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POST UTME ELIZADE UNIVERSITY 2022 Mathematics | Objective

Are you preparing for POST UTME ELIZADE UNIVERSITY exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2022 Mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1

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

A. \( x = -10 \)

Correct B. \( x = 3 \)

C. \( x = -3 \)

D. \( x = 10 \)

Correct Answer: B

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Question 2

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

A. ( 2 )

B. ( 4 )

Correct C. ( 6 )

D. ( 8 )

Correct Answer: C

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Question 3

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 4

Find the derivative of the function ( f(x) = x^3 - 2x^2 + 5x - 1 ) u\sing the chain rule.

Correct A. ( f'(x) = 3x^2 - 4x + 5 )

B. ( f'(x) = 3x^2 - 4x + 1 )

C. ( f'(x) = 3x^2 - 4x - 1 )

D. ( f'(x) = 3x^2 - 4x - 5 )

Correct Answer: A

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Question 5

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

Correct A. \( x = 1, y = 1 \)

B. \( x = 1, y = 3 \)

C. \( x = 3, y = 1 \)

D. \( x = 3, y = 3 \)

Correct Answer: A

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Question 6

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

A. 64

B. 80

Correct C. 96

D. 112

Correct Answer: C

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Question 7

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

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

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

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

D. x = \frac{7\pi}{4}

Correct Answer: A

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Question 8

Find the equation of the circle with center ( (3, 4) ) and radius ( 5 ).

Correct A. \( x - 3 \)^2 + \( y - 4 \)^2 = 25

B. \( x - 4 \)^2 + \( y - 3 \)^2 = 25

C. \( x - 3 \)^2 + \( y - 4 \)^2 = 30

D. \( x - 4 \)^2 + \( y - 3 \)^2 = 30

Correct Answer: A

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Question 9

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

A. x < -1

Correct B. x > -1

C. x < 3

D. x > 3

Correct Answer: B

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Question 10

Find the value of ( x ) in the equation \( x^3 - 6x^2 + 11x - 6 = 0 \).

A. x = 1

B. x = 2

Correct C. x = 3

D. x = 4

Correct Answer: C

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Question 11

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. If two indep\endent random variables X and Y are defined on the same probability space, and Y has a probability distribution given by P\( Y = 1 \) = 0.4, P\( Y = 2 \) = 0.3, and P\( Y = 3 \) = 0.3, what is the probability that X + Y = 4?

A. 0.1

B. 0.2

Correct C. 0.3

D. 0.4

Correct Answer: C

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Question 12

Solve the equation \( 2x^2 + 5x - 3 = 0 \) u\sing the quadratic formula.

Correct A. \( x = \frac{-5 \pm \sqrt{109}}{4} \)

B. \( x = \frac{-5 \pm \sqrt{121}}{4} \)

C. \( x = \frac{-5 \pm \sqrt{169}}{4} \)

D. \( x = \frac{-5 \pm \sqrt{225}}{4} \)

Correct Answer: A

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Question 13

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

Correct A. \( \frac{32\pi}{5} \)

B. \( \frac{64\pi}{5} \)

C. \( \frac{128\pi}{5} \)

D. \( \frac{256\pi}{5} \)

Correct Answer: A

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Question 14

Solve the system of equations \( \begin{cases} 2x + 3y = 7 \ 4x - 2y = -3 \end{cases} \) u\sing matrices.

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

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

C. \( x = 3, y = 4 \)

D. \( x = 4, y = 3 \)

Correct Answer: A

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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. \( x - 3 \)^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 16

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.

A. 168.3 cm, 182.7 cm

Correct B. 170.1 cm, 180.9 cm

C. 172.9 cm, 178.1 cm

D. 169.5 cm, 181.5 cm

Correct Answer: B

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Question 17

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

Correct A. \[ x = \frac{\pi}{4} \]

B. \[ x = \frac{\pi}{2} \]

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

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

Correct Answer: A

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Question 18

A binary number 1101 is converted to decimal. What is the decimal equivalent?

A. 13

Correct B. 15

C. 17

D. 19

Correct Answer: B

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Question 19

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

Correct A. 0.24

B. 0.36

C. 0.48

D. 0.60

Correct Answer: A

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Question 20

Solve the inequality \[ 2x^2 + 5x - 3 \geq 0 \].

Correct A. \[ x \leq -1.5 \] or \[ x \geq 1.5 \]

B. \[ x \leq -1 \] or \[ x \geq 3 \]

C. \[ x \leq 0 \] or \[ x \geq 2 \]

D. \[ x \leq -2 \] or \[ x \geq 1 \]

Correct Answer: A

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Question 21

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

A. 64

B. 80

Correct C. 96

D. 112

Correct Answer: C

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Question 22

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

A. 800\pi

Correct B. 1000\pi

C. 1200\pi

D. 1600\pi

Correct Answer: B

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Question 23

Find the derivative of the function \( y = \sin^2 x \) u\sing the chain rule.

Correct A. \cos 2x

B. \sin 2x

C. \cos x

D. \sin x

Correct Answer: A

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Question 24

Solve the system of equations u\sing matrices: \begin{align*} 2x + 3y &= 7 \ 4x - 2y &= -3 \end{align*}

Correct A. \begin{bmatrix} 1 \ 2 \end{bmatrix}

B. \begin{bmatrix} 2 \ 1 \end{bmatrix}

C. \begin{bmatrix} 3 \ 4 \end{bmatrix}

D. \begin{bmatrix} 4 \ 3 \end{bmatrix}

Correct Answer: A

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Question 25

Simplify the expression \( \frac{2^3 \cdot 3^2}{2^2 \cdot 3^4} \).

Correct A. \frac{1}{12}

B. \frac{1}{6}

C. \frac{1}{4}

D. \frac{1}{3}

Correct Answer: A

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