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Mathematics
UTME / JAMB 2018
Mensuration (Areas, Perimeters & Volumes)
Solution
An arc of a circle of radius 14cm subtends angle 300^\circ at the centre. Find the perimeter of the sector formed by the arc (take \pi = \(\frac{22}{7}\))
A
14.67cm
B
73.33 cm
C
101.33cm
D
513.33cm
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Length of the arc = \(\frac{\theta}{360} \times 2\pi r\)
= \(\frac{300}{360} \times 2 \times \frac{22}{7} \times 14\)
= \(\frac{220}{3}\)
= 73.33 cm
Perimeter of the sector = Length of the arc + 2r
= 73.33 + 2(14)
= 101.33 cm
Source: Myschool Past Questions Archive (Record #46993)
Mathematics
UTME / JAMB 2018
Plane Geometry, Polygons & Circle Theorems
Solution
Simplify
\(\frac {25^{\frac{2}{3}} \div 25^{\frac{1}{6}}} {(\frac{1}{5})^{\frac{7}{6}} \div (\frac{1}{5})^{\frac{1}{6}}}\)
A
25
B
1
C
\(\frac{1}{5}\)
D
\(\frac{1}{25}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\frac {25^{\frac{2}{3}} \div 25^{\frac{1}{6}}} {(\frac{1}{5})^{\frac{7}{6}} \div (\frac{1}{5})^{\frac{1}{6}}}\)
= \(\frac{25^{\frac{2}{3} - \frac{1}{6}}}{(\frac{1}{5})^{\frac{7}{6} - \frac{1}{6}}}\)
= \(\frac{25^{\frac{1}{2}}}{(\frac{1}{5})}\)
= \(5 \div \frac{1}{5}\)
= 25
Source: Myschool Past Questions Archive (Record #46994)
Mathematics
UTME / JAMB 2018
Algebraic Expressions, Polynomials & Factorisation
Diagram
Solution
Make T the subject of the relation.
Attached Figure / Diagram
A
T = \(\frac{R + P3}{15Q}\)
B
T = \(\frac{R - 15P^3}{Q}\)
C
T =R - \(\frac{15P^3}{Q}\)
D
T = \(\frac{15R + Q}{P^3}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
P = (\(\frac{Q( R - T )}{ 15})^\frac{1}{3}\)
take cube of both sides
\(P^3 =\frac{Q( R - T)}{ 15}\)
cross multiply
\(15P^3 = Q( R - T)\)
\(\frac{15P^3}{Q}\) = R - T
T = R - \(\frac{15P^3}{Q}\)
Source: Myschool Past Questions Archive (Record #46995)
Mathematics
UTME / JAMB 2018
Fractions, Decimals, Percentages & Approximations
What is the place value of 9 in the number 3.0492?
A
\(\frac{9}{10000}\)
B
\(\frac{9}{1000}\)
C
\(\frac{9}{100}\)
D
\(\frac{9}{10}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option B.
Source: Myschool Past Questions Archive (Record #46996)
Mathematics
UTME / JAMB 2018
Fractions, Decimals, Percentages & Approximations
If the simple interest on a sum of money invested at 3% per annum for 2\(\frac{1}{2}\) years is N123, find the principal.
A
N676.50
B
N820
C
N1,640
D
N4,920
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option C.
Source: Myschool Past Questions Archive (Record #46997)
Mathematics
UTME / JAMB 2018
Fractions, Decimals, Percentages & Approximations
Solution
A machine valued at N20,000 depreciates by 10% every year. What will be the value of the machine at the end of two years?
A
N16,200
B
N14,200
C
N12,000
D
N8,000
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Since it depreciates by 10% At the end of first year, its value = 90% of 20000
= \(\frac{90}{100}\) x 20000 =18000
At the end of second year, its value = 90% of 18000
= \(\frac{90}{100}\) x 18000 = ₦16,200
Answer is A
Source: Myschool Past Questions Archive (Record #46998)
Mathematics
UTME / JAMB 2018
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
The table shown gives the marks scored by a group of student in a test. Use the table to answer the question given.
Mark
0
1
2
3
4
5
Frequency
1
2
7
5
4
3
What is the median mark?
