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Mathematics
UTME / JAMB 2013
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
\(\begin{array}{c|c} Score & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \hline Frequency & 1 & 0 & 7 & 5 & 2 & 3 & 1 & 1 \end{array}\)
The table above shows the scores of 20 students in further mathematics test. What is the range of the distribution?
A
7
B
6
C
3
D
10
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Range = Highest score - Lowest score
= 10 - 3
= 7
Source: Myschool Past Questions Archive (Record #27125)
Mathematics
UTME / JAMB 2013
Permutations, Combinations & Probability
Solution
In how many ways can a student select 2 subjects from 5 subjects?
A
\(\frac{5!}{3!}\)
B
\(\frac{5!}{2!2!}\)
C
\(\frac{5!}{2!3!}\)
D
\(\frac{5!}{2!}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
A student can select 2 subjects from 5 subjects in;
5C3 ways, i.e. = \(\frac{5!}{2!(5 - 2)!}\)
= \(\frac{5!}{2!3!}\)
Source: Myschool Past Questions Archive (Record #27127)
Mathematics
UTME / JAMB 2013
Permutations, Combinations & Probability
Solution
In how many ways can 3 seats be occupied if 5 people are willing to sit?
A
60
B
20
C
5
D
120
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
5 people can take 3 places in;
5P3 ways, = \(\frac{5!}{(5 - 3)!}\) = \(\frac{5!}{2!}\)
= \(\frac{5 \times 4 \times 3 \times 2!}{2!}\)
= 5 x 4 x 3
= 60 ways
Source: Myschool Past Questions Archive (Record #27129)
Mathematics
UTME / JAMB 2013
Inequalities & Linear Programming
Solution
What is the probability that an integer x \((1 \leq x \leq 25)\) chosen at random is divisible by both 2 and 3?
A
\(\frac{1}{25}\)
B
\(\frac{1}{5}\)
C
\(\frac{4}{25}\)
D
\(\frac{3}{4}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\((1 \leq x \leq 25)\) = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25}
Number N of x divisible by both 2 and 3 is 4.
n(\(\varepsilon\)) = 25
= \(\frac{N}{n(\varepsilon)}\)
= \(\frac{4}{25}\)
Source: Myschool Past Questions Archive (Record #27130)
Mathematics
UTME / JAMB 2013
Permutations, Combinations & Probability
Solution
A basket contains 9 apples, 8 bananas and 7 oranges. A fruit is picked from the basket, find the probability that it is neither an apple nor an orange.
A
\(\frac{3}{8}\)
B
\(\frac{1}{3}\)
C
\(\frac{7}{24}\)
D
\(\frac{2}{3}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
n(apples) = 9
n(bananas) = 8
n(oranges) = 7
n(\(\varepsilon\)) = 24
Hence Prob(not apple, nor orange) = Prob(banana) = \(\frac{8}{24}\) = \(\frac{1}{3}\)
Source: Myschool Past Questions Archive (Record #27131)
Mathematics
UTME / JAMB 2013
Linear, Simultaneous & Quadratic Equations
Diagram
Solution
The graph above is correctly represented by
Attached Figure / Diagram
A
y = x2 - x - 2
B
y = x2 - 3x + 2
C
y = x2 - x - 1
D
y = x2 + x - 2
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
The graph crosses the x-axis at x = -1 and x = 2
Thus, x + 1 = 0 and x - 2 = 0
x\(^2\) - 2x + x - 2 = 0
x\(^2\) - x - 2 = 0
giving y = x\(^2\) - x - 2
Source: Myschool Past Questions Archive (Record #33151)
Mathematics
UTME / JAMB 2013
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram given, find the value of x.
Attached Figure / Diagram
A
30o
B
40o
C
45o
D
15o
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
In the diagram above, o
(base o - (15 + 15)o
= 180o - 30o = 150o
But x + 110o = 150o
(Sum of opp. interior o - 110o = 40o
Source: Myschool Past Questions Archive (Record #33152)
Mathematics
UTME / JAMB 2013
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
The value x in the figure given is
Attached Figure / Diagram
A
110o
B
100o
C
70o
D
130o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Sum of the angles in a triangle = 180^\circ
180^\circ - x + 60 + 70 = 180
130^\circ - x = 180^\circ - 180^\circ = 0^\circ
x = 130^\circ
Source: Myschool Past Questions Archive (Record #33153)
Mathematics
UTME / JAMB 2013
Statistics (Data Representation, Central Tendency & Dispersion)
Diagram
Solution
The bar chart above shows the allotment of time(in minutes) per week for selected subjects in a certain school. What is the total time allocated to the six subjects per week?
