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Mathematics
UTME / JAMB 2022
Fractions, Decimals, Percentages & Approximation
Solution
What will be the result obtained when the numerator of \(\frac{96}{50}\) is decreased by 37.5% and its denominator decreased by 20%.
A
1.5
B
\(\frac{5}{2}\)
C
\(\frac{96}{48}\)
D
0.5
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Numerator: 96 → 37.5% of 96 = 36
Decreased by 36 → 96 - 36
New numerator = 60
Denominator: 50 → 20% of 50 = 10
Decreased by 10 → 50 - 10 = 40
New Denominator = 40
New fraction = \(\frac{60}{40}\) or 1.5
Source: WAEC / JAMB / NECO Classroom Archive (Record #64278)
Mathematics
UTME / JAMB 2022
Fractions, Decimals, Percentages & Approximation
Solution
A poultry farmer realized 200 eggs from his birds and sold 5 \(\frac{1}{2}\) crates of eggs. What percentages of eggs are left?
A
82.5%
B
15%
C
17.5%
D
85%
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
5 crates = 30 eggs * 5 = 150eggs
1/2 crate = 15 eggs
Total sold = 165
remainder = 200 - 165 = 35
And 35 is equivalent 17.5% of the realized eggs
Source: WAEC / JAMB / NECO Classroom Archive (Record #64279)
Mathematics
UTME / JAMB 2022
Fractions, Decimals, Percentages & Approximation
Solution
If a dress is sold for #3800.00 at 20% discount. what is its original price?
A
#3,000.00
B
#4,000.00
C
#5,000.00
D
#4,750.00
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
It is given that the cost of the item reduces to #3800.00 after the discount on the item.
Let original price = x
x – (20% of x) = 100
⇒ x – 0.2x = 100
⇒ 0.8x = #3800
⇒ x = \(\frac{3800}{0.8}\)
⇒ x = 4,750
Source: WAEC / JAMB / NECO Classroom Archive (Record #64412)
Mathematics
WAEC / WASSCE 2022
Fractions, Decimals, Percentages & Approximation
Solution
Evaluate, correct to four significant figures, (573.06 x 184.25).
A
105600.00
B
105622.00
C
105500.00
D
105632.00
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
573.06 x 184.25 = 105,586.305
1,05600.00 to four significant figure
What are the Rules for significant figures?
Significant Figures
All non-zero numbers ARE significant.
Zeros between two non-zero digits ARE significant.
Leading zeros are NOT significant.
Trailing zeros to the right of the decimal ARE significant.
Trailing zeros in a whole number with the decimal shown ARE significant.
Source: WAEC / JAMB / NECO Classroom Archive (Record #64420)
Mathematics
WAEC / WASSCE 2022
Fractions, Decimals, Percentages & Approximation
Solution
A weaver bought a bundle of grass for $ 50.00 from which he made 8 mats. If each mat was sold for $ 15.00, find the percentage profit.
A
240%
B
140%
C
120%
D
40%
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
cost price = $50
Selling price = 15 * 8 = $120
percentage profit = \(\frac{sp-cp}{cp}\) * 100 → \(\frac{120-50}{50}\) * 100
percentage profit = 70 * 2 → 140%
Source: WAEC / JAMB / NECO Classroom Archive (Record #64465)
Mathematics
WAEC / WASSCE 2022
Fractions, Decimals, Percentages & Approximation
Solution
Three boys shared D 10,500.00 in the ratio 6:7:8. Find the largest share.
A
4000
B
5000
C
4500
D
3500
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Total proportion is 6+7+8 = 21
\(\frac{6 * 10500}{21}\) = 3000
\(\frac{7 * 10500}{21}\) = 3500
\(\frac{8 * 10500}{21}\) = 4000
The largest share is 4000
Source: WAEC / JAMB / NECO Classroom Archive (Record #64513)
Mathematics
WAEC / WASSCE 2022
Fractions, Decimals, Percentages & Approximation
Solution
The length of a piece of stick is 1.75 m. A boy measured it as 1.80 m. Find the percentage error
A
4\(\frac{4}{7}\)
B
2\(\frac{6}{7}\)
C
2\(\frac{7}{9}\)
D
4\(\frac{7}{9}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Error = 1.80 - 1.75 = 0.05
%error = \(\frac{error}{original length}\)
= \(\frac{0.05 * 100}{1.75}\)
= 2.85 or 2\(\frac{6}{7}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #64519)
Mathematics
WAEC / WASSCE 2022
Fractions, Decimals, Percentages & Approximation
Solution
.Find the value of x such that \(\frac{1}{x}\) +\(\frac{4}{3x}\) - \(\frac{5}{6x}\) + 1 = 0
A
\(\frac{1}{6}\)
B
\(\frac{1}{4}\)
C
\(\frac{-3}{2}\)
D
\(\frac{-7}{6}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{1}{x}\) +\(\frac{4}{3x}\) - \(\frac{5}{6x}\) + 1 = 0
using 6x as lcm
→ \(\frac{6+8-5+6x}{6x}\)
→ \(\frac{9+6x}{6x}\) = 0
9+6x = 0
6x = -9
x = \(\frac{-9}{6}\) or \(\frac{-3}{2}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #64815)
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
UTME / JAMB 2022
Sets & Set Operations
Diagram
Solution
The shaded portion in the venn diagram above represents?
Attached Figure / Diagram
A
F - (E n F) - (G n F)
B
E' n F n G'
C
E u F u G
D
F
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
-The shaded/stripped portion in the diagram is set F only.
-This implies that sets E and G though present in the Universal set, are not included in the expression.
-Mathematically; we have E' n F n G'
Source: WAEC / JAMB / NECO Classroom Archive (Record #64153)
Mathematics
UTME / JAMB 2022
Sets & Set Operations
Solution
If n(P) = 20 and n(Q) = 30 and n(PuQ) = 40, find the value n(PnQ)
A
10
B
30
C
15
D
40
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
n(PuQ) = n(p) + n(q) - n(PnQ)
40 = 20 + 30 - n(PnQ)
n(PnQ) = 50 - 40 = 10
Source: WAEC / JAMB / NECO Classroom Archive (Record #64402)
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)