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Mathematics
WAEC / WASSCE 2022
Fractions, Decimals, Percentages & Approximation
Solution
A local community has two newspapers: the morning tomes and the evening dispatch. The morning times is read by 45% of the households. The Evening Dispatch is read by 60% of the households. Twenty percent of the households read both papers. What is the probability that a particular household reads at least one paper?
A
0.45
B
0.65
C
0.85
D
0.95
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Note that the group that reads both papers is being counted twice.
(percentages add up beyond 100%)
Let M = those reading the Morning Times,
E = those reading the Evening Dispatch
P( M or E) = P(M) + P(E) – P(M and E)
= 0.45 + 0.60 – 0.20
= 0.85
Source: WAEC / JAMB / NECO Classroom Archive (Record #65392)
Mathematics
WAEC / WASSCE 2022
Fractions, Decimals, Percentages & Approximation
Solution
A trader made a loss of 15% when an article was sold. Find the ratio of the selling price : cost price
A
3:20
B
3:17
C
17:20
D
20:23
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Where the loss= (100-15)%
= 85%
Ratio = 85:100 or 17:20
Source: WAEC / JAMB / NECO Classroom Archive (Record #65398)
Mathematics
WAEC / WASSCE 2022
Sets & Set Operations
Solution
Given that A and B are sets such that n(A) = 8, n(B)=12 and n(AnB) =3, find n(AuB).
A
15
B
17
C
20
D
23
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
n(AuB) = n(A) + n(B) - n(AnB)
n(AuB) = 8 + 12 - 3
= 17
Source: WAEC / JAMB / NECO Classroom Archive (Record #64431)
Mathematics
WAEC / WASSCE 2022
Mathematical Logic
Solution
Consider the statements:
p: Stephen is intelligent
q: Stephen is good at Mathematics
If p⇒q, which of the following is a valid conclusion?
A
If Stephen is good at Mathematics, then he is intelligent
B
If Stephen is not good at Mathematics, then he is not intelligent
C
If Stephen is not intelligent, then he is not good at Mathematics
D
If Stephen is not good at Mathematics, then he is intelligent
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
If p implies (→) q
then not (~) q → not (~) p
Option B
Source: WAEC / JAMB / NECO Classroom Archive (Record #64807)
Mathematics
WAEC / WASSCE 2022
Modular Arithmetic
Solution
Evaluate 23 x 54 (mod 7)
A
2
B
3
C
5
D
6
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
23 x 54 = 1242
In mod 7;
1242 \div 7 = 177 R 3
Hence; 1242 ≡ 3
Source: WAEC / JAMB / NECO Classroom Archive (Record #64451)
Mathematics
WAEC / WASSCE 2022
Financial Arithmetic
Solution
Mary has $ 3.00 more than Ben but $ 5.00 less than Jane. If Mary has $ x, how much does Jane and Ben have altogether?
A
$(2x-8)
B
$(2x+8)
C
$(2x-2)
D
$(2x+2)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Mary(m),
Ben(b)
Jane(j)
m = b +3
m = j - 5
where m = x
b = x - 3 and j = x + 5
b+ j → x - 3 + x + 5
= 2x +2
Jane and Ben have $(2x+2)
Source: WAEC / JAMB / NECO Classroom Archive (Record #64806)
Mathematics
WAEC / WASSCE 2022
Variations
Solution
M varies directly as n and inversely as the square of p. If M= 3 when n = 2 and p = 1, find M in terms of n and p.
A
\(\frac{3n}{2p^2}\)
B
\(\frac{2n}{3p^2}\)
C
\(\frac{2n}{3p}\)
D
\(\frac{3n^2}{2p^2}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
M = \(\frac{nk}{p^2}\)
k → \(\frac{mp^2}{n}\) = \(\frac{3x1^2}{2}\)
k = \(\frac{3}{2}\)
: m = \(\frac{3xn}{2p^2}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #64504)
Mathematics
WAEC / WASSCE 2022
Change of Subject of Formula
Solution
Make t the subject of k = \(m \sqrt \frac{t-p}{r}\)
A
\(\frac{k^2r + p}{m^2}\)
B
\(\frac{k^2r + pm^2}{m^2}\)
C
\(\frac{k^2r - p}{m^2}\)
D
\(\frac{k^2r + p^2}{m^2}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
square both sides to remove the square root
k\(^2\) = m\(^2\) \(\frac{t-p}{r}\)
\(\frac{k^2r}{m^2}\) = t - p
t = \(\frac{k^2r}{m^2}\) + p
t = \(\frac{k^2r + pm^2}{m^2}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #64820)
Mathematics
WAEC / WASSCE 2022
Quadratic Equations
Solution
If the equations x\(^2\) - 5x + 6 = 0 and x\(^2\) + px + 6 = 0 have the same roots, find the value of p.
