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Mathematics
WAEC / WASSCE 2017
Sets, Logic & Venn Diagrams
Solution
If M = {x : 3 \(\leq\) x < 8} and N = {x : 8 < x \(\leq\) 12}, which of the following is true?
i. 8 \(\in\) M \(\cap\) N
ii. 8 \(\in\) M \(\cup\) N
iii. M \(\cap\) N = \(\varnothing\)
A
iii only
B
i and ii
C
ii and iii only
D
i, ii and iii
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
M = {3, 4, 5, 6, 7,}, N = {9, 10, 11, 12}
Source: Myschool Past Questions Archive (Record #49938)
Mathematics
WAEC / WASSCE 2017
Indices, Logarithms & Surds
Solution
Given that a = log 7 and b = \(\log\) 2, express log 35 in terms of a and b.
A
a + b + 1
B
ab - 1
C
a - b + 1
D
b - a + 1
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{\log 7 \times \log 10}{\log 2}\)
log 7 x log 10 \(\div\) log 2
a + 1 - b
a - b + 1
Source: Myschool Past Questions Archive (Record #49948)
Mathematics
WAEC / WASSCE 2017
Plane Geometry, Polygons & Circle Theorems
Solution
If x = \(\frac{2}{3}\) and y = - 6, evaluate xy - \(\frac{y}{x}\)
A
0
B
5
C
8
D
9
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
x = \(\frac{2}{3}\) and y = - 6
xy - \(\frac{y}{x}\)
\(\frac{2}{3} - (6)^2 - (-6) \div \frac{2}{3}\)
= -4 - (6) x \(\frac{3}{2}\)
= -4 - (-6) x \(\frac{3}{2}\)
= -4 - (-9)
= -4 + 9
= 5
Source: Myschool Past Questions Archive (Record #49951)
Mathematics
WAEC / WASSCE 2017
Linear, Simultaneous & Quadratic Equations
Solution
Solve the equation: \(\frac{1}{5x} + \frac{1}{x}\)= 3
A
\(\frac{1}{5}\)
B
\(\frac{2}{5}\)
C
\(\frac{3}{5}\)
D
\(\frac{4}{5}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\frac{1}{5x} + \frac{1}{x}\)= 3
\(\frac{1 + 5}{5x}\) = 3
6 = 15x
x = \(\frac{6}{15}\)
= \(\frac{2}{5}\)
Source: Myschool Past Questions Archive (Record #49954)
Mathematics
WAEC / WASSCE 2017
Fractions, Decimals, Percentages & Approximations
Solution
A sum of N18,100 was shared among 5 boys and 4 girls with each boy taking N20.00 more than each girl. Find a boy's share.
A
N1,820.00
B
2,000.00
C
N2,020.00
D
N2,040.00
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Let a girl's share = x + 20
4x + 5(x + 20) = 18,100
4x + 5x + 100 = 18,100
9x + 100 = 18,100
9x = 18,000
x = \(\frac{18,000}{9}\)
x = 2,000
\(\therefore\) Each boy gets N(2,000 + 20)
= N2,020.
Source: Myschool Past Questions Archive (Record #49957)
Mathematics
WAEC / WASSCE 2017
Linear, Simultaneous & Quadratic Equations
Solution
One factor of \(7x^2 + 33x - 10\) is
A
7x + 5
B
x - 2
C
7x - 2
D
x - 5
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(7x^2 + 33x - 10\)
\(7x^2 + 35x - 2x - 10\)
7x (x + 5) - 2 (x + 5)
(7x - 2) (x + 5)
Source: Myschool Past Questions Archive (Record #49963)
Mathematics
WAEC / WASSCE 2017
Plane Geometry, Polygons & Circle Theorems
Solution
Solve: - \(\frac{1}{4}\) < \(\frac{3}{4}\) (3x - 2) < \(\frac{1}{2}\)
A
-\(\frac{5}{9}\) < x <\(\frac{8}{9}\)
B
-\(\frac{8}{9}\) < x <\(\frac{7}{9}\)
C
-\(\frac{8}{9}\) < x <\(\frac{5}{9}\)
D
-\(\frac{7}{9}\) < x <\(\frac{8}{9}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\frac{3}{4}\) (3x - 2) < \(\frac{1}{2}\); \(\frac{3}{4}\) (3x - 2) > - \(\frac{1}{4}\)
3(3x - 2) < 2; 3(3x - 2) > -1
9x - 6 < 2; 9x - 6 > -1
9x < 8; 9x > 5
x < \(\frac{5}{9}\); x > \(\frac{8}{9}\)
Source: Myschool Past Questions Archive (Record #49984)
Mathematics
WAEC / WASSCE 2017
Plane Geometry, Polygons & Circle Theorems
Solution
Simplify; 3x - (p - x) - (r - p)
A
2x - r
B
2x + r
C
4x - r
D
2x - 2p - r
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
