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POST UTME NILE UNIVERSITY 2024 Mathematics | Objective

Are you preparing for POST UTME NILE UNIVERSITY 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

In the complex plane, the points $z_1 = 2 + 3i$ and $z_2 = 4 - 5i$ are represented by vectors $mathbf{z}_1$ and $mathbf{z}_2$, respectively. Find the magnitude of the vector $mathbf{z}_1 + mathbf{z}_2$.

Correct A. \sqrt{10}

B. \sqrt{20}

C. \sqrt{30}

D. \sqrt{40}

Correct Answer: A

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Question 2

Let $f(x) = \log_{10} $ x^2 $$. Find the value of $f^{-1}(4)$.

A. 2

B. 4

Correct C. 10

D. 20

Correct Answer: C

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Question 3

A circle with center $C$ and radius $r$ passes through the points $A(1, 2)$ and $B(4, 6)$. Find the equation of the circle in the form $$ x - h $^2 + $ y - k $^2 = r^2$.

A. $ x - 2.5 $^2 + $ y - 4 $^2 = 2.5^2

Correct B. $ x - 2.5 $^2 + $ y - 4 $^2 = 5^2

C. $ x - 2.5 $^2 + $ y - 4 $^2 = 7.5^2

D. $ x - 2.5 $^2 + $ y - 4 $^2 = 10^2

Correct Answer: B

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Question 4

A polynomial $p(x)$ has roots $x = 1$ and $x = -2$. If $p(0) = 12$, find the value of $p(3)$.

A. -3

B. 6

Correct C. 9

D. 12

Correct Answer: C

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Question 5

A random variable $X$ has a probability distribution given by $P$ X = x $ = \frac{1}{2} cdot \frac{1}{2} = \frac{1}{4}$ for $x = 1, 2, 3, 4$. Find the expected value of $X$.

A. 1.5

Correct B. 2

C. 2.5

D. 3

Correct Answer: B

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Question 6

Determine the value of $\int_{0}^{\pi} \frac{\sin^2 x}{1 + \cos^2 x} dx$.

Correct A. \frac{\pi}{2}

B. \frac{\pi}{4}

C. \frac{\pi}{8}

D. \frac{\pi}{16}

Correct Answer: A

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Question 7

A histogram of exam scores is shown below. If the mean score is 75, what is the median score?

A. 70

Correct B. 75

C. 80

D. 85

Correct Answer: B

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Question 8

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

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

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

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

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

Correct Answer: A

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Question 9

A vector $\vec{a}$ has a magnitude of 5 and points in the direction of $\frac{1}{\sqrt{2}} \hat{i} + \frac{1}{\sqrt{2}} \hat{j}$. Find the magnitude of the vector $\vec{a} + \vec{b}$, where $\vec{b}$ is a vector with a magnitude of 3 and points in the opposite direction of $\vec{a}$.

A. 2

B. 4

Correct C. 6

D. 8

Correct Answer: C

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Question 10

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

A. \frac{\pi}{4}

Correct B. \frac{\pi}{2}

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

D. \pi

Correct Answer: B

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Question 11

A random sample of 25 students from a university had a mean height of 175.5 cm with a s\tandard deviation of 5.2 cm. If the population s\tandard deviation is 6.1 cm, calculate the 95% confidence interval for the population mean.

Correct A. 168.1 cm, 182.9 cm

B. 170.5 cm, 180.5 cm

C. 172.1 cm, 178.9 cm

D. 174.5 cm, 176.5 cm

Correct Answer: A

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Question 12

Solve the following system of linear equations u\sing matrices: \[ \begin{align*} x + y + z &= 6 \ 2x - 3y + z &= 9 \ x - 2y + 3z &= 2 \end{align*} \]

Correct A. \[ \begin{align*} x &= 1 \ y &= 2 \ z &= 3 \end{align*} \]

B. \[ \begin{align*} x &= 2 \ y &= 1 \ z &= 3 \end{align*} \]

C. \[ \begin{align*} x &= 3 \ y &= 2 \ z &= 1 \end{align*} \]

D. \[ \begin{align*} x &= 1 \ y &= 3 \ z &= 2 \end{align*} \]

Correct Answer: A

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Question 13

A sequence is defined as: \[ a_n = \frac{1}{n} + \frac{1}{n+1} \] Calculate the sum of the first 10 terms of the sequence.

Correct A. 2.928968253

B. 2.928968253

C. 2.928968253

D. 2.928968253

Correct Answer: A

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Question 14

A set of 5 numbers has a mean of 10 and a s\tandard deviation of 2. If the numbers are 8, 12, 15, 18, and x, find the value of x.

Correct A. 20

B. 22

C. 24

D. 26

Correct Answer: A

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Question 15

A probability experiment consists of rolling a fair six-sided die. If the die lands on an even number, you win ₦100. If it lands on an odd number, you lose ₦50. What is the expected value of this experiment?

Correct A. ₦25

B. ₦50

C. ₦75

D. ₦100

Correct Answer: A

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Question 16

Determine the sum of the infinite geometric series - 3 + 6 + 12 + … with first term - 3 and common ratio 2.

Correct A. 9

B. -3

C. 12

D. -9

Correct Answer: A

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Question 17

Solve for x in the equation - 2x^2 + 5x - 3 = 0.

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 18

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

Correct A. 16

B. 32

C. 64

D. 128

Correct Answer: A

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Question 19

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

A. 1/6

B. 1/3

C. 2/3

Correct D. 5/6

Correct Answer: D

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Question 20

Simplify the expression √$ 16x^2y^2 $.

Correct A. 4xy

B. 2xy

C. 4x^2y

D. 2x^2y

Correct Answer: A

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Question 21

Find the value of $\int_0^1 \frac{1}{x^2 + 2x + 2} dx$.

Correct A. 0.5

B. 1

C. 1.5

D. 2

Correct Answer: A

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Question 22

Solve for $x$ in the equation $\log_2 $ 2x - 1 $ = 3$.

A. 2

Correct B. 3

C. 4

D. 5

Correct Answer: B

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Question 23

Find the area under the curve $y = x^2 + 2x + 1$ from $x = 0$ to $x = 2$.

A. 10

B. 12

Correct C. 15

D. 18

Correct Answer: C

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Question 24

Solve the inequality $|x - 2| > 3$.

Correct A. $ -∞, -1 $ ∪ (4, ∞)

B. $ -∞, 1 $ ∪ (2, ∞)

C. $ -∞, -1 $ ∪ (1, ∞)

D. $ -∞, 1 $ ∪ (4, ∞)

Correct Answer: A

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Question 25

Find the value of $\sum_{n=1}^5 n^2$.

Correct A. 55

B. 65

C. 75

D. 85

Correct Answer: A

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