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Mathematics
UTME / JAMB 2002
Number and Numeration
Diagram
Solution
In the diagram above, PST is a straight line, PQ = QS = RS. If ∠RST = 72o, find x
Attached Figure / Diagram
A
36o
B
18o
C
72o
D
24o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
In Δ PQS, ∠PSQ = X(base ∠s of isoc Δ PQS)
In Δ QRS, ∠RQS = ∠PSQ + X(Extr ∠ = sum of two intr. opp ∠s)
∴ ∠RQS = X + X
= 2X
Also ∠QRS = 2X(base ∠s of isoc Δ QRS in Δ PRS,
72 = ∠RPS + ∠PRS(Extr, ∠ = sum of two intr. opp ∠s)
∴ 72 = x + 2x
72 = 3x
x = 72/3
x = 24o
Source: Myschool Past Questions Archive (Record #10927)
Mathematics
UTME / JAMB 2002
Number and Numeration
Diagram
Solution
In the diagram above, a cylinder is summounted by a hemisphere bowl. Calculate the volume of the solid.
Attached Figure / Diagram
A
180 πcm3
B
162 πcm3
C
216 πcm3
D
198 πcm3
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Volume of cylinder = πr2h
= π x 32 x 20
= π x 9 x 20
= 180 πcm3
Volume of hemisphere = 2/3πr3
= 2/3 x π x 32
= 2 x π x 32
= 2 x π x 9
= 18π
= Volume of the solid = 180π x 18π
= 198πcm3
Source: Myschool Past Questions Archive (Record #10929)
Mathematics
UTME / JAMB 2002
Number and Numeration
Solution
No. of days
1
2
3
4
5
6
No. of students
20
x
50
40
2x
60
The distribution above shows the number of days a group of 260 students were absents from school in a particular term. How many students were absent for at least four days in the term
A
210
B
40
C
120
D
160
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
20 + X + 50 + 40 + 2X + 60 = 260
3X + 170 = 260
3X = 260 - 170
3x = 90
x = 30
Absent for at least 4 days
4
5
6
40
2x
60
i.e 40 + 2x + 60 = 40 + (2 x 30) + 60
= 40 + 60 + 60
= 160
Source: Myschool Past Questions Archive (Record #10931)
Mathematics
WAEC / WASSCE 2002
Number and Numeration
Solution
A right pyramid is on a square base of side 4cm. The slanting side of the pyramid is \(2\sqrt{3}\) cm. Calculate the volume of the pyramid
A
\(5\frac{1}{3}cm^3\)
B
\(10\frac{2}{3}cm^3\)
C
\(16cm^3\)
D
\(32cm^3\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(BD^2 = 4^2 + 4^2\)
\(BD = \sqrt{16 + 16} = \sqrt{32}\)
\(BD = 4\sqrt{2} cm\)
\((2\sqrt{3})^2 = (2\sqrt{2})^2 + h^2\)
\(h^2 = 12 - 8 = 4\)
\(h = \sqrt{4} = 2 cm\)
Volume of pyramid = \(\frac{a^2 h}{3}\)
= \(\frac{4^2 \times 2}{3}\)
= \(\frac{32}{3} = 10\frac{2}{3} cm^3\)
Source: Myschool Past Questions Archive (Record #26512)
Mathematics
WAEC / WASSCE 2002
Number and Numeration
Solution
The height of a right circular cone is 4cm. The radius of its base is 3cm. Find the curved surface area
A
\(9\pi cm^2\)
B
\(15\pi cm^2\)
C
\(16\pi cm^2\)
D
\(20\pi cm^2\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Curved surface area or a cone \(=\pi rl\)
from the information \(l^2 = 4^2 + 3^2 = 16+9\\
l = \sqrt{25} = 5; ∴ C.S.A\hspace{1mm} = \frac{22}{7}\times 3 \times 5\\
Since \frac{22}{7}=\pi ∴ C.S.A\hspace{1mm} =\hspace{1mm}15\pi\)
Source: Myschool Past Questions Archive (Record #26513)
Mathematics
WAEC / WASSCE 2002
Number and Numeration
Solution
Simplify \(5\frac{1}{4}\div \left(1\frac{2}{3}- \frac{1}{2}\right)\)
A
\(1\frac{3}{4}\)
B
\(3\frac{1}{2}\)
C
\(4\frac{1}{2}\)
D
\(8\frac{1}{2}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(5\frac{1}{4}\div \left(1\frac{2}{3}- \frac{1}{2}\right)\\
\frac{21}{4}\div \left(1\frac{4-3}{6}\right)\\
\frac{21}{4}\div \left(1\frac{1}{6}\right)\\
\frac{21}{4} \times \frac{6}{7}= 4\frac{1}{2}\)
Source: Myschool Past Questions Archive (Record #26522)
Mathematics
WAEC / WASSCE 2002
Number and Numeration
Solution
Find the value of x in 0.5x + 2.6 = 5x + 0.35
A
0.5
B
2
C
2.6
D
5
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(0.5x + 2.6 = 5x + 0.35\\
0.5x - 5x = 0.35-2.6\\
-4.5x = -2.25\\
x = \frac{-2.25}{-4.5}\\
0.5\)
Source: Myschool Past Questions Archive (Record #26525)
Mathematics
WAEC / WASSCE 2002
Number and Numeration
Solution
If \(M5_{ten} = 1001011_{two}\) find the value of M
A
5
B
6
C
7
D
8
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(M5_{ten} = 1001011_{two}\\
=1 \times 2^6 + 0\times 2^5 + 0\times 2^4 + 1\times 2^3 + 0\times 2^2 + 1\times 2^1 \\
=64+8+2+1=75_{ten}\\
∴ m = 7 \)
Source: Myschool Past Questions Archive (Record #26527)
Mathematics
WAEC / WASSCE 2002
Number and Numeration
Diagram
The diagram is the graph of \(y = 6 + x - x^2\). The graph intercepts the x- axis at P and R and the y- axis at Q.
