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POST UTME WELLSPRING UNIVERSITY 2024 Mathematics | Objective

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Question 1 View Details

Find the volume of the solid formed by revolving the region bounded by the curves $y = x\^2$, $y = 0$, and $x = 2$ about the x-axis.

Correct A. $\frac{32\pi}{3}$\)

B. $\frac{64\pi}{3}$\)

C. $\frac{128\pi}{3}$\)

D. $\frac{256\pi}{3}$\)

Correct Answer: A

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Question 2 View Details

Solve for x in the equation \log_{10}$x^2 = 4$.

A. \pm 10

Correct B. \pm 100

C. \pm 1000

D. \pm 10000

Correct Answer: B

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Question 3 View Details

Find the surface area of the solid formed by revolving the region bounded by the curves $y = x\^2$, $y = 0$, and $x = 2$ about the x-axis.

Correct A. $\frac{64\pi}{3}$\)

B. $\frac{128\pi}{3}$\)

C. $\frac{256\pi}{3}$\)

D. $\frac{512\pi}{3}$\)

Correct Answer: A

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Question 4 View Details

Solve the system of equations \begin{align*} x + y &= 4 \ 2x - 3y &= 5 \end{align*} using matrices.

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

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

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

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

Correct Answer: A

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Question 5 View Details

Find the determinant of the matrix \begin{pmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{pmatrix}.

Correct A. -120

B. -240

C. -360

D. -480

Correct Answer: A

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Question 6 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 7 View Details

Solve the system of equations: $egin{cases} x + y = 4 \ 2x - 3y = - 3 \end{cases}$.

A. $-1, 5$

B. (1, 3)

Correct C. (2, 2)

D. (4, 0)

Correct Answer: C

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Question 8 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 + 2 \$^2 + $y - 3$^$2 = 16$ )

C. $x - 2 \$^2 + $y + 3$^$2 = 16$ )

D. $x + 2 \$^2 + $y + 3$^$2 = 16$ )

Correct Answer: A

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Question 9 View Details

Find the sum of the first 10 terms of the geometric series with first term $a = 2$ and common ratio $r = 3$.

Correct A. 3199

B. 3198

C. 3197

D. 3196

Correct Answer: A

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Question 10 View Details

Solve the inequality $x^2 - 4x - 5 > 0$.

Correct A. $x < -1$ or $x > 5$

B. $x < 1$ or $x > 5$

C. $x < -1$ or $x < 5$

D. $x > 1$ or $x > 5$

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

B. $\frac{1}{2} \times 4^2 + 3 \times 4 - 2$

C. $\frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4^2$

D. $\frac{1}{2} \times 4^2 + 3 \times 4^3 - 2 \times 4$

Correct Answer: A

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Question 12 View Details

A fair six-sided die is rolled. If the number 5 is rolled, a second die is rolled. What is the probability that the sum of the numbers on the two dice is 10?

A. $\frac{1}{6} \times \frac{1}{6}$

Correct B. $\frac{1}{6} \times \frac{5}{6}$

C. $\frac{1}{6} + \frac{1}{6}$

D. $\frac{1}{6} \times \frac{6}{6}$

Correct Answer: B

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Question 13 View Details

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

Correct A. $x = \frac{-5 \pm \sqrt{25 + 24}}{4}$

B. $x = \frac{-5 \pm \sqrt{25 - 24}}{4}$

C. $x = \frac{-5 \pm \sqrt{25 + 24}}{2}$

D. $x = \frac{-5 \pm \sqrt{25 - 24}}{2}$

Correct Answer: A

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Question 14 View Details

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

Correct A. $2 \times 6 \times 10 - 3 \times 5 \times 10 - 4 \times 8 \times 6$

B. $2 \times 6 \times 10 + 3 \times 5 \times 10 - 4 \times 8 \times 6$

C. $2 \times 6 \times 10 - 3 \times 5 \times 10 + 4 \times 8 \times 6$

D. $2 \times 6 \times 10 + 3 \times 5 \times 10 + 4 \times 8 \times 6$

Correct Answer: A

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Question 15 View Details

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

Correct A. $\pi \times 5^2$

B. $2 \pi \times 5$

C. $\pi \times 5$

D. $2 \pi \times 5^2$

Correct Answer: A

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Question 16 View Details

Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio $3/2$.

Correct A. 2.488

B. 2.488

C. 2.488

D. 2.488

Correct Answer: A

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Question 17 View Details

Solve the inequality $\frac{x+2}{x-1}$\$) > 0.$

Correct A. $-\infty, -2$ \cup $1, \infty$

B. $-\infty, -2$ \cup $1, \infty$

C. $-\infty, -2$ \cup $1, \infty$

D. $-\infty, -2$ \cup $1, \infty$

Correct Answer: A

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Question 18 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. $x-2$^2 + $y-3$^$2 = 25$

C. $x-2$^2 + $y-3$^$2 = 36$

D. $x-2$^2 + $y-3$^$2 = 49$

Correct Answer: A

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Question 19 View Details

Solve the system of equations \begin{align*} x+y+z &= 3 \ x+2y+3z &= 7 \ x+3y+6z &= 12 \end{align*}

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

B. \begin{align*} x &= 1 \ y &= 1 \ z &= 1 \end{align*}

C. \begin{align*} x &= 1 \ y &= 1 \ z &= 1 \end{align*}

D. \begin{align*} x &= 1 \ y &= 1 \ z &= 1 \end{align*}

Correct Answer: A

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Question 20 View Details

Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).

Correct A. 6

B. 6

C. 6

D. 6

Correct Answer: A

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Question 21 View Details

Determine the value of x in the equation $$12x \$ = $sqrt{3}$ ) given that $0^circ \\(sqrt{3}) ) given that \leq x \leq 90^circ$.

A. $45^circ$

B. $30^circ$

Correct C. $60^circ$

D. $90^circ$

Correct Answer: C

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Question 22 View Details

Find the determinant of the matrix $\begin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix}$.

Correct A. 1

B. -1

C. 2

D. -2

Correct Answer: A

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Question 23 View Details

A random experiment consists of rolling a fair six-sided die. If the outcome is an even number, the experimenter wins a prize. If the outcome is an odd number, the experimenter loses a prize. What is the probability that the experimenter wins the prize?

Correct A. $1/2$

B. $1/3$

C. $2/3$

D. $1/6$

Correct Answer: A

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Question 24 View Details

Find the volume of the solid formed by revolving the region bounded by the curve (y = $x^2$\) and the line $y = 4\\((y = x^2) and the line$ about the x-axis.

A. 32\pi

B. 16\pi

Correct C. 64\pi

D. 128\pi

Correct Answer: C

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Question 25 View Details

A histogram of the heights of students in a class has a mean of 170 cm and a standard deviation of 10 cm. What is the probability that a randomly selected student is taller than 180 cm?

A. 0.1587

B. 0.3413

C. 0.5

Correct D. 0.8413

Correct Answer: D

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