POST UTME BOWEN UNIVERSITY 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \).
A. 32
B. 64
C. 96
D. 128
Question 2
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. x < -1
B. x > 1
C. x < 3
D. x > -3
Question 3
A binary operation * is defined as follows: a * b = a^2 + b^2. Find the value of \( 2 * 3 \) * 4.
A. 32
B. 40
C. 48
D. 64
Question 4
A set 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 will be between 70 and 80?
A. 0.34
B. 0.68
C. 0.85
D. 0.95
Question 5
Find the value of \sum_{n=1}^{\infty} \frac{1}{n^2}.
A. \boxed{\frac{\pi^2}{6}}
B. \frac{\pi^2}{12}
C. \frac{\pi^2}{24}
D. \frac{\pi^2}{48}
Question 6
In a certain number base, the digits 1, 2, and 3 represent the values 2, 5, and 8, respectively. What is the value of the number 432 in this base?
A. 19
B. 21
C. 23
D. 25
Question 7
Two events are indep\endent if the occurrence of one does not affect the probability of the occurrence of the other. Which of the following events are indep\endent?
A. Drawing a card from a deck and flipping a coin
B. Rolling a die and tos\sing a coin
C. Drawing a card from a deck and rolling a die
D. All of the above
Question 8
A polynomial function f(x) has a degree of 4 and the following properties: f(1) = 2, f\( -1 \) = -2, f(0) = 0, f(2) = 10. Find the value of f(3).
A. 30
B. 40
C. 50
D. 60
Question 9
Two events A and B are indep\endent. The probability of event A occurring is 0.4, and the probability of event B occurring is 0.6. Find the probability that both events A and B occur.
A. 0.2
B. 0.3
C. 0.4
D. 0.5
Question 10
In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the other sides is 6 cm. Find the length of the third side u\sing the co\sine rule.
A. 8
B. 12
C. 16
D. 20
Question 11
Solve for x in the equation \( \frac{1}{2}x^2 + 5x - 3 = 0 \).
A. x = -10
B. x = 6
C. x = -3
D. x = 2
Question 12
Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.
A. 1.999999999
B. 2.999999999
C. 3.999999999
D. 4.999999999
Question 13
In a certain number base, the representation of the number 27 is 101. What is the value of the number base?
A. 3
B. 4
C. 5
D. 6
Question 14
A random variable X has a probability distribution given by \[ P(X) = \begin{cases} 0.2 & \text{if } x = 1, \\ 0.3 & \text{if } x = 2, \\ 0.5 & \text{if } x = 3. \end{cases} \] Find the mean of X.
A. 1.5
B. 2.0
C. 2.5
D. 3.0
Question 15
The area under the curve y = x^2 from x = 0 to x = 4 can be calculated u\sing the definite integral. What is the value of this integral?
A. 64
B. 128
C. 256
D. 512

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