What is the value of y at Q?
Attached Figure / Diagram
A
\(6\frac{1}{3}\)
B
6
C
3
D
zero
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option A.
Source: Myschool Past Questions Archive (Record #26528)
Mathematics
WAEC / WASSCE 2002
Number and Numeration
Diagram
Solution
The diagram is the graph of \(y = 6 + x - x^2\). The graph intercepts the x-axis at P and R and the y-axis at Q.
When \(y = 3\frac{1}{3}\), what is the positive value of x?
Attached Figure / Diagram
A
\( 2\frac{1}{2}\)
B
\( 2\frac{1}{5}\)
C
\( 1\frac{1}{5}\)
D
zero
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Draw a straight horizontal line across the y-axis at y = 3\(\frac{1}{3}\). let the line cut through the curve.
the points where the horizontal line meets the curve, trace it down to the x-axis to obtain the values of x when y = 3\(\frac{1}{3}\)
take only the positive value of x.
Source: Myschool Past Questions Archive (Record #26530)
Mathematics
WAEC / WASSCE 2002
Number and Numeration
Solution
If log 2 = 0.3010 and log 2\(^y\) = 1.8062, find; correct to the nearest whole number, the value of y.
A
6
B
5
C
4
D
-5
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(log2 = 0.3010\hspace{1mm}given\\
log2^y = 1.8062\\
∴ ylog2 = 1.8062\\
y=\frac{1.8062}{logy}=\frac{1.8062}{0.3010}=6\)
Source: Myschool Past Questions Archive (Record #26532)
Mathematics
WAEC / WASSCE 2002
Number and Numeration
Solution
The ratio of the number of men to the number of women in a 20 member committee is 3:1. How many women must be added to the 20-member committee so as to make the ratio of men to women 3:2?
A
2
B
5
C
7
D
9
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
20 members in the ratio 3:1
Number of women = \(\frac{1}{4} \times 20\)
= 5
Let the number of women to be added = x
Total number of members in the committee = 20 + x
\(\frac{5 + x}{20 + x} = \frac{2}{5}\)
\(5(5 + x) = 2(20 + x)\)
\(25 + 5x = 40 + 2x \implies 5x - 2x = 40 - 25\)
\(3x = 15 \implies x = 5\)
Source: Myschool Past Questions Archive (Record #26534)
Mathematics
WAEC / WASSCE 2002
Number and Numeration
Solution
If (x + 3) varies directly as y and x = 3 when y = 12, what is the value of x when y = 8?
A
1
B
\(\frac{1}{2}\)
C
\(-\frac{1}{2}\)
D
-1
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\((x+3) \propto y\\
∴x + 3 = ky\hspace{1mm}when\hspace{1mm}x = 3, y = 12\\
3+3 = 12k\\
∴ k = \frac{1}{2}\\
\Longrightarrow x + 3 = \frac{1}{2}y\) to find x when y = 8
\(x + 3 = \frac{1}{2}\times 8\\
x=4-3\\
x = 1\)
Source: Myschool Past Questions Archive (Record #26535)
Mathematics
WAEC / WASSCE 2002
Number and Numeration
Solution
If (-3, -4) is a point on the line y = mx + 2 find the value of m.
A
-2
B
\(\frac{7}{4}\)
C
2
D
\(\frac{8}{3}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
If (-3, -4) is a point on the line then
-4 = -3m + 2
-4 - 2 = -3m
-6 = -3m
m = 2
Source: Myschool Past Questions Archive (Record #26538)
Mathematics
WAEC / WASSCE 2002
Number and Numeration
Solution
Simplify \(\frac{1}{1-x} + \frac{2}{1+x}\)
A
\(\frac{x+3}{1-x^2}\)
B
\(\frac{x-3}{1+x^2}\)
C
\(\frac{3-x}{1-x^2}\)
D
\(\frac{3-x}{1+x^2}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{1}{1-x} + \frac{2}{1+x}\\
\frac{1+x+2-2x}{(1-x)(1+x)} = \(\frac{3-x}{1-x^2}\)\)
Source: Myschool Past Questions Archive (Record #26542)