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POST UTME ABU 2017 Mathematics | Objective

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Question 1 View Details

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

A. 32\pi

B. 64\pi

Correct C. 128\pi

D. 256\pi

Correct Answer: C

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Question 2 View Details

A set of 5 numbers has a mean of 10 and a standard deviation of 2. Find the probability that a randomly selected number from this set is greater than 12.

A. 0.25

B. 0.5

Correct C. 0.75

D. 0.9

Correct Answer: C

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Question 3 View Details

In a geometric sequence, the first term is 2 and the common ratio is 3. Find the sum of the first 5 terms of this sequence.

Correct A. 731

B. 7311

C. 73111

D. 731111

Correct Answer: A

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Question 4 View Details

A circle has a radius of 4 cm. Find the area of the circle.

Correct A. 50.24

B. 100.48

C. 200.96

D. 201.06

Correct Answer: A

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Question 5 View Details

A set of 3 numbers has a median of 5 and a mode of 3. Find the mean of this set.

A. 4

Correct B. 5

C. 6

D. 7

Correct Answer: B

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Question 6 View Details

Determine the value of 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 7 View Details

Solve the inequality \(2x^2 + 5x - 3 > 0\).

Correct A. \(-∞, -1\) ∪ (3, ∞)

B. \(-∞, -3\) ∪ (1, ∞)

C. \(-∞, -1\) ∪ (1, ∞)

D. \(-∞, 1\) ∪ (3, ∞)

Correct Answer: A

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Question 8 View Details

Find the sum of the first 5 terms of the geometric progression 2, 6, 18, ...

Correct A. 126

B. 128

C. 130

D. 132

Correct Answer: A

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Question 9 View Details

Solve the quadratic equation \(x^2 + 4x + 4 = 0\).

Correct A. -2

B. -1

C. 0

D. 1

Correct Answer: A

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Question 10 View Details

Determine the value of y in the equation \(y = 2x^2 + 5x - 3\) when x = -1.

Correct A. -1

B. 0

C. 1

D. 2

Correct Answer: A

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Question 11 View Details

In a survey of 100 students, the mean height was 175 cm with a standard deviation of 5 cm. If the heights of the students are normally distributed, what is the probability that a randomly selected student will have a height between 170 cm and 180 cm?

Correct A. 0.68

B. 0.95

C. 0.99

D. 0.999

Correct Answer: A

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Question 12 View Details

Solve for x in the equation \(x^2 + 4x + 4 = 0\)

Correct A. -2

B. 0

C. 2

D. 4

Correct Answer: A

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Question 13 View Details

A circle has a radius of 4 cm. If the area of the circle is 50.24 \(cm^2\), what is the circumference of the circle?

Correct A. 12.56 cm

B. 25.12 cm

C. 50.24 cm

D. 100.48 cm

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 \((km/h\)\) and returns at an average speed of 40 \(km/h\\((km/h) and returns at an average speed of 40\). What is the average speed of the car for the entire trip?

A. 48 \(km/h\)

B. 50 \(km/h\)

Correct C. 52 \(km/h\)

D. 54 \(km/h\)

Correct Answer: C

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Question 15 View Details

A water tank can hold 2000 liters of water. If \(3/4\) of the \\(tank can hold 2000 liters of water. If \((3/4\)\tank is already filled, how many more liters of water can be added?

Correct A. 1000 liters

B. 1200 liters

C. 1500 liters

D. 2000 liters

Correct Answer: A

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Question 16 View Details

Find the value of x in the equation \(\frac{1}{x} + \frac{1}{x+1} = \frac{1}{2}\).

A. 1

Correct B. 2

C. 3

D. 4

Correct Answer: B

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Question 17 View Details

Solve the inequality \(2x^2 + 5x - 3 > 0\).

Correct A. \(-∞, -1\) ∪ (3, ∞)

B. \(-∞, -3\) ∪ (1, ∞)

C. \(-∞, 1\) ∪ (3, ∞)

D. \(-∞, -3\) ∪ (1, ∞)

Correct Answer: A

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Question 18 View Details

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

A. 4

B. 6

Correct C. 8

D. 10

Correct Answer: C

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Question 19 View Details

Solve the system of equations \(egin{cases} x + y = 2 \ x - y = 1 \end{cases}\).

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

B. \(x = 1\),\(y = -1\)

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

D. \(x = -1\),\(y = -1\)

Correct Answer: A

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Question 20 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 - 3 \\)^2 + \(y - 2\)^\(2 = 16\) )

C. \(x - 4 \\)^2 + \(y - 3\)^\(2 = 16\) )

D. \(x - 2 \\)^2 + \(y - 4\)^\(2 = 16\) )

Correct Answer: A

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Question 21 View Details

Find the derivative of the function ( f(x) = \(x^3 - 2x^2 + x - 1\) ).

Correct A. ( f'\((x) =\)\(3x^2 - 4x + 1\) )

B. ( f'\((x) =\)\(3x^2 - 4x - 1\) )

C. ( f'\((x) =\)\(3x^2 + 4x - 1\) )

D. ( f'\((x) =\)\(3x^2 + 4x + 1\) )

Correct Answer: A

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Question 22 View Details

Find the integral of the function ( f(x) = \(x^2\) \sin x ).

Correct A. ( int f(x) dx = -\(x^2\) \cos x - 2x \sin x + 2 \cos x + C )

B. ( int f(x) dx = -\(x^2\) \cos x + 2x \sin x - 2 \cos x + C )

C. ( int f(x) \(dx = x\^2\) \cos x + 2x \sin x + 2 \cos x + C )

D. ( int f(x) \(dx = x\^2\) \cos x - 2x \sin x + 2 \cos x + C )

Correct Answer: A

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Question 23 View Details

Solve the matrix equation \(egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix}\).

A. \(x = 1, y = 2\)

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

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

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

Correct Answer: VIEW ANSWER

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Question 24 View Details

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

A. 8π

B. 16π

Correct C. 32π

D. 64π

Correct Answer: C

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Question 25 View Details

Solve the inequality \(\frac{x}{x-1} > 0\) for ( x in mathbb{R} ).

Correct A. \(x < 0\) or \(x > 1\)

B. \(x < 0\) or \(0 < x < 1\)

C. \(x > 0\) and \(x < 1\)

D. \(x > 1\)

Correct Answer: A

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