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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)
Mathematics
WAEC / WASSCE 2019
Geometry and Trigonometry
Solution
From the top of a vertical cliff 20m high, a boat at sea can be sighted 75m away and on the same horizontal position as the cliff. Calculate, correct to the nearest degree, the angle of depression of the boat from the top of the cliff.
A
56\(^o\)
B
75\(^o\)
C
16\(^o\)
D
15\(^o\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Sin\(\theta = \frac{20}{75}\)
\(\theta = sin^{-1} (\frac{20}{75})\)
= 15\(^o\)
Source: Myschool Past Questions Archive (Record #57369)
Mathematics
WAEC / WASSCE 2019
Geometry and Trigonometry
Diagram
Solution
In the diagram, O is the centre of the circle of radius 18cm. If < zxy = 70\(^o\), calculate the length of arc ZY. [Take \(\pi = \frac{22}{7}\)]
Attached Figure / Diagram
A
11cm
B
22 cm
C
44 cm
D
80 cm
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Z\({O}\)T = 2 x 70\(^o\) 140\(^o\)
Length = \(\frac{\theta}{360}\) x 2\(\pi\)r
\(\frac{140^o}{360} \times 2 \times \frac{22}{7}\) x 18
= 44cm
Source: Myschool Past Questions Archive (Record #57378)
Mathematics
WAEC / WASSCE 2019
Geometry and Trigonometry
Diagram
Solution
In the diagram, RT is a tangent to the circle at R, < PQR = 70\(^o\), < QRT = 52\(^o\), < QSR and < PRQ = x. Find the value of y.
Attached Figure / Diagram
A
70\(^o\)
B
60\(^o\)
C
52\(^o\)
D
18\(^o\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
∠QRT = ∠SRT = 52 (opposite angles)
∠SRT = y = 52 (alternate angles)
y = 52\(^o\)
Source: Myschool Past Questions Archive (Record #57379)
Mathematics
WAEC / WASSCE 2019
Statistics and Probability
Solution
Calculate the variance of 2, 4, 7, 8 and 9
A
7.2
B
6.8
C
3.5
D
2.6
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
x
2
4
7
8
9
(\(\bar{x} - \bar{x}\))
-4
-2
1
2
4
(\(\bar{x} - \bar{x})^2\)
16
4
1
4
9
_________
\(\sum (x - x)^2\) = 34
\(\bar{x} = \frac{2 + 4 + 7 + 8 + 9}{5} = 6
variance = \(\frac{34}{5}\)
= 6.8
Source: Myschool Past Questions Archive (Record #57381)
Mathematics
WAEC / WASSCE 2019
Algebra
Solution
The fourth term of an Arithmetic Progression (A.P) is 37 and the first term is -20. Find the common difference.
A
3
B
57
C
19
D
17
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
a + 3d = 37
-20 + 3d = 37
3d = 37 + 20 = 57
d = \(\frac{57}{3}\)
= 19
Source: Myschool Past Questions Archive (Record #57382)