Exam Body

Year

Subject

Paper Type

UTME 2018 Mathematics | Objective

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Question 1

Solve the quadratic inequality \( x^2 - 5x + 6 \geq 0 \)

A. \( x \geq 2, x \leq 7 \)

Correct B. \( x \leq 3, x \geq 2 \)

C. \( x \leq -2, x \geq -3 \)

D. \( x \leq -3, x \geq 2 \)

Correct Answer: B

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Question 2

In the diagram above \( PQ \parallel RS \). The size of the angle marked x is

A. \( 100^{\circ} \)

Correct B. \( 80^{\circ} \)

C. \( 50^{\circ} \)

D. \( 30^{\circ} \)

Correct Answer: B

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Question 3

Find the gradient of a line which is perpendicular to the line with equation \( 3x + 2y + 1 = 1 \)

A. \( \frac{3}{2} \)

Correct B. \( -\frac{2}{3} \)

C. \( -\frac{2}{5} \)

D. \( -\frac{3}{2} \)

Correct Answer: B

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Question 4

Evaluate \( \int_\frac{-\pi}{2}^{\frac{\pi}{2}} \cos \mathrm{dx} \)

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 5

If the lines \( 3y = 4x - 1 \) and \( qy = x + 3 \) are parallel to each other, the value of \( q \) is

A. \( -\frac{4}{3} \)

B. \( -\frac{5}{4} \)

C. \( \frac{4}{5} \)

Correct D. \( \frac{3}{4} \)

Correct Answer: D

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Question 6

The volume of a hemispherical bowl is 718\( \frac{2}{3} \mathrm{~cm}^{3} \), find its radius

A. 4.0 cm

B. 5.6 cm

Correct C. 7.0 cm

D. 0.3 cm

Correct Answer: C

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Question 7

If \( x = 124_{\text{5}} \), find \( x \)

A. 124

B. 121

Correct C. 184

D. 180

Correct Answer: C

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Question 8

A baking recipe calls for 2.5 kg of sugar and 4.5 kg of flour. With this recipe some cakes were baked using 24.5 kg of a mixture of sugar and flour. How much sugar were used?

Correct A. 12.25 kg

B. 6.75 kg

C. 8.75 kg

D. 15.75 kg

Correct Answer: A

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Question 9

Two cars x and y start at the same point and travel towards a point P which is 150 km away. If the average speed of y is 60 km per hour and x arrives at P 25 minutes earlier than y, what is the average speed of x?

Correct A. \( 51\frac{3}{9} km \)

B. 72 km per hour

C. 66 km per hour

D. \(37 \frac{1}{2} km\) per hour

Correct Answer: A

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Question 10

The first term of an Arithmetic Progression is 3 and the fifth term is q. Find the number of terms in the progression if the sum of the terms is 81?

Correct A. 12

B. 27

C. 9

D. 7

Correct Answer: A

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Question 11

Find the eleventh term of the progression 4, 8, 16.

Correct A. \(2^{13}\)

B. \(2^{12}\)

C. \(2^{11}\)

D. \(2^{16}\)

Correct Answer: A

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Question 12

The histogram above represents the weight of students who travelled out of their schools for an examination. How many people made the trip?

A. 78

B. 58

Correct C. 29

D. 69

Correct Answer: C

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Question 13

In how many ways can 6 subjects be selected from 10 subjects for an examination?

Correct A. 218

B. 216

C. 215

D. 210

Correct Answer: A

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Question 14

Find the value of x for which the function f(x) = \( 2x^{2} - x^{2} - 4x + 4 \) has a maximum value.

Correct A. \(\frac{2}{3}\)

B. 1

C. \(-\frac{2}{3}\)

D. -1

Correct Answer: A

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Question 15

Make L the subject of the formula if d = \( \sqrt{\frac{42w}{5L}} \).

Correct A. \(\sqrt{\frac{42w}{5d}}\)

B. \(\sqrt{\frac{42w}{5d^{2}}}\)

C. \(\sqrt{\frac{42}{5dw}}\)

D. \(\frac{1}{2}\sqrt{\frac{42w}{5}}\)

Correct Answer: A

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Question 16

Calculate the simple interest on N 1,500 for 8 years at 5% per annum.

Correct A. N5,000

B. N600

C. N500

D. N150

Correct Answer: A

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Question 17

Correct each of the numbers 59.81798 and 0.0746829 to three significant figures and multiply them giving your answer to three significant figures.

Correct A. 4.46

B. 4.48

C. 4.47

D. 4.49

Correct Answer: A

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Question 18

One interior angle of a convex hexagon is 170° and each of the remaining angles is equal to x°. Find x.

Correct A. 120°

B. 110°

C. 105°

D. 102°

Correct Answer: A

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Question 19

If f(x) = \(\frac{1}{x-1} + \frac{x-1}{x^{2}-1}\), find f(1-x).

Correct A. \(\frac{1}{x} + \frac{1}{x-2}\)

B. x + \(\frac{1}{2x-1}\)

C. \(\frac{-1}{x} + \frac{1}{x-2}\)

D. \(\frac{-1}{x} + \frac{1}{x-1}\)

Correct Answer: A

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Question 20

Convert \(241_{\text{5}} \) to base 8.

Correct A. \( 71_{\text{8}} \)

B. \( 107_{\text{8}} \)

C. \( 176_{\text{8}} \)

D. \( 241_{\text{8}} \)

Correct Answer: A

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Question 21

A train moves from P to Q at an average speed of 40 km/hr and immediately returns from Q to P at 45 km/hr. Find the average speed for the entire journey.

Correct A. 55 km/hr

B. 50 km/hr

C. 67.50 km/hr

D. 75 km/hr

Correct Answer: A

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Question 22

By selling 20 oranges for #1.35, a trader makes a profit of #82. What is his percentage gain or loss if he sells the same 20 oranges for #1.10?

Correct A. 8%

B. 10%

C. 12%

D. 15%

Correct Answer: A

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Question 23

Simplify without using tables. \(\frac{2 \sqrt{14} \times 3 \sqrt{21}}{7 \sqrt{24} \times 2 \sqrt{98}}\)

Correct A. \(\frac{3 \sqrt{14}}{4}\)

B. \(\frac{3 \sqrt{2}}{4}\)

C. \(\frac{3 \sqrt{14}}{28}\)

D. \(\frac{3 \sqrt{2}}{28}\)

Correct Answer: A

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Question 24

Make y the subject of the formula: Z = x^2 + \(\frac{1}{y^{3}}\)?

Correct A. y = \(\frac{1}{(z-y^{2})^{3}}\)

B. y = \(\frac{1}{(z+x^{2})^{3}}\)

C. y = \(\frac{1}{(Z-x^{2})^{1/3}}\)

D. y = \(\frac{1}{\sqrt[3]{Z}-\sqrt{3x^{2}}}\)

Correct Answer: A

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Question 25

A cubic function f(x) is specified by the graph shown above. The values of the independent variable for which the function vanishes are:

A. \( -1,0,1 \)

Correct B. \( -1 \leq x \leq 1 \)

C. \( x < -1 \)

D. \( x > 1 \)

Correct Answer: B

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