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Mathematics
WAEC / WASSCE 2001
Statistics (Data Representation, Central Tendency & Dispersion)
Diagram
Solution
How many students are there in the group?
Attached Figure / Diagram
A
25
B
30
C
52
D
55
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Total number of students = 20 + 16 + 10 + 6
= 52 students
Source: WAEC / JAMB / NECO Classroom Archive (Record #26506)
Mathematics
NECO SSCE 2001
Permutations, Combinations & Probability
Diagram
Solution
51 women wore coloured shoes to a party, out of which 21 wore purple and 9 wore white. if a woman is selected at Random. What is the probability that she is wearing neither a purple shoe nor a white shoe?
Attached Figure / Diagram
A
\(\frac{10}{17}\)
B
\(\frac{7}{17}\)
C
\(\frac{20}{51}\)
D
\(\frac{3}{17}\)
E
\(\frac{1}{51}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
No of women wearing both purple and white shoes = 21 + 9
= 30 women.
No of women wearing neither purple nor white shoes = 51 - 30
= 21 women
\(\therefore\) Probability of picking a woman wearing neither purple nor white shoes
= \(\frac{21}{51}\)
= \(\frac{7}{17}\).
Source: WAEC / JAMB / NECO Classroom Archive (Record #41883)
Mathematics
UTME / JAMB 2001
Inequalities & Linear Programming
Diagram
Solution
Triangle SPT is the solution of the linear inequalities
Attached Figure / Diagram
A
2y - x - 2 ≤ 0, y + 2x + 2 ≥ 0, -2 ≤ x ≤ - 1
B
-2 ≤ x ≤ 2, y ≥ 0, y + 2x + 2 ≤ 0, x ≤ 0
C
2y - x - 2 ≤ 0, y + 2x + 2 ≤ 0, y ≥ 0, x ≤ 0
D
2y - x - 2 ≥ 0, y + 2x + 2 ≤ 0, x ≤ 0
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
The two major lines have their lower portions involved. Since there are no broken lines here,\(\leq\) will hold for the two major lines
that is, 2y - x - 2 = 0 becomes 2y - x - 2 \(\leq\) 0
y + 2x + 2 = 0 becomes y + 2x + 2 \(\leq\) 0
Triangle SPT is located at the positive side of the y-axis, so y \(\geq\) 0, and the negative side of the x-axis so, x \(\leq\)
Therefore, OPTION C is correct.
Source: Myschool Past Questions Archive (Record #10766)
Mathematics
UTME / JAMB 2001
Binary Operations, Matrices & Determinants
Solution
⊗
k
l
m
k
l
m
k
l
m
k
l
m
k
l
m
The identity element with respect to the multiplication shown in the table above is
A
o
B
m
C
l
D
k
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
An element e of the binary expression * is said to be the identity if for any a * e = a
from the given table the identity element is m
i.e K ⨁ m = k
k ⨁ m = k.
Source: Myschool Past Questions Archive (Record #10767)
Mathematics
UTME / JAMB 2001
Statistics (Data Representation, Central Tendency & Dispersion)
Diagram
Solution
The bar chart above shows different colours of passing a particular point of a certain street in two minutes. What fraction of the total number of cars is yellow?
Attached Figure / Diagram
A
3/25
B
2/25
C
1/5
D
4/15
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Number of yellow cars = 3
Total number of cars = 3 + 4 + 8 + 2 + 6 + 2 = 25
Fraction of yellow cars = 3/25
Source: Myschool Past Questions Archive (Record #10770)
Mathematics
WAEC / WASSCE 2001
Plane Geometry, Polygons & Circle Theorems
Solution
Which of the following correctly expresses 48 as a product of prime factors?
A
3 x 4 x 4
B
2 x 3 x 8
C
2 x 2 x 2 x 3 x 4
D
2 x 2 x 2 x 2 x 3
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
48 = 2 x 2 x 2 x 2 x 3
Source: Myschool Past Questions Archive (Record #26472)
Mathematics
WAEC / WASSCE 2001
Number Bases & Modular Arithmetic
Solution
Evaluate \((20_{three})^2 - (11_{three})^2\) in base three
A
101
B
121
C
202
D
2020
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\((20_{three})^2 - (11_{three})^2\)
= \((20_{3} - 11_{3})(20_{3} + 11_{3})\)
= \((2_{3})(101_{3})\)
= \(202_{3}\)
Source: Myschool Past Questions Archive (Record #26473)
Mathematics
WAEC / WASSCE 2001
Indices, Logarithms & Surds
Solution
Evaluate \(log_{10}5 + log_{10}20\)
A
2
B
3
C
4
D
5
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(log_{10}5 + log_{10}20\)
\(log_{10}[5\times 20]\)
\(log_{10}100\)
\(log_{10}10^2\)
\(2log_{10}10 = 2\)
Source: Myschool Past Questions Archive (Record #26474)
Mathematics
WAEC / WASSCE 2001
Sets, Logic & Venn Diagrams
Solution
In a class of 80 students, every students studies Economics or Geography or both. If 65 students study Economics and 50 study Geography, how many study both subjects?
