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Mathematics
WAEC / WASSCE 2019
Number and Numeration
Solution
Simplify, correct to three significant figures, (27.63)\(^2\) - (12.37)\(^2\)
A
614
B
612
C
611
D
610
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
(27.63)\(^2\) - (12.37)\(^2\)
= (27.63 + 12.37)(27.63 - 12.37)
= 40 x 15.26
= 610
Source: Myschool Past Questions Archive (Record #57100)
Mathematics
WAEC / WASSCE 2019
Number and Numeration
Solution
If 7 + y = 4 (mod 8), find the least value of y, 10 \(\leq y \leq 30\)
A
11
B
13
C
19
D
21
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
7 + y = 4 (mod 8)
y = 4 - 7 (mod 8)
y = -3 + 8 (mod 8)
y = 5 + 8 (mod 8)
y = 13
Source: Myschool Past Questions Archive (Record #57102)
Mathematics
WAEC / WASSCE 2019
Number and Numeration
Solution
Evaluate; \(\frac{\log_3 9 - \log_2 8}{\log_3 9}\)
A
-\(\frac{1}{3}\)
B
\(\frac{1}{2}\)
C
\(\frac{1}{3}\)
D
-\(\frac{1}{2}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{\log_3 9 - \log_2 8}{\log_3 9}\)
= \(\frac{\log_3 3^2 - \log_2 2^3}{\log_3 3^2}\)
= \(\frac{2 -3}{2}\)
= \(\frac{-1}{2}\)
Source: Myschool Past Questions Archive (Record #57125)
Mathematics
WAEC / WASSCE 2019
Number and Numeration
Solution
If 23\(_y\) = 1111\(_{\text{two}}\), find the value of y
A
4
B
5
C
6
D
7
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
23\(_y\) = 1111\(_{\text{two}}\),
2 x y\(^1\) + 3 x y\(^0\) = 1 x 2\(^3\) + 1 x 2\(^1\) + 1 x 2\(^o\)
2y + 3 = 8 + 4 + 2 + 1
2y + 3 = 15
\(\frac{2y}{2}\)
\(\frac{12}{2}\)
y = 6
Source: Myschool Past Questions Archive (Record #57128)
Mathematics
WAEC / WASSCE 2019
Algebra
Solution
If 6, P, and 14 are consecutive terms in an Arithmetic Progression (AP), find the value of P.
A
9
B
10
C
6
D
8
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
6, p, 14
14 - p = p - 6
14 + 6 = p - 6
14 + 6 = p + p
\(\frac{2p}{2}\)
= \(\frac{20}{2}\)
p = 10
Source: Myschool Past Questions Archive (Record #57150)
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)