Attached Figure / Diagram
A
460mins
B
720mins
C
960mins
D
200mins
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
80 + 160 + 200 + 80 + 128 + 72 = 720minutes
Source: Myschool Past Questions Archive (Record #33154)
Mathematics
UTME / JAMB 2013
Statistics (Data Representation, Central Tendency & Dispersion)
Diagram
Solution
The pie chart above shows the statistical distribution of 80 students in five subjects in an examination. Calculate how many student offer Mathematics.
Attached Figure / Diagram
A
30
B
11
C
50
D
20
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
5x^\circ + (16x - 24)^\circ + 5x^\circ + (4x + 12)^\circ + (6x + 12)^\circ = 360^\circ
36x^\circ - 24 + 12 + 12 = 360^\circ
36x^\circ = 360^\circ
x^\circ = \(\frac{360^\circ}{36}\)
= 10^\circ
Thus, the angle of sector representing Mathematics is 5 x 10^\circ = 50^\circ. Hence the number of students who offer mathematics is
\(\frac{50}{360} \times 80 \approx 11\)
Source: Myschool Past Questions Archive (Record #33155)
Mathematics
WAEC / WASSCE 2013
Fractions, Decimals, Percentages & Approximations
Solution
Multiply 2.7 x 10-4 by 6.3 x 106 and leave your answers in standard form
A
1.7 x 103
B
1.70 x 103
C
1.701 x 103
D
17.01 x 103
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
2.7 x 10-4 x 6.3 x 106
= 2.7 x 6.3 x 10-4 x 106
= 17.01 x 10-4 + 6
= 17.01 x 102
= 1.701 x 101 x 102
= 1.701 x 101 + 2
= 1.701 x 103
Source: Myschool Past Questions Archive (Record #36835)
Mathematics
WAEC / WASSCE 2013
Plane Geometry, Polygons & Circle Theorems
Solution
If 9(2 - x) = 3, find x
A
1
B
\(\frac{3}{2}\)
C
2
D
\(\frac{5}{2}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
9(2 - x) = 3
32(2 - x) = 3
2(2 - x) = 1
4 - 2x = 1
-2x = 1 - 4
-2x = -3
x = \(\frac{-3}{-2}\)
x = \(\frac{3}{2}\)
Source: Myschool Past Questions Archive (Record #36837)
Mathematics
WAEC / WASSCE 2013
Plane Geometry, Polygons & Circle Theorems
In what number base is the addition 465 + 24 + 225 = 1050?
A
ten
B
nine
C
eight
D
seven
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option D.
Source: Myschool Past Questions Archive (Record #36838)
Mathematics
WAEC / WASSCE 2013
Plane Geometry, Polygons & Circle Theorems
Solution
Simplify \(\frac{1\frac{7}{8} \times 2\frac{2}{5}}{6\frac{3}{4} \div \frac{3}{4}}\)
A
9
B
4\(\frac{1}{2}\)
C
2
D
\(\frac{1}{2}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{1\frac{7}{8} \times 2\frac{2}{5}}{6\frac{3}{4} \div \frac{3}{4}}\)
from numerator \(1 \frac{7}{8} \times 2 \frac{2}{5}\)
= \(\frac{15}{8} \times \frac{12}{5}\)
= \(\frac{3 \times 3}{2 \times 1} = \frac{9}{2}\)
from denominator \(6\frac{3}{4} \div \frac{3}{4}\)
= \(\frac{27}{4} \div \frac{3}{4}\)
= \(\frac{27}{4} \times \frac{4}{3}\)
= \(\frac{9 \times 1}{1 \times 1} = \frac{9}{1}\)
\(\frac{9}{2} \div \frac{9}{1} = \frac{9}{2} \times \frac{1}{9}\)
= \(\frac{1}{2}\)
Source: Myschool Past Questions Archive (Record #36844)
Mathematics
WAEC / WASSCE 2013
Plane Geometry, Polygons & Circle Theorems
Solution
If Un = n(n2 + 1), evaluate U5 - U4
A
18
B
56
C
62
D
80
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Un = n(n2 + 1)
U5 = 5(2 + 1)
= 5(25 + 1)
= 5(26) = 130
U4 = 4(42 + 1) = 4(16 + 1)
= 4(17) = 68
U5 - U4 = 130 - 68
= 62
Source: Myschool Past Questions Archive (Record #36850)