A
15
B
30
C
35
D
45
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Let c = no of students that offered both subjects
\(\therefore\) No of students offering Economics = 65 - c
No of students offering Geography = 50 - c
65 - c + c + 50 - c = 80
115 - c = 80
c = 35
35 students offer both Economics and Geography.
Source: Myschool Past Questions Archive (Record #26475)
Mathematics
WAEC / WASSCE 2001
Variations
Solution
If N varies directly as M and N = 8 when M = 20 find M when N = 7
A
13
B
15
C
\(17\frac{1}{2}\)
D
\(18\frac{1}{2}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
N ∝ M
∴N = kM where k is a constant
N = 8 when M = 20
∴ 8 = k x 20
\(k = \frac{8}{20}\) = \(\frac{2}{5}\)
∴ N = \(\frac{2 M}{5}\)
If N = 7
∴ 7 = \(\frac{2 M}{5}\)
M = \(\frac{35}{2}\) = 17\(\frac{1}{2}\)
Source: Myschool Past Questions Archive (Record #26476)
Mathematics
WAEC / WASSCE 2001
Fractions, Decimals, Percentages & Approximations
Solution
Express 0.0462 in standard form
A
0.460 x 10-1
B
0.462 x 10-2
C
4.62 x 10-1
D
4.62 x 10-2
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
0.0462 in standard form
= 4.62 x \(10^{-2}\)
Option D
Source: Myschool Past Questions Archive (Record #26477)
Mathematics
WAEC / WASSCE 2001
Fractions, Decimals, Percentages & Approximations
Solution
In a bag of oranges, the ratio of the good ones to the bad ones is 5:4. If the number of bad oranges in the bag is 36, how many oranges are there in the altogether?
A
81
B
72
C
54
D
45
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Ratio of good ones to bad ones is 5:4; If 36 is bad;
∴ the good ones = \(\frac{5\times 36}{4}=45\) oranges.
The total number of oranges is 36 + 45 = 81.
Source: Myschool Past Questions Archive (Record #26478)
Mathematics
WAEC / WASSCE 2001
Fractions, Decimals, Percentages & Approximations
Solution
A boy estimated his transport fare for a journey as N190 instead of N200. Find the percentage error in his estimate
A
95%
B
47.5%
C
5.26%
D
5%
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
The percentage error is \(\frac{error}{actual value}\times \frac{100}{1}\)%
= \(\frac{200-190}{200}\times \frac{100}{1}\)
= \(\frac{10}{200}\times \frac{100}{1}\)% = 5%
Source: Myschool Past Questions Archive (Record #26479)
Mathematics
WAEC / WASSCE 2001
Plane Geometry, Polygons & Circle Theorems
Solution
Evaluate \(5\frac{2}{5}\times \left(\frac{2}{3}\right)^2\div\left(1\frac{1}{2}\right)^{-1}\)
A
\(\frac{8}{25}\)
B
\(\frac{12}{25}\)
C
\(3\frac{3}{5}\)
D
\(4\frac{1}{8}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(5\frac{2}{5}\times \left(\frac{2}{3}\right)^2 \div \left(1\frac{1}{2}\right)^{-1}\)
\(\frac{27}{5}\times \frac{4}{9} \times \frac{3}{2} = 3\frac{3}{5}\)
Source: Myschool Past Questions Archive (Record #26480)
Mathematics
WAEC / WASSCE 2001
Sequences & Series (AP & GP)
Solution
The nth term of a sequence is \(2^{2n-1}\). Which term of the sequence is \(2^9?\)
A
3rd
B
4th
C
5th
D
6th
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(T_{n} = 2^{2n - 1}\)
\(2^{2n - 1} = 2^9\)
\(2n - 1 = 9 \implies 2n = 9 + 1\)
\(2n = 10 \implies n = 5\)
The 5th term = 2\(^9\)
Source: Myschool Past Questions Archive (Record #26481)