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POST UTME NOUN 2025 Mathematics | Objective

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Question 1

Determine the volume of the frustum of a cone with height $h$ and radii $r_1$ and $r_2$, where $r_1 > r_2$.

Correct A. \frac{1}{3}\pi h$ r_1^2+r_2^2+r_1r_2 $

B. \frac{1}{3}\pi h$ r_1^2-r_2^2 $

C. \frac{1}{3}\pi h$ r_1^2+r_2^2-r_1r_2 $

D. \frac{1}{3}\pi h$ r_1^2-r_2^2+r_1r_2 $

Correct Answer: A

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Question 2

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

A. -\frac{2x}{$ x^2+1 $^2}

Correct B. \frac{2x}{$ x^2+1 $^2}

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

D. \frac{1}{$ x^2+1 $^2}

Correct Answer: B

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Question 3

A set $S$ is defined as $S = \{x \in \mathbb{R} : x^2 - 6x + 8 \geq 0\}$. Find the set $S$.

Correct A. \{x \in \mathbb{R} : x \leq 2\}

B. \{x \in \mathbb{R} : x \geq 2\}

C. \{x \in \mathbb{R} : x \leq 4\}

D. \{x \in \mathbb{R} : x \geq 4\}

Correct Answer: A

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Question 4

Find the sum of the first $n$ terms of the geometric series $\sum_{k=1}^{n} \frac{1}{2^k}$.

Correct A. 1-\frac{1}{2^n}

B. 1-\frac{1}{2^{n+1}}

C. 1-\frac{2}{2^n}

D. 1-\frac{2}{2^{n+1}}

Correct Answer: A

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Question 5

Solve the inequality $|x-2| \geq 3$.

Correct A. x \leq -1 \text{ or } x \geq 5

B. x \leq 1 \text{ or } x \geq 5

C. x \leq -1 \text{ or } x \geq 4

D. x \leq 1 \text{ or } x \geq 4

Correct Answer: A

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Question 6

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 u\sing the Pythagorean theorem.

A. 8 cm

Correct B. 12 cm

C. 16 cm

D. 20 cm

Correct Answer: B

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Question 7

A random variable X has a probability distribution given by P$ X = 1 $ = 0.3, P$ X = 2 $ = 0.4, and P$ X = 3 $ = 0.3. Find the expected value of X.

A. 1.1

B. 1.3

Correct C. 1.5

D. 1.7

Correct Answer: C

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Question 8

A circle has a radius of 4 cm. Find the area of the circle.

Correct A. 50.24 cm^2

B. 50.24 m^2

C. 50.24 cm^3

D. 50.24 m^3

Correct Answer: A

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Question 9

A vector →A = 3→i + 4→j. Find the magnitude of the vector.

A. 5

Correct B. 10

C. 15

D. 20

Correct Answer: B

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Question 10

A function f(x) = 2x^2 + 3x - 1 has a local maximum at x = -1. Find the value of the function at this point.

A. -3

Correct B. -1

C. 1

D. 3

Correct Answer: B

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Question 11

Solve the inequality $ \frac{x}{x-1} > 2 $ for $ x > 1 $.

Correct A. $ x > 3 $

B. $ x < 3 $

C. $ x > 5 $

D. $ x < 5 $

Correct Answer: A

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Question 12

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

A. $ 14 $

B. $ 16 $

Correct C. $ 18 $

D. $ 20 $

Correct Answer: C

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Question 13

A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?

A. $ \frac{1}{2} $

Correct B. $ \frac{2}{5} $

C. $ \frac{3}{8} $

D. $ \frac{4}{7} $

Correct Answer: B

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Question 14

The mean of 5 numbers is 12. If one of the numbers is 15, what is the mean of the remaining 4 numbers?

A. $ 10 $

Correct B. $ 11 $

C. $ 12 $

D. $ 13 $

Correct Answer: B

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Question 15

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 = 20 \)

C. $ x-2 $^2 + $ y-3 $^2 = 24 \)

D. $ x-2 $^2 + $ y-3 $^2 = 28 \)

Correct Answer: A

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Question 16

Solve the system of equations $ x + y = 4 $ and $ x - y = 2 $.

Correct A. $ x = 3, y = 1 $

B. $ x = 1, y = 3 $

C. $ x = 2, y = 2 $

D. $ x = 4, y = 0 $

Correct Answer: A

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Question 17

Find the area of the triangle with vertices ( (0, 0), (3, 0), ) and ( (0, 2) ).

A. $ 6 $

B. $ 8 $

Correct C. $ 10 $

D. $ 12 $

Correct Answer: C

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Question 18

A car travels from point A to point B at an average speed of 60 km/h. If the dis\tance between the two points is 240 km, how long does the journey take?

A. $ 4 $

Correct B. $ 5 $

C. $ 6 $

D. $ 7 $

Correct Answer: B

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Question 19

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

Correct A. $ y = x + 1 $

B. $ y = x - 1 $

C. $ y = x + 2 $

D. $ y = x - 2 $

Correct Answer: A

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Question 20

In a random sample of 100 students, the mean height is 175 cm with a s\tandard deviation of 5 cm. If the mean height of the entire population is 180 cm, what is the s\tandard error of the mean?

A. 2.5 cm

Correct B. 5 cm

C. 10 cm

D. 15 cm

Correct Answer: B

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Question 21

A rec\tangular prism has a length of 10 cm, a width of 5 cm, and a height of 8 cm. What is the volume of the prism?

Correct A. 400 cm³

B. 500 cm³

C. 600 cm³

D. 800 cm³

Correct Answer: A

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Question 22

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

Correct A. x < -1 or x > 3

B. x < 1 or x > 3

C. x < -3 or x > 1

D. x < 3 or x > 1

Correct Answer: A

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Question 23

In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the acute angles is 30°. What is the length of the side opposite the 30° angle?

A. 5 cm

Correct B. 7.5 cm

C. 10 cm

D. 12.5 cm

Correct Answer: B

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Question 24

A circle has a radius of 4 cm. What is the area of the circle?

Correct A. 50.24 cm²

B. 62.83 cm²

C. 75.40 cm²

D. 100.53 cm²

Correct Answer: A

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Question 25

Let X be a random variable with probability density function ( f(x) = egin{cases} 2x & 0 leq x leq 1 \ 0 & \text{otherwise} \end{cases} ). Find the probability that X is greater than 0.5.

Correct A. $ \frac{1}{2} $

B. $ \frac{1}{4} $

C. $ \frac{3}{4} $

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

Correct Answer: A

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