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POST UTME OSUSTECH 2018 Mathematics | Objective

Are you preparing for POST UTME OSUSTECH exams? Reviewing past questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2018 Mathematics (Objective) questions designed to simulate the real exam environment.

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Question 1

Solve the inequality \( \frac{x}{x-1} > 2 \) for \( x > 1 \).

Correct A. \( x > 3 \)

B. \( x < 3 \)

C. \( x > 5 \)

D. \( x < 5 \)

Correct Answer: A

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Question 2

Find the area under the curve \( y = x^2 + 2x + 1 \) from \( x = 0 \) to \( x = 2 \).

A. ( 10 )

Correct B. ( 12 )

C. ( 14 )

D. ( 16 )

Correct Answer: B

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Question 3

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

A. \( x = 1, y = 3 \)

Correct B. \( x = 2, y = 2 \)

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

D. \( x = 4, y = 0 \)

Correct Answer: B

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Question 4

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

Correct A. \( y = 2x - 1 \)

B. \( y = 2x + 1 \)

C. \( y = x + 2 \)

D. \( y = x - 2 \)

Correct Answer: A

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Question 5

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 = 20 )

C. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 24 )

D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 28 )

Correct Answer: A

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Question 6

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

A. 64\pi

B. 128\pi

Correct C. 256\pi

D. 512\pi

Correct Answer: C

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Question 7

A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?

A. 0.9544

Correct B. 0.9772

C. 0.9987

D. 0.9999

Correct Answer: B

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Question 8

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

A. 64\pi

B. 128\pi

Correct C. 256\pi

D. 512\pi

Correct Answer: C

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Question 9

Solve the system of equations u\sing matrices: \begin{bmatrix} 1 & 2 3 & 4 \end{bmatrix} \begin{bmatrix} x y \end{bmatrix} = \begin{bmatrix} 5 11 \end{bmatrix}.

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

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

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

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

Correct Answer: A

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Question 10

Find the derivative of the function f(x) = 3x^2 + 2x - 5 u\sing the chain rule.

Correct A. 6x + 2

B. 3x + 1

C. 2x - 1

D. x - 3

Correct Answer: A

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Question 11

Determine the mean of the following data set: 2, 4, 6, 8, 10. If the mean is increased by 2, what is the new mean?

A. 6

Correct B. 8

C. 10

D. 12

Correct Answer: B

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Question 12

A bakery sells 250 loaves of bread per day. If they make a profit of ₦5 per loaf, what is their total daily profit?

A. ₦1250

Correct B. ₦12500

C. ₦125000

D. ₦1250000

Correct Answer: B

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Question 13

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

Correct A. \( x = -3 \)

B. \( x = -1 \)

C. \( x = 1 \)

D. \( x = 3 \)

Correct Answer: A

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Question 14

A car travels from city A to city B at an average speed of 60 km/h. On the return trip, the average speed is 40 km/h. What is the average speed for the entire trip?

A. 40

B. 50

Correct C. 60

D. 70

Correct Answer: C

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Question 15

A histogram is shown below. What is the mode of the data set?

Correct A. A

B. B

C. C

D. D

Correct Answer: A

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Question 16

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. 48\pi cm^3

B. 64\pi cm^3

Correct C. 96\pi cm^3

D. 128\pi cm^3

Correct Answer: C

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Question 17

A particle moves along the curve y = 2x^2 + 3x - 4. Find the equation of the \tangent line at the point where x = 1.

Correct A. y = 11x - 7

B. y = 10x - 5

C. y = 9x - 3

D. y = 8x - 1

Correct Answer: A

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Question 18

Solve the inequality |x - 2| > 3.

Correct A. x < -1 or x > 5

B. x < -1 or x > 4

C. x < 1 or x > 5

D. x < 1 or x > 4

Correct Answer: A

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Question 19

Find the area of the region bounded by the curves y = x^2 and y = 2x.

A. 4/3

Correct B. 8/3

C. 16/3

D. 32/3

Correct Answer: B

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Question 20

A force of 5 N acts on an object, cau\sing it to accelerate at 2 m/s^2. Find the mass of the object.

A. 2.5 kg

Correct B. 5 kg

C. 10 kg

D. 20 kg

Correct Answer: B

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Question 21

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

Correct A. 10

B. 100

C. 1000

D. 10000

Correct Answer: A

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Question 22

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

Correct A. 25π

B. 50π

C. 75π

D. 100π

Correct Answer: A

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Question 23

A water \tank has a height of 10 m and a base radius of 2 m. Find the volume of water in the \tank.

A. 100π

Correct B. 200π

C. 300π

D. 400π

Correct Answer: B

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Question 24

A quadratic equation has the form \( ax^2 + bx + c = 0 \). If the equation has two real roots, which of the following is true?

A. The equation has no real roots.

B. The equation has one real root.

Correct C. The equation has two real roots.

D. The equation has no real roots, but has complex roots.

Correct Answer: C

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Question 25

A set of 5 cards is drawn from a deck of 52 cards. What is the probability that the set contains at least one ace?

A. 1/52

B. 1/26

C. 1/13

Correct D. 1/4

Correct Answer: D

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