Exam Body

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POST UTME UNIBEN 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1

Find the area under the curve $ y = x^2 + 2x - 3 $ from $ x = 0 $ to $ x = 3 $.

A. 27

B. 30

C. 33

D. 36

Question 2

A sequence is defined as $ a_n = 2n + 1 $. Find the sum of the first 5 terms of the sequence.

A. 15

B. 25

C. 35

D. 45

Question 3

A set A contains 5 elements. If we select 2 elements from set A, what is the number of ways to do this?

A. 10

B. 15

C. 20

D. 25

Question 4

Find the area under the curve $ y = x^2 $ from $ x = 0 $ to $ x = 2 $.

A. 4

B. 6

C. 8

D. 10

Question 5

Solve the inequality $\frac{x}{x-1} > 0$.

A. x < 0 \text{ or } x > 1

B. x < 1

C. x > 1

D. x > 0

Question 6

Simplify the expression $ \frac{1}{2} \log_2 \( x^2 + 1 \ $ + \frac{3}{2} \log_2 $ x^2 - 1 $ ).

A. $ \log_2 \( x^2 + 1 \ $ )

B. $ \log_2 \( x^2 - 1 \ $ )

C. $ \log_2 \( x^2 + 1 \ $ + \log_2 $ x^2 - 1 $ )

D. $ \log_2 \( x^2 + 1 \ $ - \log_2 $ x^2 - 1 $ )

Question 7

Find the derivative of the function $f(x) = \frac{1}{x^2 + 1}$.

A. f'(x) = \frac{-2x}{$ x^2 + 1 $^2}

B. f'(x) = \frac{2x}{$ x^2 + 1 $^2}

C. f'(x) = \frac{x}{$ x^2 + 1 $^2}

D. f'(x) = \frac{-x}{$ x^2 + 1 $^2}

Question 8

Find the area under the curve $ y = x^2 $ from x = 0 to x = 4.

A. 16

B. 32

C. 64

D. 128

Question 9

A quadratic equation has roots 2 and 3. What is the product of the roots?

A. 1

B. 2

C. 3

D. 4

Question 10

Find the vector ( mathbf{a} ) such that $ mathbf{a} cdot mathbf{b} = 10 $ and $ mathbf{a} cdot mathbf{c} = 5 $, where $ mathbf{b} = 2mathbf{i} + 3mathbf{j} $ and $ mathbf{c} = mathbf{i} - 2mathbf{j} $.

A. $ 3mathbf{i} - mathbf{j} $

B. $ 2mathbf{i} + mathbf{j} $

C. $ mathbf{i} + 2mathbf{j} $

D. $ mathbf{i} - 2mathbf{j} $

Question 11

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?

A. 1.5

B. 2.0

C. 2.5

D. 3.0

Question 12

Let ( S ) be the set of all real numbers ( x ) such that $ x^2 + 2x - 3 > 0 $. Find the set ( S ) in interval notation.

A. $ -∞, -1 $ ∪ (3, ∞)

B. $ -∞, 1 $ ∪ (3, ∞)

C. $ -∞, -1 $ ∪ (1, ∞)

D. $ -∞, 1 $ ∪ (1, ∞)

Question 13

A bakery sells a total of 480 loaves of bread per day. They sell a combination of whole wheat and white bread. If the ratio of whole wheat to white bread is 5:4, how many loaves of whole wheat bread are sold per day?

A. 200

B. 250

C. 300

D. 350

Question 14

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. 0.8413

B. 0.8419

C. 0.8423

D. 0.8431

Question 15

Solve the equation $ 2x^2 + 5x - 3 = 0 $ u\sing the quadratic formula.

A. $ -1 ± √13 $/4

B. (1 ± √13)/4

C. $ -1 ± √5 $/4

D. (1 ± √5)/4

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