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Mathematics
UTME / JAMB 2002
Plane Geometry, Polygons & Circle Theorems
Solution
The range of the data: k+2, k-3, k+4, k-2, k, k-5, k+3, k-1, and k+6 is
A
10
B
11
C
6
D
8
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Range = Highest value - Lowest value
= (k + 6) - (k - 5)
= 11
Source: Myschool Past Questions Archive (Record #3385)
Mathematics
UTME / JAMB 2002
Permutations, Combinations & Probability
Solution
The probability of a student passing any exam is 2/3. If the student takes three exams, what is the probability that he will not pass any of them?
A
2/3
B
4/9
C
8/27
D
1/27
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
P(not passing exam) = \(1 - \frac{2}{3} = \frac{1}{3}\)
P(not passing any of the three exams) = \(\frac{1}{3} \times \frac{1}{3} \times \frac{1}{3}\)
= \(\frac{1}{27}\)
Source: Myschool Past Questions Archive (Record #3388)
Mathematics
UTME / JAMB 2002
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
The acres for rice, pineapple, cassava, cocoa, and palm oil in a certain district are given respectively as 2, 5, 3, 11, and 9. What is the angle sector for cassava in a pie chart?
A
108°
B
180°
C
36°
D
60°
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Total: 2 + 5 + 3 + 11 + 9 = 30
Cassava: \(\frac{3}{30} \times 360^\circ = 36^\circ\)
Source: Myschool Past Questions Archive (Record #3390)
Mathematics
UTME / JAMB 2002
Plane Geometry, Polygons & Circle Theorems
Solution
How many three-digit numbers can be formed from 32564 without repeating any of the digits?
A
120
B
10
C
20
D
60
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
To get the answer, we simply do
\(\frac{5!}{(5 - 3)!}\)
= \(\frac{5 \times 4 \times 3 \times 2 \times 1}{2 \times 1}\)
= 60
Source: Myschool Past Questions Archive (Record #3393)
Mathematics
UTME / JAMB 2002
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
The mean of a set of six numbers is 60. If the mean of the first five is 50, find the sixth number in the set.
A
105
B
100
C
95
D
110
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Let the sum of the first five numbers and the sixth number be x and t respectively.
\(\frac{x + t}{6} = 60 \implies x + t = 360\)
\(\frac{x}{5} = 50 \implies x = 250\)
\(\therefore t = 360 - 250 = 110\)
Source: Myschool Past Questions Archive (Record #3395)
Mathematics
UTME / JAMB 2002
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
Calculate the mean deviation of the set of numbers 7, 3, 14, 9, 7, and 8.
A
13/6
B
5/2
C
7/6
D
7/3
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
x
7
3
14
9
7
8
Total
\(x - \bar{x}\)
-1
-5
6
1
-1
0
\(|x - \bar{x}|\)
1
5
6
1
1
0
14
Mean : \(\frac{7 + 3 + 14 + 9 + 7 + 8}{6} = \frac{48}{6} = 8\)
Mean deviation : \(\frac{\sum |x - \bar{x}|}{n} = \frac{14}{6} = \frac{7}{3}\)
Source: Myschool Past Questions Archive (Record #3396)
Mathematics
UTME / JAMB 2002
Indices, Logarithms & Surds
Diagram
Solution
In the diagram above , XZ is the diameter of the circle XZW, with center O and radius 15/2 cm. If XY = 12 cm, find the area of the triangle XYZ
Attached Figure / Diagram
A
54 cm2
B
45 cm2
C
27 cm2
D
75 cm2
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Since radius = \(\frac{15}{2}\) diameter = 2 * (\(\frac{15}{2}\)) = 15cm
XYZ is a right-angled triangle (since
Source: Myschool Past Questions Archive (Record #7728)
Mathematics
UTME / JAMB 2002
Sets, Logic & Venn Diagrams
Diagram
Solution
The venn diagram above shows the numbers of students offering music and history in a class of 80 students. If a student is picked at random from the class, what is the probability that he offers Music only?
