POST UTME OSUSTECH 2018 Mathematics | Objective

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Question 1 View Details
Solve the inequality (\(\frac{x}{x-1}\(> 2\)\) for \\((frac{x}{x-1} > 2\(x > 1\)\).
Correct A. \(x > 3\)
B. \(x < 3\)
C. \(x > 5\)
D. \(x < 5\)

Correct Answer: A

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Question 2 View Details
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 View Details
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 View Details
Find the equation of the line passing 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 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 + \(y - 3\)^\(2 = 20\) )
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 View Details
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 View Details
A histogram of exam scores has a mean of 75 and a standard 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 View Details
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 View Details
Solve the system of equations using 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 View Details
Find the derivative of the function f(x) = \(3x^2 + 2x - 5\) using 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 View Details
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 View Details
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 View Details
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 View Details
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 \(km/h\\((km/h). On the return trip, the average speed is 40\). 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 View Details
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 View Details
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 View Details
A particle moves along the curve (y = 2x\^2 + 3x - 4\). Find the equation of the \\((y = 2x^2 + 3x - 4\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 View Details
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 View Details
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 View Details
A force of 5 N acts on an object, causing 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 View Details
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 View Details
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 View Details
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 View Details
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 View Details
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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