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Mathematics
WAEC / WASSCE 2017
Number and Numeration
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
Number and Numeration
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
Geometry and Trigonometry
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
Number and Numeration
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
Geometry and Trigonometry
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
Number and Numeration
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
Geometry and Trigonometry
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
Geometry and Trigonometry
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
Number and Numeration
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)
Mathematics
WAEC / WASSCE 2017
Geometry and Trigonometry
A bearing of 320\(^o\) expressed as a compass bearing is
A
N 50\(^o\) W
B
N 40\(^o\) W
C
N 50\(^o\) E
D
N 40\(^o\) E
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option B.
Source: Myschool Past Questions Archive (Record #50005)
Mathematics
WAEC / WASSCE 2017
Geometry and Trigonometry
Solution
Given that cos 30\(^o\) = sin 60\(^o\) = \(\frac{3}{2}\) and sin 30\(^o\) = cos 60\(^o\) = \(\frac{1}{2}\), evaluate \(\frac{tan 60^o - 1}{1 - tan 30^o}\)
A
\(\sqrt{3 - 2}\)
B
2 - \(\sqrt{3}\)
C
\(\sqrt{3}\)
D
-2
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
From the figure above, tan30º = \(\frac{1}{\sqrt3}\) and tan60º = \(\sqrt{3}\)
so \(\frac{tan60 - 1}{1 - tan30}\)
= \(\frac{\sqrt{3}}{1}\div(1 - (\frac{1}{\sqrt{3}}\)))
= \(\frac{\sqrt{3} - 1}{1}\div\frac{\sqrt{3} - 1}{\sqrt3}\)
= \(\frac{\sqrt{3} - 1}{1}\times \frac{\sqrt3}{\sqrt{3} - 1}\) = \(\sqrt{3}\)
Source: Myschool Past Questions Archive (Record #50014)
Mathematics
WAEC / WASSCE 2017
Number and Numeration
Solution
In what number base was the addition 1 + nn = 100, where n > 0, done?
A
n - 1
B
n + 1
C
n
D
n + 2
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Assuming the numbers 1 + nn =100 were added in base n + 1
n
n
1
1 0
0
n + 1 = n +1 and n + 1 in base n + 1 = 10, write 0 and carry 1, which will be added to the second n, resulting in another n + 1 in base n + 1 = 10.
So, putting the result together 1 + nn = 100 provided, the addition was carried out in base n + 1.
Source: Myschool Past Questions Archive (Record #50025)
Mathematics
WAEC / WASSCE 2017
Number and Numeration
Solution
Simplify; \(\sqrt{2}(\sqrt{6} + 2\sqrt{2}) - 2\sqrt{3}\)
A
4
B
\(\sqrt{3} + 4\)
C
4 \(\sqrt{2}\)
D
4\(\sqrt{3} + 4\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\sqrt{2}(\sqrt{6} + 2\sqrt{2}) - 2\sqrt{3}\)
\(\sqrt{12}\) + 2 x 2 - 2\(\sqrt{3}\)
2 \(\sqrt{3}\) - 2 \(\sqrt{3}\) + 4
= 4
Source: Myschool Past Questions Archive (Record #50027)
Mathematics
WAEC / WASSCE 2017
Geometry and Trigonometry
Solution
Three exterior angles of a polygon are 30\(^o\), 40\(^o\) and 60\(^o\). If the remaining exterior angles are 46\(^o\) each, name the polygon.
A
decagon
B
nonagon
C
octagon
D
hexagon
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Sum of all exterior angles is 360\(^o\)
360\(^o\) (30\(^o\) - 40\(^o\))
360 - (130\(^o\))
230\(^o\)
remaining is 46\(^o\) = \(\frac{230}{46}\) = 5
5 + 3 = 8 sides; Octagon
Source: Myschool Past Questions Archive (Record #50029)
Mathematics
WAEC / WASSCE 2017
Number and Numeration
Solution
Simplify the expression \(\frac{a^2 b^4 - b^2 a^4}{ab(a + b)}\)
A
\(a^2 - b^2\)
B
\(b^2 - a^2\)
C
\(a^2b - ab^2\)
D
\(ab^2 - a^2b\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{a^2 b^4 - b^2 a^4}{ab(a + b)}\) = \(\frac{a^2 b^2(b^2 - a^2)}{ab(a + b)}\)
= \(\frac{ab [(b - a) (b + a)]}{a + b}\)
= ab(b - a)
= \(ab^2 - a^2b\)
Source: Myschool Past Questions Archive (Record #50112)