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POST UTME LEAD CITY UNIVERSITY 2023 Mathematics | Objective

Are you preparing for POST UTME LEAD CITY UNIVERSITY exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2023 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

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

Correct A. \frac{x - 2}{4 - 2} = \frac{y - 3}{5 - 3}

B. \frac{x - 4}{2 - 4} = \frac{y - 5}{3 - 5}

C. \frac{x - 2}{4 - 2} = \frac{y - 5}{3 - 5}

D. \frac{x - 4}{2 - 4} = \frac{y - 3}{5 - 3}

Correct Answer: A

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Question 2

Solve the system of linear equations u\sing matrices:

Correct A. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 2 \end{bmatrix}

B. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 2 \ 3 \end{bmatrix}

C. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 1 \ 4 \end{bmatrix}

D. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 4 \ 1 \end{bmatrix}

Correct Answer: A

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Question 3

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

Correct Answer: A

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Question 4

Solve the quadratic equation x^2 + 4x + 4 = 0.

Correct A. x = -2

B. x = 2

C. x = -1

D. x = 1

Correct Answer: A

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Question 5

Find the mean of the data set: 2, 4, 6, 8, 10.

A. 6

Correct B. 8

C. 10

D. 12

Correct Answer: B

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Question 6

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 7

Solve for y in the equation \( y = \frac{1}{2} \left\( \frac{1}{3} \right \ \)^x ).

A. 3

B. 6

Correct C. 9

D. 12

Correct Answer: C

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Question 8

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

A. 50π

B. 100π

Correct C. 150π

D. 200π

Correct Answer: C

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Question 9

Find the value of x in the equation \( x^2 + 4x + 4 = 0 \).

Correct A. -2

B. -1

C. 0

D. 1

Correct Answer: A

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Question 10

A right triangle has a hypotenuse of 10 cm and one leg of 6 cm. Find the length of the other leg.

Correct A. 8

B. 6

C. 4

D. 2

Correct Answer: A

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Question 11

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

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

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

Correct Answer: A

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Question 12

A random variable ( X ) has a probability distribution given by ( P(X) = egin{cases} 0.2 & \text{if } X = 1 \ 0.3 & \text{if } X = 2 \ 0.5 & \text{if } X = 3 \end{cases} ). Find the expected value of ( X ).

Correct A. \( 1 \times 0.2 + 2 \times 0.3 + 3 \times 0.5 \)

B. \( 1 \times 0.3 + 2 \times 0.2 + 3 \times 0.5 \)

C. \( 1 \times 0.5 + 2 \times 0.3 + 3 \times 0.2 \)

D. \( 1 \times 0.5 + 2 \times 0.2 + 3 \times 0.3 \)

Correct Answer: A

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Question 13

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{-2}{\( x^2 + 1 \ \)^2} )

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

Correct Answer: A

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Question 14

A matrix ( A ) is given by \( A = egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \). Find the determinant of ( A ).

Correct A. \( 1 \times 4 - 2 \times 3 \)

B. \( 1 \times 3 - 2 \times 4 \)

C. \( 2 \times 4 - 1 \times 3 \)

D. \( 2 \times 3 - 1 \times 4 \)

Correct Answer: A

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Question 15

A histogram of exam scores is given below. Find the mean of the scores.

A. ( 15 )

Correct B. ( 20 )

C. ( 25 )

D. ( 30 )

Correct Answer: B

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Question 16

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

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 17

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

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 18

Find the determinant of the matrix \( \begin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 3 & 1 & 2 \end{bmatrix} \).

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 19

Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).

Correct A. x = -2

B. x = -1

C. x = 0

D. x = 1

Correct Answer: A

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Question 20

Find the area of the triangle with vertices ( A(1, 2) ), ( B(3, 4) ), and ( C(2, 1) ).

A. 5

B. 6

Correct C. 7

D. 8

Correct Answer: C

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Question 21

Determine the probability of the event that a randomly selected student from a class of 30 students is a member of the school debate team, given that 8 students are members of the debate team.

Correct A. \frac{1}{3}

B. \frac{1}{5}

C. \frac{2}{5}

D. \frac{1}{4}

Correct Answer: A

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Question 22

Solve for x in the equation \(\log_2 \( x^2 \) = 4\).

A. 4

B. 8

Correct C. 16

D. 32

Correct Answer: C

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Question 23

Find the determinant of the matrix \[\begin{bmatrix} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{bmatrix}\].

Correct A. 0

B. 1

C. -1

D. 2

Correct Answer: A

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Question 24

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 25

Solve the trigonometric equation \(\sin^2 x + \cos^2 x = 1\).

Correct A. \sin x = \cos x

B. \sin x = -\cos x

C. \cos x = 0

D. \sin x = 0

Correct Answer: A

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