Exam Body

Year

Subject

Paper Type

UTME 2019 Mathematics | Objective

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Question 1

If 5,8,6 and k occur with frequencies 3,2,4 and 1 respectively and have a mean of 5.7. Find the value of k.

A. 4

B. 3

Correct C. 2

D. 1

Correct Answer: C

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Question 2

In how many ways can a delegation of 3 be chosen from 5 men and 3 women, if at least 1 man and 1 woman must be included?

A. 15

B. 28

C. 30

Correct D. 45

Correct Answer: D

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Question 3

The probability of a student passing any examination is \( \frac{2}{3} \). If the student takes three examinations, what is the probability that he will not pass any of them?

A. \frac{2}{3}

B. \frac{4}{9}

C. \frac{8}{27}

Correct D. \frac{1}{27}

Correct Answer: D

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Question 4

What is the value of p if the gradient of the line joining (-1, p) and (p, 4) is \( \frac{2}{3} \) ?

A. -2

B. -1

C. 1

Correct D. 2

Correct Answer: D

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Question 5

A chord is drawn 5 cm away from the centre of a circle of radius 13 cm. Calculate the length of the chord.

A. 7 cm

B. 9 cm

C. 12 cm

Correct D. 24 cm

Correct Answer: D

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Question 6

If the hypotenuse of a right-angled isosceles triangles is 2 cm, what is the area of the triangle?

A. 1 / 2 cm²

Correct B. 1 cm²

C. \( \sqrt{2} \) cm²

D. 2 \( \sqrt{2} \) cm²

Correct Answer: B

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Question 7

The pie chart above represents 400 fruits on display in a grocery store. How many apples are in the store?

A. 45

Correct B. 50

C. 60

D. 75

Correct Answer: B

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Question 8

A regular polygon has \( 150^{\circ} \) as the size of each interior angle. How many sides does it have?

Correct A. 12

B. 10

C. 9

D. 8

Correct Answer: A

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Question 9

\[ \begin{array}{|l|c|c|c|c|c|c|} \hline Marks & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9\\ \hline \text{No of Students} & 3 & 4 & 1 & 0 & 4 & 5 & 2 & 1 \\ \hline \end{array} \] The table above shows the distribution of marks of students in a test. Find the probability of passing the test if the pass mark is 5.

Correct A. \( \frac{3}{5} \)

B. \( \frac{2}{5} \)

C. \( \frac{7}{20} \)

D. \( \frac{1}{5} \)

Correct Answer: A

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Question 10

A cylindrical pipe, made of metal, is 3 cm thick if the internal radius of the pipe is 10 cm. Find the volume of metal used in making 3 cm of the pipe.

A. 153 \pi cm³

Correct B. 207 \pi cm³

C. 15300 \pi cm³

D. 20700 \pi cm³

Correct Answer: B

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Question 11

4,16,30,20,10,14 and 26 are represented on a pie chart. Find the sum of the angles of the bisector representing all numbers equals to or greater than 16.

A. 48°

B. 84°

C. 92°

Correct D. 276°

Correct Answer: D

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Question 12

Find the probability of selecting a figure which is a parallelogram from a square, a rectangle, a rhombus, a kite and a trapezium.

Correct A. \frac{3}{5}

B. \frac{2}{5}

C. \frac{4}{5}

D. \frac{1}{5}

Correct Answer: A

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Question 13

Ice forms on a refrigerator ice-box at the rate of (4 - 0.6t)g per minute after minutes. If initially there are of ice in the box, find the mass of ice formed in 5 minutes.

A. 19.5

B. 170

Correct C. 14.5

D. 12.5

Correct Answer: C

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Question 14

Obtain a maximum value of the function \( f(x) = x^3 - 12x + 11 \).

A. -5

B. -2

C. 2

Correct D. 27

Correct Answer: D

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Question 15

A student blows a balloon and its volume increases at a rate of \( \pi(20-t^{2}) cm³ \) after t seconds. If the initial volume is 0 cm³, find the volume of the balloon after 2 seconds.

A. 37.00 \pi

Correct B. 37.33 \pi

C. 40.00 \pi

D. 42.67 \pi

Correct Answer: B

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Question 16

If \( 9^{(x-\frac{1}{2})} = 3 x^{2} \), find the value of x.

A. \( \frac{1}{2} \)

Correct B. 1

C. 2

D. 3

Correct Answer: B

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Question 17

Solve for y in the equation \( 10^{y} \times 5^{(2y-2)} \times 4^{(y-1)}=1 \).

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

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

C. 1

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

Correct Answer: B

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Question 18

If \( \log_{3} y+\log_{3} x^{2}=4 \), then y is

A. \( 4-\log_{3} x^{2} \)

B. \( \frac{4}{\log_{3} x^{2}} \)

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

Correct D. +\( \frac{9}{x} \)

Correct Answer: D

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Question 19

If # 225.00 yields # 27.00 in x years simple interest at the rate of 4% per annum, find x.

Correct A. 3

B. 4

C. 12

D. 17

Correct Answer: A

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Question 20

Solve without using tables \( \log_{5}(62.5)-\log_{5}(\frac{1}{2}) \)

Correct A. 3

B. 4

C. 5

D. 8

Correct Answer: A

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Question 21

Evaluate \( \frac{3 5 2 4}{0.05} \) correct to 3 significant figures.

A. 705

B. 70,000

C. 70,480

Correct D. 70,500

Correct Answer: D

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Question 22

Find the radius of a sphere whose surface area is \( 154 \mathrm{~cm}^{2} (\pi=22 / 7) \).

A. 7.00 cm

Correct B. 3.50 cm

C. 3.00 cm

D. 1.75 cm

Correct Answer: B

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Question 23

Find the area of the sector of a circle with radius 3 m, if the angle of the sector is \( 60^{0} \).

A. 4.0 \mathrm{~m}^{2}

B. 4.1 \mathrm{~m}^{2}

Correct C. 4.7 \mathrm{~m}^{2}

D. 5.0 \mathrm{~m}^{2}

Correct Answer: C

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Question 24

If \( \sin \theta=\cos \theta \), find \( \theta \) between \( 0^{\circ} \) and \( 360^{\circ} \).

Correct A. 45,\( 225^{0} \)

B. \( 135^{0} , 315^{0} \)

C. \( 45^{0} \),\( 315^{0} \)

D. \( 135^{0} \),\( 225^{0} \)

Correct Answer: A

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Question 25

The angle between latitudes \( 30^{0} \mathrm{~S} \) and \( 13^{0} \mathrm{~N} \) is

A. 17^{0}

B. 33^{0}

Correct C. 43^{0}

D. 53^{0}

Correct Answer: C

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