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POST UTME DELSU 2024 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 2024 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

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

Correct A. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) )

B. \( \frac{1}{2} left\( \frac{0^3}{3} + 3 cdot 0^2 - 2 cdot 0 \right \ \) )

C. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) + \frac{1}{2} left\( \frac{0^3}{3} + 3 cdot 0^2 - 2 cdot 0 \right \) )

D. \( \frac{1}{2} left\( \frac{4^3}{3} + 3 cdot 4^2 - 2 cdot 4 \right \ \) - \frac{1}{2} left\( \frac{0^3}{3} + 3 cdot 0^2 - 2 cdot 0 \right \) )

Correct Answer: A

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Question 2

Solve for ( x ) in the equation \( 2^x = 8 \).

A. \( x = 2 \)

Correct B. \( x = 3 \)

C. \( x = 4 \)

D. \( x = 5 \)

Correct Answer: B

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Question 3

Find the volume of the solid formed by revolving the region bounded by the curve \( y = x^2 \), the ( x )-axis, and the line \( x = 2 \) about the ( x )-axis.

A. \( \frac{16}{3} pi \)

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

Correct C. \( \frac{64}{3} pi \)

D. \( \frac{128}{3} pi \)

Correct Answer: C

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Question 4

A circle has a radius of 5 cm. Find the area of the circle.

Correct A. ( 25 pi )

B. ( 50 pi )

C. ( 75 pi )

D. ( 100 pi )

Correct Answer: A

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Question 5

Find the equation of the line pas\sing through the points ( (2, 3) ) and ( (4, 5) ).

Correct A. \( y = 2x - 1 \)

B. \( y = 2x + 1 \)

C. \( y = -2x + 1 \)

D. \( y = -2x - 1 \)

Correct Answer: A

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Question 6

In a geometric sequence with first term 2 and common ratio 3, find the sum of the first five terms.

Correct A. 2 + 6 + 18 + 54 + 162

B. 2 + 6 + 18 + 54 + 162 + 486

C. 2 + 6 + 18 + 54 + 162 + 486 + 1458

D. 2 + 6 + 18 + 54 + 162 + 486 + 1458 + 4374

Correct Answer: A

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Question 7

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

A. x = -10

Correct B. x = -6

C. x = 1

D. x = 2

Correct Answer: B

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Question 8

A circle with center (0, 0) and radius 4 passes through the point (3, 4). Find the equation of the circle.

Correct A. x^2 + y^2 = 16

B. x^2 + y^2 = 25

C. x^2 + y^2 = 36

D. x^2 + y^2 = 49

Correct Answer: A

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Question 9

A polynomial f(x) has degree 3 and zeros at x = -2, x = 1, and x = 3. Find the polynomial.

Correct A. f(x) = \( x + 2 \)\( x - 1 \)\( x - 3 \)

B. f(x) = \( x + 2 \)\( x - 1 \)\( x + 3 \)

C. f(x) = \( x + 2 \)\( x - 1 \)\( x - 3 \)

D. f(x) = \( x + 2 \)\( x - 1 \)\( x + 1 \)

Correct Answer: A

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Question 10

A set A has 5 elements, and a set B has 3 elements. Find the number of elements in the union of sets A and B.

A. 8

Correct B. 10

C. 12

D. 15

Correct Answer: B

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Question 11

Find the equation of the circle pas\sing through the points (2, 3), (4, 1), and \( -1, 2 \).

Correct A. x^2 + y^2 - 6x + 4y + 5 = 0

B. x^2 + y^2 - 4x - 2y + 3 = 0

C. x^2 + y^2 + 2x - 4y + 2 = 0

D. x^2 + y^2 - 2x + 6y - 1 = 0

Correct Answer: A

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Question 12

A right circular cone has a height of 10 cm and a base radius of 4 cm. Find the volume of the cone.

A. 40\pi cm^3

B. 80\pi cm^3

Correct C. 120\pi cm^3

D. 160\pi cm^3

Correct Answer: C

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Question 13

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

Correct A. 0.2

B. 0.24

C. 0.3

D. 0.36

Correct Answer: A

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Question 14

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

Correct A. x ≤ -1 or x ≥ \frac{3}{2}

B. x ≤ -1 or x ≥ -\frac{3}{2}

C. x ≤ 1 or x ≥ -\frac{3}{2}

D. x ≤ -1 or x ≥ 1

Correct Answer: A

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Question 15

Find the area under the curve y = x^2 + 2x - 3 from x = 1 to x = 3.

A. 20

B. 22

Correct C. 24

D. 26

Correct Answer: C

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Question 16

Solve the inequality \( x+2 \ \)^2 - 4\( x-1 \)^2 > 0).

Correct A. \(x < -3\) or \(x > 2\)

B. \(x > -3\) or \(x < 2\)

C. \(x < -3\) and \(x > 2\)

D. \(x > -3\) and \(x < 2\)

Correct Answer: A

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Question 17

Find the area under the curve [y = \frac{1}{x^2 + 1}, \quad x \in [0, 1]\].

Correct A. \pi - 1

B. \frac{\pi}{2}

C. \frac{\pi}{4}

D. \frac{\pi}{8}

Correct Answer: A

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Question 18

Solve the equation [x^3 - 6x^2 + 11x - 6 = 0].

Correct A. 1, 2, 3

B. 1, 2, -3

C. 2, 3, -1

D. -1, 2, 3

Correct Answer: A

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Question 19

Find the value of [\log_{10} \( x^2 + 1 \) = 4].

Correct A. \frac{1}{10}

B. \frac{1}{100}

C. \frac{1}{1000}

D. \frac{1}{10000}

Correct Answer: A

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Question 20

Solve the equation [\sin^2 x + \cos^2 x = 1\].

A. x = \frac{\pi}{2}

Correct B. x = \frac{\pi}{4}

C. x = \frac{3\pi}{4}

D. x = \frac{5\pi}{4}

Correct Answer: B

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Question 21

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

Correct A. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 \)

B. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \)

C. \( \frac{1}{2} \times 4^3 - 3 \times 4^2 - 2 \times 4 \)

D. \( \frac{1}{2} \times 4^2 - 3 \times 4 - 2 \)

Correct Answer: A

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Question 22

Solve the vector equation \( overrightarrow{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( overrightarrow{b} = egin{pmatrix} 4 \ 5 \end{pmatrix} \). Find the magnitude of \( overrightarrow{a} + overrightarrow{b} \).

Correct A. \( \sqrt{2^2 + 3^2 + 4^2 + 5^2} \)

B. \( \sqrt{2^2 + 3^2 - 4^2 - 5^2} \)

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

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

Correct Answer: A

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Question 23

Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \) for ( x ) in the interval ( [0, 2pi] ).

Correct A. \( x = \frac{pi}{4} \)

B. \( x = \frac{pi}{2} \)

C. \( x = \frac{3pi}{4} \)

D. \( x = \frac{5pi}{4} \)

Correct Answer: A

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Question 24

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 = 4 )

C. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 9 )

D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 25 )

Correct Answer: A

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Question 25

Convert the decimal number ( 123.45 ) to binary.

Correct A. ( 1111011.011 )

B. ( 1111011.110 )

C. ( 1111011.101 )

D. ( 1111011.0111 )

Correct Answer: A

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