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POST UTME DELSU 2018 Mathematics | Objective

Are you preparing for POST UTME DELSU 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

Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.

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 2

Solve for ( x ) in the equation \( 2^x + 3^x = 5^x \).

A. \( x = 2 \)

B. \( x = 3 \)

Correct C. \( x = 4 \)

D. \( x = 5 \)

Correct Answer: C

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Question 3

Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \).

Correct A. \( \frac{64}{3} \)

B. \( \frac{32}{3} \)

C. \( \frac{16}{3} \)

D. \( \frac{8}{3} \)

Correct Answer: A

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Question 4

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

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

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

C. \( x - 4 \ \)^2 + \( y - 3 \)^2 = 16 )

D. \( x - 2 \ \)^2 + \( y - 4 \)^2 = 16 )

Correct Answer: A

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Question 5

Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).

Correct A. ( 0 )

B. ( 1 )

C. \( -1 \)

D. ( 2 )

Correct Answer: A

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Question 6

A particle moves in a straight line with a velocity of \( mathbf{v} = 2t , mathbf{i} + 3t^2 , mathbf{j} \) m/s, where ( t ) is in seconds. Find the position vector of the particle at time \( t = 2 \) seconds.

Correct A. 8\mathbf{i} + 12\mathbf{j}

B. 4\mathbf{i} + 12\mathbf{j}

C. 8\mathbf{i} + 8\mathbf{j}

D. 4\mathbf{i} + 8\mathbf{j}

Correct Answer: A

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Question 7

A rec\tangular box has dimensions ( x ) cm by ( y ) cm by ( z ) cm. If the surface area of the box is 600 cm^2, and the volume is 1200 cm^3, find the value of \( x + y + z \).

A. 20

B. 25

Correct C. 30

D. 35

Correct Answer: C

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Question 8

Two events, A and B, are indep\endent. If P(A) = 0.4 and P(B) = 0.6, find P(A ∩ B).

Correct A. 0.24

B. 0.36

C. 0.48

D. 0.60

Correct Answer: A

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Question 9

Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.

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

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

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

D. \frac{2}{\( x^2 + 1 \)^2}

Correct Answer: A

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Question 10

A number is represented in base 8 as 1234. What is the value of this number in base 10?

A. 512

B. 1024

Correct C. 1536

D. 2048

Correct Answer: C

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Question 11

Solve for x in the equation \( \frac{1}{2}x^2 + 5x - 3 = 0 \).

A. x = -10

B. x = 6

Correct C. x = -3

D. x = 2

Correct Answer: C

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Question 12

A binary operation \( * \) on the set of real numbers is defined as \( a * b = ab + 1 \). Find the value of \( 2 * 3 \).

Correct A. 7

B. 9

C. 11

D. 13

Correct Answer: A

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Question 13

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

A. 1/3

B. 1/2

Correct C. 2/3

D. 1/6

Correct Answer: C

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Question 14

Solve the inequality \( 2x^2 + 5x - 3 > 0 \).

Correct A. x < -3 or x > 1

B. x < -1 or x > 3

C. x < 1 or x > 3

D. x < -3 or x < 1

Correct Answer: A

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Question 15

A number is divisible by 3 if the sum of its digits is divisible by 3. What is the smallest 3-digit number that is divisible by 3?

A. 100

B. 102

Correct C. 105

D. 108

Correct Answer: C

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Question 16

Find the value of x in the equation \( 2x^2 + 5x - 3 = 0 \)

A. 1

Correct B. -1

C. 3

D. -3

Correct Answer: B

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Question 17

Solve for y in the equation \( y = \log_{10} \( x^2 \ \) = 4 )

Correct A. 10^4

B. 10^2

C. 10^8

D. 10^6

Correct Answer: A

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Question 18

Find the determinant of the matrix \( \begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \)

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 19

A sequence is defined by the formula \( a_n = 2n + 1 \). Find the sum of the first 5 terms of the sequence.

A. 15

B. 20

Correct C. 25

D. 30

Correct Answer: C

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Question 20

A vector \( \vec{a} = \begin{bmatrix} 1 \ 2 \ 3 \end{bmatrix} \) is given. Find the magnitude of the vector.

A. 3

B. 4

Correct C. 5

D. 6

Correct Answer: C

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Question 21

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 22

Solve the inequality \( 2x^2 + 5x - 3 > 0 \).

Correct A. \( -∞, -1 \) ∪ (3, ∞)

B. \( -∞, -3 \) ∪ (1, ∞)

C. \( -∞, 1 \) ∪ (3, ∞)

D. \( -∞, -3 \) ∪ (1, ∞)

Correct Answer: A

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Question 23

Find the derivative of the function ( f(x) = 3x^2 - 2x + 1 ).

Correct A. 6x - 2

B. 6x + 2

C. 3x^2 - 2

D. 3x^2 + 2

Correct Answer: A

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Question 24

A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 50 and 70?

A. 0.5

B. 0.6

Correct C. 0.7

D. 0.8

Correct Answer: C

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Question 25

Solve the equation \( 2^x + 3^x = 5^x \).

A. x = 2

Correct B. x = 3

C. x = 4

D. x = 5

Correct Answer: B

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