3x - (p - x) - ( r - p)
= 3x - p + x - r + p
= 4x - r
Source: Myschool Past Questions Archive (Record #49987)
Mathematics
WAEC / WASSCE 2017
Plane Geometry, Polygons & Circle Theorems
Solution
An arc of a circle of radius 7.5cm is 7.5cm long. Find, correct to the nearest degree, the angle which the arc subtends at the centre of the circle. [Take \(\pi = \frac{22}{7}\)]
A
29\(^o\)
B
57\(^o\)
C
65\(^o\)
D
115\(^o\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
lac = \(\frac{\theta}{360}\) x 2\(\pi\)r
7.5 = \(\frac{\theta}{360}\) x 2 x \(\frac{22}{7}\) x 7.5
7.5 = \(\frac{330\theta}{2520}\)
\(\theta\) = \(\frac{7.5}{0.1309}\)
\(\theta\) = 57.29
\(\theta\) = 57 \(^o\)
Source: Myschool Past Questions Archive (Record #49990)
Mathematics
WAEC / WASSCE 2017
Mensuration (Areas, Perimeters & Volumes)
Solution
Water flows out of a pipe at a rate of 40\(\pi cm^2\) per seconds into an empty cylinder container of base radius 4cm. Find the height of water in the container after 4 seconds.
A
10 cm
B
14 cm
C
16 cm
D
20 cm
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Volume of a cylinder = \(\pi r^2h\)
40\(\pi cm^3\) = \(\pi. 4^2h\)
40\(cm^3\) = 16h
h = 2.5cm/sec
In 4 seconds, 2.5cm x 4
= 10cm
Source: Myschool Past Questions Archive (Record #49992)
Mathematics
WAEC / WASSCE 2017
Plane Geometry, Polygons & Circle Theorems
Solution
The dimensions of water tank are 13cm, 10cm and 70cm. If it is half-filled with water, calculate the volume of water in litres
A
4.55 litres
B
7.50 litres
C
8.10 litres
D
9.55 litres
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Vol of a cubiod = L x b x h
v = 13cm x 10cm x 70cm
= 9100cm
Since it is half-filled = \(\frac{9100}{2}\)cm
= 4550cm
4550cm \(\to\) 4.55 litres
Source: Myschool Past Questions Archive (Record #49995)
Mathematics
WAEC / WASSCE 2017
Mensuration (Areas, Perimeters & Volumes)
Solution
If the total surface area of a solid hemisphere is equal to its volume, find the radius
A
3.0cm
B
4.5cm
C
5.0cm
D
9.0cm
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
T.S.A of hemisphere = 3\(\pi r^2\)
vol of hemisphere = \(\frac{2}{3} \pi r^3\)
3\(\pi r^2\) = \(\frac{2}{3} \pi r^3\)
3 = \(\frac{2}{3}r\)
9 = 2r
r = \(\frac{9}{2}\)
r = 4.5cm
Source: Myschool Past Questions Archive (Record #49998)
Mathematics
WAEC / WASSCE 2017
Plane Geometry, Polygons & Circle Theorems
Which of the following is true about parallelogram?
A
opposite angles are supplementary
B
opposite angles are complementary
C
opposite angles are equal
D
opposite angles are reflex angles
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option C.
Source: Myschool Past Questions Archive (Record #50000)
Mathematics
WAEC / WASSCE 2017
Plane Geometry, Polygons & Circle Theorems
Solution
Calculate the gradient (slope) of the joining points (-1, 1) and (2, -2)
A
-1
B
\(\frac{-1}{2}\)
C
\(\frac{1}{2}\)
D
1
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Gradient = m = \(\frac{y_2 - y_1}{x_2 - x_1}\)
= \(\frac{-2 -1}{2 + 1}\)
= \(\frac{-3}{3}\)
= -1
Source: Myschool Past Questions Archive (Record #50001)
Mathematics
WAEC / WASSCE 2017
Indices, Logarithms & Surds
Solution
If P(2,3) and Q)2, 5) are points on a graph, calculate the length PQ
A
6 units
B
5 units
C
4 units
D
2 units
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\sqrt{(x_2 - x_1)^2 + (y_2 - Y_1)^2}\)
= \(\sqrt{(2 - 2)^2 + (5 - 3)^2}\)
= \(\sqrt{0^2 + 2^2}\)
= \(\sqrt{4}\)
= 2 units
Source: Myschool Past Questions Archive (Record #50002)