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POST UTME BABCOCK UNIVERSITY 2021 Mathematics | Objective

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Question 1 View Details

A random variable X has a probability distribution given by P\(X = 1 = 0.3\), P\(X = 2 = 0.4\), and P\(X = 3 = 0.3\). What is the expected value of X?

Correct A. 1.1

B. 1.2

C. 1.3

D. 1.4

Correct Answer: A

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Question 2 View Details

Solve the equation \(x^2 + 4x + 4 = 0\) using the quadratic formula. What is the value of x?

Correct A. -2

B. -1

C. 1

D. 2

Correct Answer: A

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Question 3 View Details

In the diagram below, what is the value of x?

A. 3

Correct B. 4

C. 5

D. 6

Correct Answer: B

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Question 4 View Details

A function f(x) is defined as f(x) = \((2x^2 + 3x - 1\)\). What is the value of f\(-2\\((2x^2 + 3x - 1). What is the value of f\)?

Correct A. -5

B. -4

C. -3

D. -2

Correct Answer: A

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Question 5 View Details

Solve the trigonometric equation (2 \\(sin^2\) x + 3 \(1x - 2 = 0\) for x in the interval [0, 2\\((2 sin^2 x + 3\)\(1x - 2 = 0\)\pi].

Correct A. \(\frac{\pi}{6}\)\)

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

C. \(\frac{\pi}{2}\)\)

D. \(\frac{5\pi}{6}\)\)

Correct Answer: A

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Question 6 View Details

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 7 View Details

Solve for ( x ) in the equation \(\left| x - 2 \right| + \left| x + 1 \right| = 3\).

A. 1

B. 2

Correct C. 3

D. 4

Correct Answer: C

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Question 8 View Details

Find the value of \(\(1\left \arc\)1\frac{3}{5} \right \\) ).

A. 0.6

Correct B. 0.8

C. 0.4

D. 0.2

Correct Answer: B

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Question 9 View Details

A fair six-sided die is rolled. What is the probability that the number obtained is greater than 4?

A. \(1/6\)

B. \(1/3\)

C. \(1/2\)

Correct D. \(2/3\)

Correct Answer: D

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Question 10 View Details

Find the sum of the first 10 terms of the geometric series \(2x^2 + 3x + 1\).

Correct A. \(200x^2 + 300x + 10\)

B. \(100x^2 + 150x + 5\)

C. \(50x^2 + 75x + 2\).5

D. \(25x^2 + 37\).5x + 1.25

Correct Answer: A

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Question 11 View Details

Let X be a random variable with probability density function f(x) = \(egin{cases} 2x & 0 \leq x \leq 1 \ 0 & \text{otherwise} \end{cases}\). Find the probability that X is greater than 0.5.

A. 0.25

Correct B. 0.5

C. 0.75

D. 1

Correct Answer: B

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Question 12 View Details

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

Correct A. 0.5

B. 1

C. 1.5

D. 2

Correct Answer: A

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Question 13 View Details

The equation of a circle is given by \(x^2 + y^2 - 6x + 4y + 4 = 0\). Find the center and radius of the circle.

Correct A. Center: \(3, -2\), Radius: 2

B. Center: (2, 3), Radius: 3

C. Center: (3, 2), Radius: 2

D. Center: \(2, -3\), Radius: 3

Correct Answer: A

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Question 14 View Details

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

Correct A. \(-∞, -1\) ∪ (4, ∞)

B. \(-∞, 1\) ∪ (4, ∞)

C. \(-∞, -1\) ∪ (1, ∞)

D. \(-∞, 4\) ∪ (1, ∞)

Correct Answer: A

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Question 15 View Details

Find the mean and standard deviation of the data set {2, 4, 6, 8, 10}.

Correct A. Mean: 6, Standard Deviation: 2

B. Mean: 5, Standard Deviation: 2

C. Mean: 6, Standard Deviation: 3

D. Mean: 5, Standard Deviation: 3

Correct Answer: A

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Question 16 View Details

A random sample of 25 students from a population of 500 students has a mean height of 170 cm with a standard deviation of 5 cm. Calculate the standard error of the mean.

A. 2.5 cm

Correct B. 3.5 cm

C. 4.5 cm

D. 5.5 cm

Correct Answer: B

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Question 17 View Details

A circle has a diameter of 10 cm. Find the area of the circle.

Correct A. 78.5 \(cm^2\)

B. 87.5 \(cm^2\)

C. 97.5 \(cm^2\)

D. 107.5 \(cm^2\)

Correct Answer: A

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Question 18 View Details

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

Correct A. 6x + 2

B. 6x - 2

C. 3x + 2

D. 3x - 2

Correct Answer: A

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Question 19 View Details

A rectangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find the volume of the prism.

Correct A. 30 \(cm^3\)

B. 40 \(cm^3\)

C. 50 \(cm^3\)

D. 60 \(cm^3\)

Correct Answer: A

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Question 20 View Details

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

Correct A. x < -1 or \(x > 3/2\)\)

B. \(x < 1\) or x > \(-3/2\)

C. \(x <\)\(-3/2\) or \(x > 1\)

D. \(x < 3/2\)\) or x > -1

Correct Answer: A

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Question 21 View Details

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

Correct A. 25.13 cm

B. 26.18 cm

C. 27.23 cm

D. 28.28 cm

Correct Answer: A

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Question 22 View Details

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

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

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

C. \(3x^2 + 4x + 1\)

D. \(3x^2 + 4x - 1\)

Correct Answer: A

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Question 23 View Details

A rectangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. Find the surface area of the prism.

Correct A. 104 \(cm^2\)

B. 114 \(cm^2\)

C. 124 \(cm^2\)

D. 134 \(cm^2\)

Correct Answer: A

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Question 24 View Details

Find the volume of the solid formed by rotating the region bounded by the curves \(y = x\^2\), \(y = 0\), and \(x = 2\) 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 25 View Details

Solve the inequality \(\frac{x^2 - 4}{x^2 - 9} > 0\).

Correct A. \(-\infty, -3\) \cup (1, \infty)\)

B. \(-\infty, -3\) \cup (1, \infty)\)

C. \(-\infty, -3\) \cup (1, \infty)\)

D. \(-\infty, -3\) \cup (1, \infty)\)

Correct Answer: A

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