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POST UTME LEAD CITY UNIVERSITY 2023 Mathematics | Objective

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Question 1 View Details

Find the equation of the line passing 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 View Details

Solve the system of linear equations using 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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

A random variable ( X ) has a probability distribution given by ( P(X) = egin{cases} 0.2 & text{if } \(X = 1\) \\(text{if} (X = 1\ 0.3 & text{if} \(X = 2\) \\(text{if} (X = 2\ 0.5 & text{if} \(X = 3\) \\(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 View Details

Find the derivative of ( f(x) = \(\frac{1}{x^2 + 1}\)\)\) ) using 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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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 View Details

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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