Attached Figure / Diagram
A
0.38
B
0.13
C
0.50
D
0.25
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
30 - x + x + 40 - x = 80 - 20
70 - x = 60
- x = 60 - 70
- x = - 10
∴ x = 10
Music only = 30 - x
= 30 - 10
20
P(music only) = 20/80
= 1/4
= 0.25
Source: Myschool Past Questions Archive (Record #7734)
Mathematics
UTME / JAMB 2002
Inequalities & Linear Programming
Diagram
Solution
Use the graph above to find the values of p and q if px + qy \(\geq\) 4
Attached Figure / Diagram
A
p = 2, q = -1
B
p = -1, q = 2
C
p = 2, q = 2
D
p = 1, q = 2
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
m = \(\frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 0}{0 - (4)} = \frac{2}{4} = \frac{1}{2}\)
\(\frac{y_2 - y_1}{x_2 - x_1} \geq m\)
\(\frac{y - 0}{x + 4} \geq \frac{1}{2}\)
2y \(\geq\) x + 4, -x + 2y \(\geq\) 4 = px + qy \(\geq\) 4
p = -1, q = 2
Source: WAEC / JAMB / NECO Classroom Archive (Record #33102)
Mathematics
NECO SSCE 2002
Mensuration (Areas, Perimeters & Volumes)
Solution
A wire was shaped to form a square of area 81cm\(^2\). An equilateral triangle was formed by the same wire,What is the length of a side of the triangle formed?
A
3cm
B
6cm
C
9cm
D
12cm
E
27cm
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Area of a square = L X L = 81
: L = 9
Perimeter of square = 4 X L
4 X 9 = 36cm
An equilateral triangle with equal sides:
36/3 = 12cm
Source: WAEC / JAMB / NECO Classroom Archive (Record #42139)
Mathematics
NECO SSCE 2002
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
The mean and the range of the set of numbers: 1.20, 1.00, 0.90, 1.40, 0.80, 0.80, 1.20 and 1.10 are p and q respectively. What is the value of p ÷ q?
A
1.11
B
65
C
1.85
D
2.45
E
3.85
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Mean of 1.20, 1.00, 0.90, 1.40, 0.80, 0.80, 1.20 and 1.10
→ \(\frac{8.4}{8}\) = 1.05 → p
Range = 1.40 - 0.80 = 0.60 → q
p \div q = 1.05 \div 0.60
= 1.75
Source: WAEC / JAMB / NECO Classroom Archive (Record #42203)
Mathematics
UTME / JAMB 2002
Plane Geometry, Polygons & Circle Theorems
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
Mensuration (Areas, Perimeters & Volumes)
Diagram
Solution
In the diagram above are two concentric circles of radii r and R respectively with center O. If r = 2/3R, express the area of the shaded portion in terms of π and R
Attached Figure / Diagram
A
21/25πR2
B
9/25πR2
C
21/23πR2
D
5/9πR2
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
r = \(\frac{2}{3}\)R
∴R = \(\frac{3}{3}\)R
Area of small circle = πr2
= π(\(\frac{2R}{3}\))2
Area of the big circle πr2 = π\(\frac{(3R)^2}{3}\)
Area of shaded portion = π(\(\frac{3R}{3}\))2 - π(\(\frac{2R}{3}\))2
= π[(\(\frac{3R}{3}\))2 - (\(\frac{2R}{3}\))2]
= π[(\(\frac{3R}{3}) + (\frac{2R}{3}) - (\frac{3R}{3}\)) - (\(\frac{2R}{3}\))]
= π[(\(\frac{5R}{3}\)) (\(\frac{R}{3}\))]
= π x \(\frac{5R}{3}\) x \(\frac{R}{3}\)
= 5/9πR2
Source: Myschool Past Questions Archive (Record #10928)
Mathematics
UTME / JAMB 2002
Mensuration (Areas, Perimeters & Volumes)
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
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
The triangle PQR above is
Attached Figure / Diagram
A
an obtuse-angled triangle
B
a scalene triangle
C
an isosceles triangle
D
an equilateral triangle
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
∠PQR = 180 - 128 (∠s on a straight line)
= 52o
∠QPR + 76 + 52 = 180(extr ∠ = sum of intr. opp ∠s)
∠QPR + 128 = 180
∠QPR = 180 - 128
= 52o
∴ΔPQR is an isosceles triangle
Source: Myschool Past Questions Archive (Record #10930)