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Subject

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UTME 2018 Mathematics | Objective

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Question 1 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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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