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POST UTME OAU 2024 Mathematics | Objective

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Question 1

Find the value of x in the quadratic equation \( x^2 + 5x + 6 = 0 \).

Correct A. -2

B. -1

C. 1

D. 2

Correct Answer: A

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Question 2

Solve the system of linear equations u\sing matrices:\n\( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 7 \ 10 \end{bmatrix} \).

Correct A. \( egin{bmatrix} 1 \ 2 \end{bmatrix} \)

B. \( egin{bmatrix} 2 \ 1 \end{bmatrix} \)

C. \( egin{bmatrix} 3 \ 4 \end{bmatrix} \)

D. \( egin{bmatrix} 4 \ 3 \end{bmatrix} \)

Correct Answer: A

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Question 3

Find the volume of the frustum of a cone with radii 6 cm and 4 cm and height 10 cm.

A. 120π cm³

Correct B. 150π cm³

C. 180π cm³

D. 200π cm³

Correct Answer: B

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Question 4

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

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

Correct Answer: A

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Question 5

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 6

Find the equation of the circle pas\sing through the points (2, 3), (4, 1), and \( -1, 2 \).

Correct A. x^2 + y^2 - 4x - 2y - 3 = 0

B. x^2 + y^2 + 4x + 2y - 3 = 0

C. x^2 + y^2 - 2x + 4y - 3 = 0

D. x^2 + y^2 + 2x - 4y - 3 = 0

Correct Answer: A

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Question 7

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

Correct A. \frac{\pi}{6} \text{ and } \frac{5\pi}{6}

B. \frac{\pi}{4} \text{ and } \frac{3\pi}{4}

C. \frac{\pi}{3} \text{ and } \frac{2\pi}{3}

D. \frac{\pi}{2} \text{ and } \frac{3\pi}{2}

Correct Answer: A

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Question 8

A random experiment has two indep\endent events A and B. The probability of event A occurring is 0.4, and the probability of event B occurring is 0.6. What is the probability that both events A and B occur?

Correct A. 0.24

B. 0.48

C. 0.64

D. 0.76

Correct Answer: A

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Question 9

The mean of a set of numbers is 25, and the s\tandard deviation is 5. What is the range of the set?

A. 10

B. 20

Correct C. 30

D. 40

Correct Answer: C

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Question 10

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 11

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

Correct A. 59049

B. 59048

C. 59050

D. 59051

Correct Answer: A

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Question 12

Solve for x in the equation \frac{1}{x} + \frac{1}{x+1} = \frac{1}{2}.

Correct A. 1

B. -1

C. 2

D. -2

Correct Answer: A

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Question 13

A bakery sells 250 loaves of bread per day. If they make a profit of ₦5 per loaf, how much profit do they make in a day?

Correct A. ₦1250

B. ₦1251

C. ₦1252

D. ₦1253

Correct Answer: A

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Question 14

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

Correct A. 6

B. 7

C. 8

D. 9

Correct Answer: A

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Question 15

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

Correct A. x = 3, y = 1

B. x = 1, y = 3

C. x = 2, y = 2

D. x = 4, y = 0

Correct Answer: A

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

A. 1

Correct B. -1

C. 2

D. -2

Correct Answer: B

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Question 18

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

A. 16/3

Correct B. 32/3

C. 64/3

D. 128/3

Correct Answer: B

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Question 19

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

Correct A. 1, 1

B. 1, -1

C. -1, 1

D. -1, -1

Correct Answer: A

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Question 20

Find the surface area of the solid formed by rotating the region bounded by \( y = x^2 \) and \( y = 2x \) about the x-axis.

A. 16π

Correct B. 32π

C. 64π

D. 128π

Correct Answer: B

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Question 21

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

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

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

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

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

Correct Answer: A

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Question 22

A random variable X has a probability distribution given by \( P\( X = k \ \) = \frac{1}{2^k}) for \( k = 1, 2, 3, ldots \). Find the probability that (X) is greater than 2.

A. \( \frac{1}{4} \)

B. \( \frac{1}{2} \)

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

Correct D. \( \frac{7}{8} \)

Correct Answer: D

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Question 23

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

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

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

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

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

Correct Answer: B

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Question 24

A rec\tangular box has dimensions 5 cm, 8 cm, and 3 cm. Find the surface area of the box.

A. \( 2\( 5 \times 8 + 8 \times 3 + 3 \times 5 \ \) )

B. \( 2\( 5 \times 8 + 8 \times 3 + 3 \times 5 \ \) + 2\( 5 \times 3 + 8 \times 3 + 5 \times 8 \) )

Correct C. \( 2\( 5 \times 8 + 8 \times 3 + 3 \times 5 \ \) + 2\( 5 \times 3 + 8 \times 3 + 5 \times 8 \) + 2\( 5 \times 8 + 5 \times 3 + 8 \times 3 \) )

D. \( 2\( 5 \times 8 + 8 \times 3 + 3 \times 5 \ \) + 2\( 5 \times 3 + 8 \times 3 + 5 \times 8 \) + 2\( 5 \times 8 + 5 \times 3 + 8 \times 3 \) + 2\( 5 \times 5 + 8 \times 8 + 3 \times 3 \) )

Correct Answer: C

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Question 25

Solve the inequality \( |2x - 1| > 3 \).

Correct A. \( x < -1 \) or \( x > 2 \)

B. \( x < -2 \) or \( x > 1 \)

C. \( x < -3 \) or \( x > 2 \)

D. \( x < -1 \) or \( x > 3 \)

Correct Answer: A

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