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POST UTME LEAD CITY UNIVERSITY 2024 Mathematics | Objective

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Question 1 View Details

Find the derivative of the function ( f(x) = \(\frac{1}\){\sqrt{1 - \(x^2}}\)\) ) using the chain rule.

Correct A. \(\frac{1}{2} 1 - x^2 \\)^{-\(\frac{3}{2}\)\)} )

B. \(\frac{1}{2} 1 - x^2 \\)^{-\(\frac{1}{2}\)\)} )

C. \(\frac{x}{1 - x^2 \\)^{\(\frac{3}{2}\)\)}} )

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

Correct Answer: A

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Question 2 View Details

Solve the system of equations \(egin{cases} x + y + z = 6 \ 2x + 3y - z = 2 \ x - 2y + 3z = -3 \end{cases}\) using matrices.

Correct A. \(x = 1, y = 2, z = 3\)

B. \(x = 2, y = 1, z = 3\)

C. \(x = 3, y = 2, z = 1\)

D. \(x = 1, y = 3, z = 2\)

Correct Answer: A

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Question 3 View Details

Find the volume of the solid formed by revolving the region bounded by the curves \(y = x^2\) and \(y = 2x\) about the x-axis.

A. \(\frac{1}{3} \pi\)

B. \(\frac{2}{3} \pi\)

Correct C. \(\frac{4}{3} \pi\)

D. \(\frac{8}{3} \pi\)

Correct Answer: C

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Question 4 View Details

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

Correct A. \(x = \frac{\pi}{4}, \frac{3\pi}{4}, \frac{5\pi}{4}, \frac{7\pi}{4}\)

B. \(x = \frac{\pi}{2}, \frac{3\pi}{2}\)

C. \(x = \frac{\pi}{4}, \frac{3\pi}{4}\)

D. \(x = \frac{\pi}{2}, \frac{3\pi}{2}, \frac{5\pi}{2}\)

Correct Answer: A

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Question 5 View Details

Find the area of the triangle with vertices ( A(1, 2), B(3, 4), C(5, 6) ).

A. ( 10 )

B. ( 15 )

Correct C. ( 20 )

D. ( 25 )

Correct Answer: C

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Question 6 View Details

In a probability experiment, two events A and B are independent. If P(A) = 0.4 and P(B) = 0.6, what is the probability that both events occur?

Correct A. 0.24

B. 0.48

C. 0.64

D. 0.76

Correct Answer: A

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Question 7 View Details

Find the area under the curve \(y = 3x\^2 + 2x - 5\) from \(x = 0\) to \(x = 2\).

A. 22

Correct B. 24

C. 26

D. 28

Correct Answer: B

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Question 8 View Details

Solve the trigonometric 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 9 View Details

A quadratic equation has roots 2 and 3. Write the equation in the form \\((ax^2 + bx + c\)\(= 0.\)\)

Correct A. \\((x^2 - 5x + 6\)\(= 0\)\)

B. \\((x^2 - 4x + 3\)\(= 0\)\)

C. \\((x^2 - 6x + 4\)\(= 0\)\)

D. \\((x^2 - 3x + 2\)\(= 0\)\)

Correct Answer: A

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Question 10 View Details

A number is chosen at random from the set {1, 2, 3, 4, 5, 6}. What is the probability that the number is even?

Correct A. 0.5

B. 0.6

C. 0.7

D. 0.8

Correct Answer: A

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Question 11 View Details

Find the volume of the solid formed by revolving the region bounded by the curve (y = \(\frac{1}{2}\\()x^2 + 1\)\), the \\((y = frac{1}{2}x^2 + 1\(x)-axis, and the line \(x = 2\) about the \\()-axis, and the line (x = 2\(x\)-axis.

Correct A. \(\frac{8\pi}{3}\)\)

B. \(\frac{16\pi}{3}\)\)

C. \(\frac{32\pi}{3}\)\)

D. \(\frac{64\pi}{3}\)\)

Correct Answer: A

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Question 12 View Details

Solve the equation \(\log_{10} x^2\)\(= 4\)\) for \(x\).

A. \pm 10

Correct B. \pm 20

C. \pm 40

D. \pm 80

Correct Answer: B

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Question 13 View Details

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

A. 4

B. 6

Correct C. 8

D. 10

Correct Answer: C

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Question 14 View Details

A histogram of exam scores has a mean of 70 and a standard deviation of 10. If 80% of the scores fall below 90, what is the value of the score that corresponds to the 80th percentile?

A. 80

Correct B. 85

C. 90

D. 95

Correct Answer: B

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Question 15 View Details

Find the area of the triangle formed by the points \((0, 0)\), \((3, 0)\), and \((0, 4)\).

A. 6

B. 12

Correct C. 18

D. 24

Correct Answer: C

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Question 16 View Details

Find the derivative of the function ( f(x) = \(\frac{x^2 + 2x - 3}{x + 1}\)\)\) ) using the quotient rule.

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

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

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

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

Correct Answer: B

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Question 17 View Details

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

Correct A. \begin{pmatrix} x \ y \end{pmatrix} = \begin{pmatrix} 1 \ 1 \end{pmatrix}

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

C. \begin{pmatrix} x \ y \end{pmatrix} = \begin{pmatrix} 3 \ 2 \end{pmatrix}

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

Correct Answer: A

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Question 18 View Details

Find the equation of the circle passing through the points (1, 2), (3, 4), and (5, 6).

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

B. \(x - 2\)^2 + \(y - 3\)^\(2 = 9\)

C. \(x - 1\)^2 + \(y - 2\)^\(2 = 4\)

D. \(x - 4\)^2 + \(y - 5\)^\(2 = 25\)

Correct Answer: A

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Question 19 View Details

Solve the inequality \(\frac{x^2 - 4}{x + 2}\)\)\\() > 0.\)

Correct A. \(x > -2\)

B. \(x < -2\)

C. \(x > 2\)

D. \(x < 2\)

Correct Answer: A

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Question 20 View Details

Find the derivative of the function ( f(x) = \\(\sin^2\) x ) using the chain rule.

Correct A. \\(\cos^2\) x

B. -\\(\cos^2\) x

C. \\(\sin^2\) x

D. -\\(\sin^2\) x

Correct Answer: A

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Question 21 View Details

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

Correct A. \begin{pmatrix} x \ y \end{pmatrix} = \begin{pmatrix} 1 \ 1 \end{pmatrix}

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

C. \begin{pmatrix} x \ y \end{pmatrix} = \begin{pmatrix} 3 \ 2 \end{pmatrix}

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

Correct Answer: A

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Question 22 View Details

Find the equation of the circle passing through the points (1, 2), (3, 4), and (5, 6).

Question 23 View Details

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

Correct A. \(\frac{\pi}{4}\)\)

B. \(\frac{\pi}{2}\)\)

C. \(\frac{\pi}{3}\)\)

D. \(\frac{\pi}{6}\)\)

Correct Answer: A

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Question 24 View Details

Solve the inequality \(|x-2| > 3\).

Correct A. \(-\infty, -1\) \cup \(5, \infty\)

B. \(-\infty, -1\) \cup \(1, \infty\)

C. \(-\infty, 1\) \cup \(5, \infty\)

D. \(-\infty, 5\) \cup \(1, \infty\)

Correct Answer: A

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Question 25 View Details

A histogram of exam scores has a mean of 75 and a standard deviation of 10. If 75% of the scores fall below 85, what is the z-score corresponding to 85?

A. 0.5

Correct B. 1

C. 1.5

D. 2

Correct Answer: B

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