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Mathematics
WAEC / WASSCE 2019
Number and Numeration
Solution
Which of these values would make \(\frac{3p - 1}{p^{2} - p}\) undefined?
A
1
B
\(\frac{1}{3}\)
C
-\(\frac{1}{3}\)
D
-1
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
P\(^2\) - p = 0
p(p - 1) = 0
p = 0 or p = 1
Source: Myschool Past Questions Archive (Record #57223)
Mathematics
WAEC / WASSCE 2019
Number and Numeration
Solution
The total surface area of a solid cylinder 165cm\(^2\). Of the base diameter is 7cm, calculate its height. [Take \(\pi = \frac{22}{7}\)]
A
7.5 cm
B
4.5 cm
C
4.0 cm
D
2.0 cm
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
165 = 2 x \(\frac{22}{7}\) x \(\frac{7}{2}\) x h + 2 x \(\frac{22}{7}\) x \(\frac{7}{2}\) x \(\frac{7}{2}\)
165 = 22h + 77
\(\frac{22h}{22} = \frac{88}{22}\)
height = 4cm
Source: Myschool Past Questions Archive (Record #57228)
Mathematics
WAEC / WASSCE 2019
Number and Numeration
Solution
If 2\(^{a}\) = \(\sqrt{64}\) and \(\frac{b}{a}\) = 3, evaluate a\(^2 + b^{2}\)
A
250
B
160
C
90
D
48
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
2\(^a\) = \(\sqrt{64}\)
2\(^a\) = 8
2\(^a\) = 2\(^3\)
a = 3
b = 3\(^a\)
b = 3 x 3 = 9
a\(^2\) + b\(^2\) = 3\(^2\) + 9\(^2\)
= 9 + 81 = 90
Source: Myschool Past Questions Archive (Record #57238)
Mathematics
WAEC / WASSCE 2019
Number and Numeration
Solution
If log\(_x\) 2 = 0.3, evaluate log\(_x\) 8.
A
2.4
B
1.2
C
0.9
D
0.6
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
log\(_x\)2 = 0.3
log\(_x\)8 = log\(_x\)2\(^3\) = 3 log\(_x\)2
= 3 x 0.3
= 0.9
Source: Myschool Past Questions Archive (Record #57255)
Mathematics
WAEC / WASSCE 2019
Geometry and Trigonometry
Solution
An arc subtends an angle of 72\(^o\) at the centre of a circle. Find the length of the arc if the radius of the circle is 3.5 cm. [Take \(\pi = \frac{22}{7}\)]
A
6.6 cm
B
8.8 cm
C
4.4 cm
D
2.2 cm
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Length = \(\frac{\theta}{360}\) x 2\(\pi\)r
= \(\frac{72}{360} \times 2 \frac{22}{7} \times \frac{0.5}{3.5}\)
= 4.4
Source: Myschool Past Questions Archive (Record #57257)
Mathematics
WAEC / WASSCE 2019
Number and Numeration
Solution
Make b the subject of the relation lb = \(\frac{1}{2}\) (a + b)h
A
\(\frac{ah}{2l - h}\)
B
\(\frac{2l - h}{al}\)
C
\(\frac{al}{2l - h}\)
D
\(\frac{al}{2 - h}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
lb = \(\frac{1}{2} (a + b)h
2lb = ah + bh
2lb - bh = ah
\(\frac{b(2l - h)}{2l - h} = \frac{ah}{2l - h}\)
b = \(\frac{ah}{2l - h}\)
Source: Myschool Past Questions Archive (Record #57261)
Mathematics
WAEC / WASSCE 2019
Number and Numeration
Solution
Eric sold his house through an agent who charged 8% commission on the selling price. If Eric received $117,760.00 after the sale, what was the selling price of the house?
A
$130,000.00
B
$128,000.00
C
$125,000.00
D
$120,000.00
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\frac{8}{100} \times x + 117,760 = x\)
x - \(\frac{8x}{100} = 117,760
\(\frac{92x}{100} = 117,760\)
x = \(\frac{117,760 \times 100}{92}\)
Selling price = N128,000
Source: Myschool Past Questions Archive (Record #57268)
Mathematics
WAEC / WASSCE 2019
Geometry and Trigonometry
Solution
Find the angle at which an arc of length 22 cm subtends at the centre of a circle of radius 15cm. [Take \(\pi = \frac{22}{7}\)]
A
70\(^o\)
B
84\(^o\)
C
96\(^o\)
D
156\(^o\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
L = \(\frac{\theta}{360} \times 2 \pi r\)
22 = \(\frac{\theta}{360} \times 2 \times \frac{22}{7} \times 15\)
\(\theta = \frac{22 \times 360 \times 7}{2 \times 22 \times 15}\)
\(\theta\) = 84\(^o\)
Source: Myschool Past Questions Archive (Record #57272)
Mathematics
WAEC / WASSCE 2019
Geometry and Trigonometry
Solution
A rectangular board has a length of 15cm and width x cm. If its sides are doubled, find its new area.