A
5
B
6
C
-5
D
-6
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
If "x" is the same for both equations, then they are equivalent.
(i.e., the equations have same roots), then the equations are equivalent.
Then p = -5
Source: WAEC / JAMB / NECO Classroom Archive (Record #65396)
Mathematics
WAEC / WASSCE 2022
Quadratic Equations
Solution
Solve 6x\(^2\) = 5x - 1
A
x = 2,3
B
x = 0,3
C
x = \(\frac{1}{2}\), \(\frac{1}{3}\)
D
x = \(\frac{1}{2}\), \(\frac{-1}{3}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
6x\(^2\) = 5x - 1
→ 6x\(^2\) - 5x + 1 = 0
Factorization:
factors are -3x and -2x
6x\(^2\) - 3x -2x + 1 = 0
(6x\(^2\) - 3x) (-2x + 1) = 0
3x(2x-1) -1(2x-1) = 0
(3x-1) (2x-1) = 0
x = \(\frac{1}{2}\), \(\frac{1}{3}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #65404)
Mathematics
WAEC / WASSCE 2022
Algebraic Fractions
Solution
If a = 3 and b = -7, find the value of \(\frac{5b+(a+b)^2}{(a-b)^2}\)
A
0.51
B
0.91
C
-0.19
D
-0.51
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{5b+(a+b)^2}{(a-b)^2}\)
= \(\frac{5 * -7 +(3+ -7)^2}{(3- -7)^2}\)
= \(\frac{-35 + 16}{10^2}\)
= \(\frac{-19}{100}\) or -0.19
Source: WAEC / JAMB / NECO Classroom Archive (Record #64510)
Mathematics
WAEC / WASSCE 2022
Progressions (AP & GP)
Solution
Find the 17term of the Arithmetic Progression (A.P):-6,-1,4
A
-91
B
-86
C
74
D
79
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
common difference d = -1 - [-6] → -1 + 6
d = 5; a = -6
T\(_n\) = a + (n-1)d
: T\(_{17}\) = -6 + (17 - 1) 5
→ -6 + (16)5
→ -6 + 80 = 74
Source: WAEC / JAMB / NECO Classroom Archive (Record #64499)
Mathematics
WAEC / WASSCE 2022
Mensuration
Solution
The lengths of the parallel sides of a trapezium are 9cm and 12cm. If the area of the trapezium is 105cm\(^2\), find the perpendicular distance between the parallel sides.
A
5cm
B
7cm
C
10cm
D
15cm
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Area of a trapezium = \(\frac{[a+b]h}{2}\)
105 = \(\frac{[9+12]h}{2}\) → 105 x 2 =21h
h = \(\frac{210}{21}\) → 10cm
Source: WAEC / JAMB / NECO Classroom Archive (Record #65389)
Mathematics
WAEC / WASSCE 2022
Mensuration
Solution
Find the volume of a cone of radius 3.5cm and vertical height 12cm. [Take π = 22/7]
A
15.5cm\(^3\)
B
21.0cm\(^3\)
C
142cm\(^3\)
D
154cm\(^3\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
volume of a cone = ⅓ \pi r2h → \(\frac{1*22*3.5*3.5*12}{3*7}\)
= 154cm\(^3\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #65391)
Mathematics
WAEC / WASSCE 2022
Lengths and Perimeters
Diagram
Solution
In the diagram, ∠POQ = 150 and the radius of the circle PSQR is 4.2cm. [take π = 22/7]
What is the length of the minor arc?
Attached Figure / Diagram
A
11cm
B
15.4cm
C
17.64cm
D
23.10cm
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\frac{\theta}{360}\) * 2 * \pi * r → \(\frac{150 * 2 * 22 * 4.2}{360 x 7}\)
= 11cm
Source: WAEC / JAMB / NECO Classroom Archive (Record #64823)