ge$ 4
y $\ge$ 4 + 3
y $\ge$ 7
Therefore p = {3, 4, 5, 6, 7} and Q = {7, 6, 5, 4, 3....}
P$\cap$

Q = {3, 4, 5, 6, 7}

Question 44

Find the values of k in the equation 6k² = 5k + 6

Options

A) {$\frac{-2}{3},\frac{-3}{2}$

}

B) {$\frac{-2}{3},\frac{3}{2}$

}

C) {$\frac{2}{3},\frac{-3}{2}$

}

D) {$\frac{2}{3},\frac{3}{2}$

}

The correct answer is B.

Explanation:

6k² = 5k + 6
6k² - 5k - 6 = 0
6k² - 0k + 4k - 6 = 0
3k(2k - 3) + 2(2k - 3) = 0
(3k + 2)(2k - 3) = 0
3k + 2 = 0 or 2k - 3 = 0
3k = -2 or 2k = 3
k = $\frac{-2}{3}$

or k = $\frac{3}{2}$
k = ($\frac{-2}{3}$, k = $\frac{3}{2}$

)

Question 45

If y varies directly as the square root of (x + 1) and y = 6 when x = 3, find x when y = 9

Options

A) 8

B) 7

C) 6

D) 5

The correct answer is A.

Explanation:

y $\alpha$

$\sqrt{x+1}$, y = $k\sqrt{x+1}$
6 = k$\sqrt{3+1}$
6 = k$\sqrt{4}$
6 = 2k
k = $\frac{6}{2}$ = 3
y = $\sqrt{(x+1)}$
9 = 3$\sqrt{(x+1)}$(divide both side by 3)
$\frac{9}{3}$ = $\frac{3\sqrt{x+1}}{3}$
3 = $\sqrt{x+1}$

(square both sides)
9 = x + 1
x = 9 - 1
x = 8

Question 46

The graph of the relation y = x² + 2x + k passes through the point (2, 0). Find the values of k

Options

A) zero

B) -2

C) -4

D) -8

The correct answer is D.

Explanation:

y = x² + 2x + k at point(2,0) x = 2, y = 0
0 = (2)2 + 2(20 + k)
0 = 4 + 4 + k
0 = 8 + k
k = -8

Question 47

What is the locus of the point X which moves relative to two fixed points P and M on a plane such that on a plane such that < PXM = 30^o

Options

A) the bisector of the straight line joining P and M

B) an arc of a circle with PM as a chord

C) the bisector of angle PXM

D) a circle centre X and radius PM

The correct answer is B.

Question 48

When a number is subtracted from 2, the result equals 2 less than one-fifth of the number. Find the number

Options

A) $11$

B) $\frac{15}{2}$

C) $5$

D) $\frac{5}{2}$

The correct answer is C.

Explanation:

Let the number be y, subtract y from 2 i.e 2 - y
2 - y = 4
2 - y - 4
2 - 4 - y $\frac{x}{5}-4$

, multiplying through by 5
5(2 - x) = 5($\frac{x}{5}$) - 5(4)
10 - 5x = x - 20
-5x - x = -20 - 10
-6x = -30
x = $\frac{-30}{-6}$

= 5

Question 49

Express $\frac{2}{x+3}-\frac{1}{x-2}$

as a simple fraction

Options

A) $\frac{x-7}{x^2+x-6}$

B) $\frac{x-1}{x^2+x-6}$

C) $\frac{x-2}{x^2+x-6}$

D) $\frac{x-27}{x^2+x-6}$

The correct answer is A.

Explanation:

$\frac{2}{x+3}-\frac{1}{x-2}$

= $\frac{2(x-2)-(x-3)}{(x+3)(x-2)}$
= $\frac{2x-4-x-3}{x^2-2x+3x-6}$
= $\frac{x-7}{x^2+x-6}$
= $\frac{x-7}{x^2+x-6}$

Question 50

An interior angle of a regular polygon is 5 times each exterior angle. How many sides has the polygon?

Options

A) 15

B) 12

C) 9

D) 6

The correct answer is B.

Explanation:

Let the interior angle = x°
interior angle = 5x° (sum of int. angle ann exterior)
(angles = angle or straight line)
6x = 180
x = $\frac{180}{6}$

x = 30°
no. of sides = $\frac{\text{sum of exterior angles}}{\text{exterior angle}}$
= $\frac{360}{30}$

= 12

Question 51

Given that P = x² + 4x - 2, Q = 2x - 1 and Q - P = 2, find x.

Options

A) -2

B) -1

C) 1

D) 2

The correct answer is B.