A
60x cm\(^2\)
B
45x cm\(^2\)
C
30x cm\(^2\)
D
15x cm\(^2\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
New are = (2 x 15) x (2 x \(x\))
= 60cm\(^2\)
Source: Myschool Past Questions Archive (Record #57274)
Mathematics
WAEC / WASSCE 2019
Geometry and Trigonometry
Diagram
Solution
In the diagram, POS and ROT are straight lines. OPQR is a parallelogram, |OS| = |OT| and ∠OST = 50^\circ. Calculate the value of ∠OPQ.
Attached Figure / Diagram
A
100\(^o\)
B
120\(^o\)
C
140\(^o\)
D
160\(^o\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
S\(O\)T = 180\(^o\) - (50 + 50)
= 80\(^o\)
P\(Q\)R = 80\(^o\)
= \(\frac{360^o - 160^o}{2}\) = 100\(^o\)
Source: Myschool Past Questions Archive (Record #57313)
Mathematics
WAEC / WASSCE 2019
Number and Numeration
Solution
Factorize completely; (2x + 2y)(x - y) + (2x - 2y)(x + y)
A
4(x - y)(x + y)
B
(4(x - y)
C
2(x - y)(x + y)
D
2(x - y)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
(2x + 2y)(x - y) + (2x - 2y)(x - y)
2(x + y)(x - y) + 2(x - y)(x + y)
4(x - y)(x + y)
Source: Myschool Past Questions Archive (Record #57320)
Mathematics
WAEC / WASSCE 2019
Geometry and Trigonometry
Solution
The interior angles of a polygon are 3x\(^o\), 2x\(^o\), 4x\(^o\), 3x\(^o\) and 6x\(^o\). Find the size of the smallest angle of the polygon.
A
80\(^o\)
B
60\(^o\)
C
40\(^o\)
D
30\(^o\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
3\(x^o\) + 2\(x^o\) + 4\(x^o\) + 3\(x^o\) + 6\(x^o\) = 540\(^o\)
\(\frac{18x^o}{18} = \frac{540^o}{18}\)
\(x^o\) = 30\(^o\)
Smallest angle = 2 x 30\(^o\) = 60\(^o\)
Source: Myschool Past Questions Archive (Record #57323)
Mathematics
WAEC / WASSCE 2019
Algebra
Solution
Find the equation of a straight line passing through the point (1, -5) and having gradient of \(\frac{3}{4}\)
A
3x + 4y - 23 = 0
B
3x + 4y +23 = 0
C
3x - 4y +23 = 0
D
3x - 4y - 23 = 0
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{3}{4} = \frac{y + 5}{x - 1}\)
3(x - 1) = 4(y + 5)
3x - 3 = 4y + 20
3x - 4y - 23 = 0
Source: Myschool Past Questions Archive (Record #57338)
Mathematics
WAEC / WASSCE 2019
Number and Numeration
Solution
The foot of a ladder is 6m from the base of an electric pole. The top of the ladder rest against the pole at a point 8m above the ground. How long is the ladder?
A
14m
B
12m
C
10m
D
7m
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
H\(^2\) = 8\(^2\) + 6\(^2\) + 6\(^2\)
H\(^2\) = 64 + 36 = 100
H = \(\sqrt{100}\) = 10m
Source: Myschool Past Questions Archive (Record #57361)
Mathematics
WAEC / WASSCE 2019
Geometry and Trigonometry
Solution
If tan x = \(\frac{3}{4}\), 0 < x < 90\(^o\), evaluate \(\frac{\cos x}{2 sin x}\)
A
\(\frac{8}{3}\)
B
\(\frac{3}{2}\)
C
\(\frac{4}{3}\)
D
\(\frac{2}{3}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
y\(^2\) = 3\(^2\) + 4\(^2\)
y\(^2\) = 9 + 16
y = \(\sqrt{25}\)
= 5
\(\frac{\cos x}{2 \sin x} = \frac{4}{5} + 2 \times \frac{3}{5}\)
= \(\frac{4}{5} \times \frac{5}{6}\)
= \(\frac{2}{3}\)
Source: Myschool Past Questions Archive (Record #57365)