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POST UTME MADONNA UNIVERSITY 2024 Mathematics | Objective

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Question 1

Find the volume of the frustum of a cone with height 15 cm, lower base radius 6 cm, and upper base radius 3 cm.

A. 450\pi\text{ cm}^3

Correct B. 600\pi\text{ cm}^3

C. 750\pi\text{ cm}^3

D. 900\pi\text{ cm}^3

Correct Answer: B

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Question 2

Solve for x in the equation $ 2^x + 3^x = 5^x $.

A. x = 2

B. x = 3

Correct C. x = 4

D. x = 5

Correct Answer: C

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Question 3

Find the equation of the circle pas\sing through the points (2, 3), (4, 5), and (6, 7).

Correct A. $ x - 4 $^2 + $ y - 5 $^2 = 9

B. $ x - 3 $^2 + $ y - 4 $^2 = 16

C. $ x - 5 $^2 + $ y - 6 $^2 = 25

D. $ x - 6 $^2 + $ y - 7 $^2 = 36

Correct Answer: A

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Question 4

A right-angled triangle has a hypotenuse of length 10 cm and one of the acute angles is 30°. Find the length of the side opposite the 30° angle.

A. 5\text{ cm}

Correct B. 7.5\text{ cm}

C. 10\text{ cm}

D. 12.5\text{ cm}

Correct Answer: B

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Question 5

Find the value of $ \log_{10} \( 2^3 $.

Correct A. 3

B. 6

C. 9

D. 12

Correct Answer: A

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Question 6

In the coordinate plane, the line $y = 2x + 3$ intersects the circle $x^2 + $ y - 2 $^2 = 4$ at two points. Find the coordinates of the point where the line is \tangent to the circle.

Correct A. (1, 5)

B. (2, 7)

C. (3, 9)

D. (4, 11)

Correct Answer: A

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Question 7

A bag contains 5 red marbles, 4 blue marbles, and 3 green marbles. If a marble is drawn at random, what is the probability that it is not blue?

A. 1/3

Correct B. 2/3

C. 3/4

D. 4/5

Correct Answer: B

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Question 8

Solve the inequality $|2x - 1| geq 3$.

Correct A. $x leq -1$ or $x geq 2$

B. $x leq -2$ or $x geq 1$

C. $x leq -3$ or $x geq 2$

D. $x leq -1$ or $x geq 3$

Correct Answer: A

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Question 9

A right triangle has legs of length 3 and 4. Find the length of the hypotenuse.

A. 5

Correct B. 6

C. 7

D. 8

Correct Answer: B

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Question 10

Find the value of $x$ in the equation $2^x + 2^x = 64$.

A. 3

Correct B. 4

C. 5

D. 6

Correct Answer: B

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Question 11

Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.

A. 64\pi cm^3

B. 96\pi cm^3

Correct C. 128\pi cm^3

D. 192\pi cm^3

Correct Answer: C

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Question 12

A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is not blue?

Correct A. \frac{2}{3}

B. \frac{3}{4}

C. \frac{4}{5}

D. \frac{5}{6}

Correct Answer: A

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Question 13

Solve the equation $ x^2 + 2x - 6 = 0 $ u\sing the quadratic formula.

A. \frac{-2 \pm \sqrt{4 + 24}}{2}

Correct B. \frac{-2 \pm \sqrt{28}}{2}

C. \frac{-2 \pm \sqrt{4 - 24}}{2}

D. \frac{-2 \pm \sqrt{28 - 4}}{2}

Correct Answer: B

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Question 14

Find the surface area of the sphere with radius 5 cm.

A. 100\pi cm^2

B. 200\pi cm^2

Correct C. 300\pi cm^2

D. 400\pi cm^2

Correct Answer: C

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Question 15

A snail is at the bottom of a 20-foot well. Each day, it climbs up 3 feet, but at night, it slips back 2 feet. How many days will it take for the snail to reach the top of the well?

A. 18 days

Correct B. 19 days

C. 20 days

D. 21 days

Correct Answer: B

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Question 16

Solve for x in the equation $ \sin^2\( x \ $ + \cos^2(x) = 1 ) u\sing the identity $ \sin^2\( x \ $ + \cos^2(x) = 1 ).

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 17

A bakery sells a total of 480 loaves of bread per day. They sell a combination of whole wheat and white bread. If the ratio of whole wheat to white bread is 5:3, how many loaves of whole wheat bread are sold per day?

A. 120

Correct B. 150

C. 180

D. 200

Correct Answer: B

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Question 18

Find the derivative of the function ( 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{-x}{$ x^2 + 1 $^2}

D. \frac{x}{$ x^2 + 1 $^2}

Correct Answer: A

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Question 19

Solve the inequality $ 2x^2 + 5x - 3 > 0 $ u\sing the quadratic formula.

Correct A. x < -1 or x > \frac{3}{2}

B. x < -1 or x < \frac{3}{2}

C. x > -1 or x < \frac{3}{2}

D. x > -1 or x > \frac{3}{2}

Correct Answer: A

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Question 20

A circle has a radius of 4 cm. Find the area of the circle u\sing the formula $ A = \pi r^2 $.

Correct A. 50.24 cm^2

B. 50.24 m^2

C. 50.24 cm^3

D. 50.24 m^3

Correct Answer: A

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Question 21

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

Correct A. \frac{x}{$ 1 - x^2 $^{3/2}}

B. \frac{1}{$ 1 - x^2 $^{3/2}}

C. \frac{1}{$ 1 - x^2 $^{1/2}}

D. \frac{-x}{$ 1 - x^2 $^{3/2}}

Correct Answer: A

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Question 22

Solve the system of linear equations u\sing matrices: \begin{align*} x + y &= 3 \ 2x - 3y &= -5 \end{align*}

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

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

C. \begin{pmatrix} 1 \ -2 \end{pmatrix}

D. \begin{pmatrix} -1 \ -2 \end{pmatrix}

Correct Answer: A

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Question 23

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

Correct A. 0

B. 1

C. 2

D. 3

Correct Answer: A

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Question 24

Solve the quadratic equation $ x^2 + 4x + 4 = 0 $ u\sing the quadratic formula.

A. \frac{-4 \pm \sqrt{16 - 16}}{2}

Correct B. \frac{-4 \pm \sqrt{16 - 4}}{2}

C. \frac{-4 \pm \sqrt{16 + 4}}{2}

D. \frac{-4 \pm \sqrt{16 - 4}}{2}

Correct Answer: B

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Question 25

Find the derivative of the function $ f(x) = x^2 \sin(x) $ u\sing the product rule.

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

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

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

D. \cos(x) + x^2 \sin(x)

Correct Answer: A

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