Explanation:

P = x² + 4x - 2, Q = 2x - 1
Q - p = 2, (2x - 1) - (x² + 4x - 2) = 2
2x - 1 - x² - 4x + 2 = 2
-2x - x² + 1
-x² - 2x - 1 = 0
x² + 2x + 1 = 0
x² + x + x + 1 = 0
x(x + 1) + 1(x + 1) = 0
(x + 1)(x + 1) = 0
x + 1 = 0 or x + 1 = 0
x = -1 or x = -1
x = -1

Question 52

A pyramid has a rectangular base with dimensions 12m by 8m. If its height is 14m, calculate the volume

Options

A) 322 m³

B) 448 m³

C) 632 m³

D) 840 m³

The correct answer is B.

Explanation:

Volume of pyramid = $\frac{1}{3}$

× base area × height
= $\frac{1}{3}\times {12}^4\times 8\times 14$

= 4 × 8 × 14 = 448 m³

Question 53

The slant height of a cone is 5cm and the radius of its base is 3cm. Find, correct to the nearest whole number, the volume of the cone. (Take $\pi =\frac{22}{7}$

)

Options

A) 48cm³

B) 47cm³

C) 38cm³

D) 12cm³

The correct answer is C.

Explanation:

Volume of a cone = $\frac{1}{3}\pi r^{2}h$

h² = 5² - 3²
= 25 - 9 = 16
h = $\sqrt{16}$
h = 4 cm
v = $\frac{1}{3}\times \frac{22}{7}\times 3^2\times 4$
$\frac{1}{3}\times \frac{22}{7}\times 9\times 4$
= $\frac{22\times 3\times 4}{7}$

= 37.7 cm³
= 38 cm³

Question 54

The distance between two towns is 50km. It is represented on a map by 5cm. Find the scale used

Options

A) 1: 1,000,000

B) 1: 500,000

C) 1: 100,000

D) 1: 10,000

The correct answer is A.

Explanation:

1km = 100,000cm
On the map 1 cm represent every 10 km which is equal to (10 x 100,000cm)
= 1,000,000cm
The scale is 1:1,000,000

Question 55

Given that (x + 2)(x² - 3x + 2) + 2(x + 2)(x - 1) = (x + 2) M, find M

Options

A) (x + 2)²

B) x(x + 2)

C) xv + 2

D) x² - x

The correct answer is D.

Explanation:

(x = 2)(x² - 3x + 2) + 2(x + 2)(x - 1) = (x + 2)m
(m + 2)[(x² - 3x + 2) + 2(x - 1)] = (x + 2)M
divide both side by (x + 2)
(x² - 3x + 2) + 2(x - 1) = M
x² - 3x + 2 + 2x - 2 = M
x² - 3x + 2 + 2x - 2 = M
x² - 3x + 2x = M
x² - x = M
M = x² - x

Question 56

An open cone with base radius 28cm and perpendicular height 96cm was stretched to form sector of a circle. Calculate the arc of the sector (Take $\pi =\frac{22}{7}$

)

Options

A) 8800cm²

B) 8448cm²

C) 4400cm²

D) 4224cm²

The correct answer is A.

Explanation:

L² = 96² + 28²
= 9216 + 784
= 10000
L = $\sqrt{10000}$

= 100cm
Curved surface area = $\pi rl$
= $\frac{22}{7}\times 28\times 100$

= 8800cm²
Area of cone = Area of sector
Area of sector = 8800cm²

Question 57

In the diagram, PRST is a square. If |PQ| = 24cm. |QR| = 10cm and < PQR = 90°, find the perimeter of the polygon PQRST.

Options

A) 112cm

B) 98cm

C) 86cm

D) 84cm

The correct answer is A.

Question 58

In the diagram, the height of a flagpole |TF| and the length of its shadow |FL| re in the ratio 6:8. Using k as a constant of proportionality, find the shortest distance between T and L

Options

A) 7K units

B) 10K units

C) 12K units

D) 14K units

The correct answer is B.

Explanation:

By Pythagoras theorem: x² = 6² + 8²
36 + 64 = 100
x = $\sqrt{100}$

x = 10

Question 59

the diagrams, |XZ| = |MN|, |ZY| = |MO| and |XY| = |NO|. Which of the following statements is true?

Options

A) $△$

ZYX = $△$

OMN

B) $△$

YZX = $△$

NOM

C) $△$

ZXY = $△$

MON

D) $△$

XYZ = $△$

NOM

The correct answer is D.

Question 60

In the diagram, PQRS is a rhombus and < PSQ = 35°. Calculate the size of < PRO

Options

A) 65°

B) 55°

C) 45°

D) 35°

The diagonals of rhombus bisects its angles.

The correct answer is D.

Explanation:

The diagonals of rhombus bisects its angles.

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