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POST UTME RSU 2018 Mathematics | Objective

Are you preparing for POST UTME RSU exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2018 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

In a circle of radius 4 cm, a chord of length 6 cm subt\ends an angle of 60° at the centre. Find the area of the sector.

A. 12π cm²

Correct B. 16π cm²

C. 20π cm²

D. 24π cm²

Correct Answer: B

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Question 2

If $x^2 + 2x + 1 = 0$, find the value of $x^3 + 2x^2 + x + 1$.

Correct A. -1

B. 0

C. 1

D. 2

Correct Answer: A

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Question 3

A random variable $X$ has a probability distribution given by $P$ X=x $=\frac{1}{2}$. Find the expected value of $X$.

A. 0

Correct B. 1

C. 2

D. 3

Correct Answer: B

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Question 4

In a triangle $ABC$, the length of side $AB$ is 5 cm, the length of side $BC$ is 6 cm, and the length of side $AC$ is 7 cm. Find the area of the triangle.

A. 12 cm²

B. 15 cm²

Correct C. 18 cm²

D. 20 cm²

Correct Answer: C

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Question 5

If $f(x)=\frac{x^2-4}{x-2}$, find the value of $f(4)$.

A. 0

Correct B. 2

C. 4

D. 6

Correct Answer: B

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Question 6

Find the area under the curve $ y = \frac{1}{2}x^2 + 3x - 4 $ from $ x = 0 $ to $ x = 2 $.

A. 10

B. 12

Correct C. 14

D. 16

Correct Answer: C

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Question 7

A right circular cone has a height of 15 cm and a base radius of 8 cm. Find its volume.

A. 1000π cm^3

B. 1200π cm^3

Correct C. 1500π cm^3

D. 1800π cm^3

Correct Answer: C

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Question 8

Solve the inequality $ 2x^2 + 5x - 3 > 0 $.

Correct A. $ -∞, -1 $ ∪ (3, ∞)

B. $ -∞, -3 $ ∪ (1, ∞)

C. $ -∞, -1 $ ∪ (1, ∞)

D. $ -∞, -3 $ ∪ (3, ∞)

Correct Answer: A

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Question 9

Find the equation of the circle with center $ -2, 3 \ $ ) and radius 4.

Correct A. $ x + 2 \ $^2 + $ y - 3 $^2 = 16 )

B. $ x - 2 \ $^2 + $ y + 3 $^2 = 16 )

C. $ x + 2 \ $^2 + $ y + 3 $^2 = 16 )

D. $ x - 2 \ $^2 + $ y - 3 $^2 = 16 )

Correct Answer: A

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Question 10

A number is 5 times the sum of its digits. If the number is divisible by 3, what is the number?

A. 135

Correct B. 315

C. 531

D. 753

Correct Answer: B

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Question 11

Find the value of x in the equation $ \log_{10} \( x^2 \ $ = 4 ).

A. 10

B. 100

C. 1000

Correct D. 10000

Correct Answer: D

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Question 12

Solve the quadratic equation $ x^2 + 5x + 6 = 0 $.

Correct A. x = -2

B. x = -3

C. x = 2

D. x = 3

Correct Answer: A

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Question 13

A right-angled triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. Find the length of the other leg.

Correct A. 8 cm

B. 6 cm

C. 10 cm

D. 12 cm

Correct Answer: A

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Question 14

A car travels from city A to city B at an average speed of 60 km/h and returns at an average speed of 40 km/h. What is the average speed for the round trip?

A. 48 km/h

B. 50 km/h

Correct C. 52 km/h

D. 55 km/h

Correct Answer: C

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Question 15

A solid cylinder has a height of 10 cm and a radius of 4 cm. Find the volume of the cylinder.

A. 800π cm^3

Correct B. 1000π cm^3

C. 1200π cm^3

D. 1600π cm^3

Correct Answer: B

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Question 16

In a random sample of 100 students, the mean height is 175 cm with a s\tandard deviation of 5 cm. If the population s\tandard deviation is 3 cm, calculate the s\tandard error of the mean.

Correct A. 1.67 cm

B. 2.5 cm

C. 3.33 cm

D. 4.24 cm

Correct Answer: A

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Question 17

Find the equation of the circle with center $ -2, 3 $ and radius 4.

Correct A. \left$ x + 2 \right $^2 + \left$ y - 3 \right $^2 = 16

B. \left$ x - 2 \right $^2 + \left$ y + 3 \right $^2 = 16

C. \left$ x + 3 \right $^2 + \left$ y - 2 \right $^2 = 16

D. \left$ x - 3 \right $^2 + \left$ y + 2 \right $^2 = 16

Correct Answer: A

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Question 18

A sequence is defined by the recurrence relation a_n = 2a_{n-1} + 1, with a_1 = 3. Find the sum of the first 5 terms of the sequence.

Correct A. 3 + 7 + 15 + 31 + 63

B. 3 + 5 + 11 + 23 + 47

C. 3 + 6 + 12 + 24 + 48

D. 3 + 8 + 16 + 32 + 64

Correct Answer: A

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Question 19

Find the determinant of the matrix \begin{bmatrix} 2 & 3 & 1 \\ 4 & 5 & 2 \\ 1 & 2 & 3 \end{bmatrix}.

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 20

In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the other sides is 6 cm. Find the length of the third side.

Correct A. 8 cm

B. 6 cm

C. 10 cm

D. 12 cm

Correct Answer: A

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Question 21

Solve the inequality $ \frac{x-2}{x+1} > 0 $ for $ x in \( -infty, -1 \ $ cup $ -1, 2 $ cup (2, infty) ).

Correct A. $ x < -1 $ or $ x > 2 $

B. $ x > -1 $ and $ x < 2 $

C. $ x < -1 $ or $ x = 2 $

D. $ x > -1 $ or $ x = 2 $

Correct Answer: A

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Question 22

Find the equation of the circle with center $ C\( -2, 3 \ $ ) and radius ( 4 ).

Correct A. $ x+2 \ $^2 + $ y-3 $^2 = 16 )

B. $ x-2 \ $^2 + $ y+3 $^2 = 16 )

C. $ x+2 \ $^2 + $ y+3 $^2 = 16 )

D. $ x-2 \ $^2 + $ y-3 $^2 = 16 )

Correct Answer: A

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Question 23

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

A. ( f'(x) = \frac{-2x}{$ x^2 + 1 $^2} )

Correct B. ( f'(x) = \frac{2x}{$ x^2 + 1 $^2} )

C. ( f'(x) = \frac{2}{$ x^2 + 1 $^2} )

D. ( f'(x) = \frac{-2}{$ x^2 + 1 $^2} )

Correct Answer: B

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Question 24

A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?

A. $ \frac{1}{6} $

B. $ \frac{1}{3} $

C. $ \frac{2}{3} $

Correct D. $ \frac{5}{6} $

Correct Answer: D

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Question 25

Solve the system of equations $ egin{cases} x + y = 3 \ 2x - 3y = - 5 \end{cases} $.

Correct A. $ x = 2, y = 1 $

B. $ x = 1, y = 2 $

C. $ x = 2, y = 2 $

D. $ x = 1, y = 1 $

Correct Answer: A

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