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Mathematics
WAEC / WASSCE 2019
Number and Numeration
Solution
Evaluate: 2\(\sqrt{28} - 3\sqrt{50} + \sqrt{72}\)
A
4\(\sqrt{7} - 21 \sqrt{2}\)
B
4\(\sqrt{7} - 11 \sqrt{2}\)
C
4\(\sqrt{7} - 9 \sqrt{2}\)
D
4\(\sqrt{7} + \sqrt{2}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
2\(\sqrt{28} - 3\sqrt{50} + \sqrt{22}\)
4\(\sqrt{7} - 15\sqrt{2} + 6\sqrt{2}\)
6\(\sqrt{7} - 9\sqrt{2}\)
Source: Myschool Past Questions Archive (Record #57156)
Mathematics
WAEC / WASSCE 2019
Number and Numeration
Solution
If m : n = 2 : 1, evaluate \(\frac{3m^2 - 2n^2}{m^2 + mn}\)
A
\(\frac{4}{3}\)
B
\(\frac{5}{3}\)
C
\(\frac{3}{4}\)
D
\(\frac{3}{5}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
m = 2, n = 1
\(\frac{3m^2 - 2n^2}{m^2 _ mn}\)
= \(\frac{3(2)^2 - 2(1)^2}{2^2 + 2(1)}\)
= \(\frac{12 - 2}{4 + 2} = \frac{10}{6}\)
= \(\frac{5}{3}\)
Source: Myschool Past Questions Archive (Record #57161)
Mathematics
WAEC / WASSCE 2019
Number and Numeration
Solution
H varies directly as p and inversely as the square of y. If H = 1, p = 8 and y = 2, find H in terms of p and y.
A
H = \(\frac{p}{4y^2}\)
B
H = \(\frac{2p}{y^2}\)
C
H = \(\frac{p}{2y^2}\)
D
H = \(\frac{p}{y^2}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
H \(\propto\) \(\frac{p}{y^2}\)
H = \(\frac{pk}{y^2}\)
1 = \(\frac{8k}{2^2}\)
k = \(\frac{4}{8}\)
= \(\frac{1}{2}\)
H = \(\frac{p}{2y^2}\)
Source: Myschool Past Questions Archive (Record #57165)
Mathematics
WAEC / WASSCE 2019
Number and Numeration
Solution
Solve \(4x^{2}\) - 16x + 15 = 0.
A
x = 1\(\frac{1}{2}\) or x = -2\(\frac{1}{2}\)
B
x = 1\(\frac{1}{2}\) or x = 2\(\frac{1}{2}\)
C
x = 1\(\frac{1}{2}\) or x = -1\(\frac{1}{2}\)
D
x = -1\(\frac{1}{2}\) or x -2\(\frac{1}{2}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
4x\(^2\) - 16x + 15 = 0
\(4x^2\) - 6x - 10x + 15 = 0
2x(2x - 3) - 5(2x - 3) = 0
(2x - 3)(2x - 5) = 0
x = 1\(\frac{1}{2}\) or x = 2\(\frac{1}{2}\)
Source: Myschool Past Questions Archive (Record #57175)
Mathematics
WAEC / WASSCE 2019
Number and Numeration
Solution
Simplify: \(\log_{10}\) 6 - 3 log\(_{10}\) 3 + \(\frac{2}{3} \log_{10} 27\)
A
3 \(\log_{10}^2\)
B
\(\log_{10}^2\)
C
\(\log_{10}^3\)
D
2 \(\log_{10}^3\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
log\(_{10}\) 6 - log\(_{10}\)3\(^3\) + log\(_{10}\) (\(\sqrt[3]{27}\))\(^2\)
= log \(_{10}\) 6 - log \(_{10}\) 27 + log\(_{10}\) 9
= log\(_{10}\) \(\frac{6 \times 9}{27}\)
= log\(_{10}\)2
Source: Myschool Past Questions Archive (Record #57197)
Mathematics
WAEC / WASSCE 2019
Number and Numeration
Solution
Bala sold an article for #6,900.00 and made a profit of 15%. Calculate his percentage profit if he had sold it for N6,600.00.
A
5%
B
10%
C
12%
D
13%
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
15 = (\(\frac{6,900 - C.P \times 100}{C.P}\))
15 C.P = 690000 - C.P 100
C.P = \(\frac{690000}{115}\)
C.P = N6,000
%profit = \(\frac{6,600 - 6,000}{6,000}\) x 100
= \(\frac{600}{6,000}\) x 100
= 10%
Source: Myschool Past Questions Archive (Record #57203)
Mathematics
WAEC / WASSCE 2019
Number and Numeration
Solution
If 3p = 4q and 9p = 8q - 12, find the value of pq.
A
12
B
7
C
-7
D
-12
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
9p = 8q - 12
9p = 2(4q) - 12
9p = 2(3q) - 12
9p = 6p - 12
3p = -12
p = -4
\(\frac{3 \times -4}{4} = \frac{4q}{4}\)
q = 13
pq = -3 x -4
= 12
Source: Myschool Past Questions Archive (Record #57206)
Mathematics
WAEC / WASSCE 2019
Number and Numeration
Solution
If (0.25)\(^y\) = 32, find the value of y.
A
y = - \(\frac{5}{2}\)
B
y = -\(\frac{3}{2}\)
C
y = \(\frac{3}{2}\)
D
y = \(\frac{5}{2}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
(0.25)\(^y\) = 32
2\(^{-2y}\) = 3\(^{2}\)
2 - 2y = 5
y = - \(\frac{5}{2}\)
Source: Myschool Past Questions Archive (Record #57211)
Mathematics
WAEC / WASSCE 2019
Statistics and Probability
Solution
There are 8 boys and 4 girls in a lift. What is the probability that the first person who steps out of the lift will be a boy?
A
\(\frac{1}{6}\)
B
\(\frac{1}{4}\)
C
\(\frac{2}{3}\)
D
\(\frac{1}{2}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Total number of people in the lift = 8 boys + 4 girls
= 12 people
probability that a boy comes out = \(\frac{8}{12}\) = \(\frac{2}{3}\)
Source: Myschool Past Questions Archive (Record #57215)
Mathematics
WAEC / WASSCE 2019
Number and Numeration
Solution
Simplify: \(\frac{x^2 - 5x - 14}{x^2 - 9x + 14}\)
A
\(\frac{x - 7}{x + 7}\)
B
\(\frac{x + 7}{x - 7}\)
C
\(\frac{x - 2}{x + 4}\)
D
\(\frac{x + 2}{x - 2}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{x^2 - 5x - 14}{x^2 - 9x + 14}\)
\(\frac{(x - 7)(x + 2)}{(x - 7)(x - 2)}\)
= \(\frac{x + 2}{x - 2}\)
Source: Myschool Past Questions Archive (Record #57221)
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)