A
1
B
2
C
3
D
4
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Total frequency = 1 + 2 + 7 + 5 + 4 + 3 = 22
Median is the middle number
= \(\frac{Nth}{2}\)
term = \(\frac{22th}{2}\) = 11th term
Going in ascending order, 11th term is 3, going in descending order 11th term is 3
Median = 3 + \(\frac{3}{2}\) = \(\frac{6}{2}\) = 3
Answer is C
Source: Myschool Past Questions Archive (Record #46999)
Mathematics
UTME / JAMB 2018
Statistics (Data Representation, Central Tendency & Dispersion)
The table shown gives the marks scored by a group of student in a test. Use the table to answer the question given.
Mark
0
1
2
3
4
5
Frequency
1
2
7
5
4
3
What is the probability of selecting a student from the group that scored 2 or 3
A
\(\frac{1}{11}\)
B
\(\frac{5}{22}\)
C
\(\frac{7}{22}\)
D
\(\frac{6}{11}\)
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 #47000)
Mathematics
UTME / JAMB 2018
Linear, Simultaneous & Quadratic Equations
A boy walks 800m in 20 minutes. Calculate his average speed in Km/H
A
2.4
B
4
C
24
D
6
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 #47001)
Mathematics
UTME / JAMB 2018
Fractions, Decimals, Percentages & Approximations
Solution
A car uses one litre of petrol for every 14km. If one litre of petrol cost N63.00, how far can the car go with N900.00 worth of petrol?
A
420Km
B
405Km
C
210Km
D
200Km
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
since 1litre cost ₦63
So ₦900 is the cost of \(\frac{900}{63}\) litres
= 14.2857litres of petrol
nbsp; The car uses 1 litre for 14km
So 14.2857 litres will be used for (14.2857 x 14)
= 200km
Answer is D
Source: Myschool Past Questions Archive (Record #47002)
Mathematics
UTME / JAMB 2018
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram, GI is a tangent to the circle at H. If EF||GI, calculate the size of ∠EHF
Attached Figure / Diagram
A
126°
B
72°
C
54°
D
28°
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Source: Myschool Past Questions Archive (Record #47003)
Mathematics
UTME / JAMB 2018
Fractions, Decimals, Percentages & Approximations
Solution
How many times, correct to the nearest whole number, will a man run round a circular track of diameter 100m to cover a distance of 1000m?
A
3
B
4
C
5
D
6
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
In terms of distance, a circle has a total distance or perimeter of 2\pir or \pid
Where r is radius and d is the diameter
So perimeter = \(\frac{22}{7}\) x 100
= 314.2857m
To cover a distance of 1000m, he is going to round the circular track for \(\frac{1000}{314.2857}\) = 3.18
\(\approxeq\) 3 (to the nearest whole number)
Source: Myschool Past Questions Archive (Record #47004)
Mathematics
UTME / JAMB 2018
Indices, Logarithms & Surds
\(\frac{0.00256 \times 0.0064}{0.025 \times 0.08}\)
A
8.8 x 10\(^{-1}\)
B
8.8 x 10\(^{-2}\)
C
8.2 x 10\(^{-3}\)
D
8.8 x 10\(^{3}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option C.
Source: Myschool Past Questions Archive (Record #47007)
Mathematics
UTME / JAMB 2018
Fractions, Decimals, Percentages & Approximations
Two sisters, Taiwo and Kehinde, own a store. The ratio of Taiwo's share to Kehinde's is 11:9. Later Kehinde sells \(\frac{2}{3}\) of her share to Taiwo for N720.00. Find the value of the store
A
N1,080.00
B
N2,400.00
C
N3,000.00
D
N3,600.00
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option B.
Source: Myschool Past Questions Archive (Record #47008)
Mathematics
UTME / JAMB 2018
Plane Geometry, Polygons & Circle Theorems
Solution
A room is 12m long, 9m wide and 8m high. Find the cosine of the angle which a diagonal of the room makes with the floor of the room.
A
\(\frac{15}{17}\)
B
\(\frac{9}{17}\)
C
\(\frac{8}{15}\)
D
\(\frac{12}{17}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Given length of the room = 12m; breadth = 9m and height = 8m.
The room is a cuboid in shape, therefore the length of the diagonal = \(\sqrt{l^2 + b^2 + h^2}\)
= \(\sqrt{12^2 + 9^2 + 8^2}\)
=\(\sqrt{289}\)
= 17m.
The diagonal makes an angle with the diagonal of the floor: \(\sqrt{12^2 + 9^2}\)
= \(\sqrt{225}\)
= 15m
The cosine of the angle that the diagonal makes with the floor (\(\theta\)) = \(\frac{15}{17}\).
Source: Myschool Past Questions Archive (Record #47009)