Exam Body

Year

Subject

Paper Type

UTME 2017 Mathematics | Objective

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Question 1

Find \( \int\left\{x^{2}+3 x-5\right) d x \).

A. \( \frac{x^{3}}{3}-\frac{3 x^{3}}{2}-5 x+k \)

Correct B. \( \frac{x^{3}}{3}-\frac{3 x^{2}}{2}+5 x+k \)

C. \( \frac{x^{3}}{3}+\frac{3 x^{2}}{2}-5 x+k \)

D. \( \frac{x^{3}}{3}+\frac{3 x^{3}}{2}+5 x+k \)

Correct Answer: B

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Question 2

Evaluate : \( \frac{0.0028213}{0.634} \) and give your answer in standard form.

Correct A. 4.45 x \( 10^{-3} \)

B. 4.45 x \( 10^{-6} \)

C. 4.45 x \( 10^{-5} \)

D. 4.45 x \( 10^{-4} \)

Correct Answer: A

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Question 3

Calculate the simple interest on N6500 for 4 years at 6%.

A. N1 200

Correct B. N1 560

C. N2 400

D. N2 200

Correct Answer: B

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Question 4

Given the quadrilateral RSTQ inscribed in the circle above with Q as centre. Find the size of the angle x.

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

B. \( 140^{\circ} \)

Correct C. \( 120^{\circ} \)

D. \( 10^{\circ} \)

Correct Answer: C

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Question 5

The locus of a point which is equidistant from the line P Q forms a.

A. circle centre P

Correct B. pair of parallel lines each opposite to P Q

C. circle centre Q

D. perpendicular line to P Q

Correct Answer: B

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Question 6

Evaluate \( \sin 45^{\circ}+\sin 30^{\circ} \) in surd form.

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

B. \( \frac{\sqrt{3-1}}{2} \)

C. \( \frac{1}{2 \sqrt{2}} \)

D. \( \frac{1+\sqrt{2}}{2} \)

Correct Answer: A

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Question 7

From the table above calculate the mean of the scores.

Correct A. 3.2

B. 3.4

C. 3.1

D. 3.3

Correct Answer: A

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Question 8

Evaluate \( 1-\left(\frac{1}{5} \times 1 \frac{2}{3}\right)+\left(5 \div 1 \frac{2}{3}\right) \).

A. 4

Correct B. 3

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

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

Correct Answer: B

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Question 9

Find the gradient of the line joining the points \( (3,2) \) and \( (1,4) \).

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

B. 1

Correct C. -1

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

Correct Answer: C

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Question 10

If a rod 10 cm in length was measured as 10.5 cm , calculate the percentage error.

A. 5 %

Correct B. 10 %

C. 8 %

D. 7 %

Correct Answer: B

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Question 11

Given \( M=N \sqrt{\frac{SL}{T}} \) make T the subject of the formula.

Correct A. \( \frac{NSL}{M} \)

B. \( \frac{N^{2}SL}{M^{2}} \)

C. \( \frac{N^{2}SL}{M} \)

D. \( \frac{NSL}{M^{2}} \)

Correct Answer: A

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Question 12

Evaluate: \( \frac{0.00000231}{0.007} \) and leave the answer in standard form.

Correct A. 3.3 x \( 10^{-5} \)

B. 3.3 x \( 10^{-3} \)

C. 03.3 x \( 10^{-4} \)

D. 3.3 x \( 10^{-6} \)

Correct Answer: A

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Question 13

In many ways can the word MACICITA be arranged?

A. \( \frac{8!}{2!} \)

Correct B. \( \frac{8!}{3!2!} \)

C. \( \frac{8!}{2!2!2!} \)

D. 8 !

Correct Answer: B

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Question 14

Differentiate \( y=3 \cos 2 x-\sin 4 x \).

Correct A. \( -6 \sin 2 x+4 \cos 4 x \)

B. \( 6 \sin 2 x+4 \cos 4 x \)

C. \( -6 \sin 2 x-4 \cos 4 x \)

D. \( 6 \sin 2 x-4 \cos 4 x \)

Correct Answer: A

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Question 15

Given \( T=\{ \) even numbers from 1 to 12 } and \( N=\{ \) common factors of 6,8 and 12 } . Find \( T \cap N \).

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

B. \( \{2,3,4\} \)

C. \( \{3,4,6\} \)

Correct D. \( \{2\} \)

Correct Answer: D

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Question 16

What is the product of \( 2 x^{2}-x+1 \) and \( 3-2 x \)?

A. \( 4 x^{3}-8 x^{2} +5 x+3 \)

Correct B. \( -4 x^{3}+8 x^{2}-5 x+3 \)

C. \( -4 x^{3}-8 x^{2}+5 x+3 \)

D. \( 4 x^{3}+8 x^{2}- 5 x+3 \)

Correct Answer: B

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Question 17

What is the geometric mean of 9 and 16 ?

A. 14

Correct B. 18

C. 15

D. 12

Correct Answer: B

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Question 18

\( y \) is inversely proportional to x and \( y=6 \) when \( x=7 \). Find the constant of the variation.

A. 47

Correct B. 42

C. 54

D. 48

Correct Answer: B

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Question 19

Solve \( (x-3)(x+2)<0 \)

A. 2

B. -3

Correct C. -2

D. -3

Correct Answer: C

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Question 20

In the figure above find \( x \).

A. \( 40^{\circ} \)

Correct B. \( 55^{\circ} \)

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

D. \( 60^{\circ} \)

Correct Answer: B

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Question 21

Find the base in which the following addition was performed. \( \begin{array} {r@{\quad}cccc} & \quad 2 \quad 3 \quad 1 \quad 2 \\ + & \quad 1 \quad 0 \quad 1 \quad 3 \\ + & \quad 2 \quad 1 \quad 3 \quad 1 \\ \hline 1 & \quad 1 \quad 0 \quad 1 \quad 1 \\ \hline \end{array} \)

A. 7

B. 6

C. 5

Correct D. 8

Correct Answer: D

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Question 22

If temperature \( t \) is directly proportional to heat \( h \), and when \( t=20^{\circ} \mathrm{c}, h=50 \mathrm{~J} \), find \( t \) when \( h=60 \mathrm{~J} \).

Correct A. \( 24^{\circ} \mathrm{c} \)

B. \( 20^{\circ} \mathrm{c} \)

C. \( 34^{\circ} \mathrm{c} \)

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

Correct Answer: A

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Question 23

In class of 45 students, 20 offer Geography while 28 offer Chemistry. How many students offer both?

A. 4

Correct B. 5

C. 7

D. 6

Correct Answer: B

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Question 24

The base in which the operation was performed was \( \begin{array}{rcccccccc} & & & 1 & 1 & 0 & 1 & . & 0 & 1 \\ + & & & 1 & 1 & 1 & 0 & . & 1 & 1 \\ + & & & 1 & 0 & 1 & 1 & . & 1 & 0 \\ \hline & 1 & 0 & 0 & 1 & 1 & 1 & . & 1 & 0 \\ \hline \end{array} \)

A. 6

B. 2

Correct C. 4

D. 5

Correct Answer: C

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Question 25

Find the number of ways that the letters of the word EXCELLENCE be arranged.

A. \( \frac{10!}{2!2!2!} \)

B. \( \frac{10!}{4!2!} \)

Correct C. \( \frac{10!}{4!2!2!} \)

D. \( \frac{10!}{2!2!} \)

Correct Answer: C

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