POST UTME UNIOSUN 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A set of exam scores has a mean of 80 and a s\tandard deviation of 10. If a new score of 90 is added to the set, what is the new mean?
A. 70
B. 75
C. 80
D. 85
Question 2
A rec\tangular box has a length of 6 cm, a width of 4 cm, and a height of 3 cm. Find the surface area of the box.
A. 88
B. 96
C. 104
D. 112
Question 3
Solve the inequality \( 2x^3 - 5x^2 + 3x - 1 > 0 \).
A. \( -\infty, -1 \) \cup \( 1, \infty \)
B. \( -\infty, 0 \) \cup \( 1, \infty \)
C. \( -\infty, -1 \) \cup (0, 1)
D. \( -\infty, 1 \)
Question 4
A histogram of exam scores is shown below. What is the mean score?
A. 40
B. 50
C. 60
D. 70
Question 5
Find the area under the curve \( y = \sin\( x \ \) ) from \( x = 0 \) to \( x = \frac{pi}{2} \).
A. \( \frac{1}{2} \)
B. \( \frac{pi}{2} \)
C. \( \frac{pi}{4} \)
D. \( \frac{pi}{8} \)
Question 6
A vector \overrightarrow{a} has magnitude 5 and direction 60°. Find the magnitude of the vector \overrightarrow{a} + \overrightarrow{b}, where \overrightarrow{b} has magnitude 3 and direction 120°.
A. 4
B. 5
C. 6
D. 7
Question 7
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{1}{2} \times 4^3 + 3 \times \frac{4^2}{2} - 2 \times 4 \)
B. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \)
C. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 \)
D. \( \frac{1}{2} \times 4^2 + 3 \times \frac{4^2}{2} - 2 \times 4 \)
Question 8
Find the value of $\int_0^1 2x \sqrt{1-x^2} dx$.
A. \frac{\pi}{2}
B. \frac{\pi}{4}
C. \frac{\pi}{6}
D. \frac{\pi}{8}
Question 9
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -1 \) or \( x > \frac{3}{2} \)
B. \( x < -1 \) or \( x < \frac{3}{2} \)
C. \( x > -1 \) or \( x > \frac{3}{2} \)
D. \( x > -1 \) or \( x < \frac{3}{2} \)
Question 10
Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3/2.
A. 2047
B. 2048
C. 2049
D. 2050
Question 11
Find the determinant of the matrix \( egin{pmatrix} 2 & 1 & 3 \ 4 & 2 & 1 \ 3 & 1 & 2 \end{pmatrix} \).
A. \( 2 \times \( 2 \times 2 - 1 \times 1 \ \) - 1 \times \( 4 \times 2 - 3 \times 1 \) + 3 \times \( 4 \times 1 - 3 \times 2 \) )
B. \( 2 \times \( 2 \times 2 - 1 \times 1 \ \) - 1 \times \( 4 \times 2 - 3 \times 1 \) - 3 \times \( 4 \times 1 - 3 \times 2 \) )
C. \( 2 \times \( 2 \times 2 - 1 \times 1 \ \) + 1 \times \( 4 \times 2 - 3 \times 1 \) + 3 \times \( 4 \times 1 - 3 \times 2 \) )
D. \( 2 \times \( 2 \times 2 - 1 \times 1 \ \) - 1 \times \( 4 \times 2 - 3 \times 1 \) - 3 \times \( 4 \times 1 - 3 \times 2 \) )
Question 12
A random experiment has two possible outcomes: A and B. The probability of outcome A is 0.4, and the probability of outcome B is 0.6. If the experiment is repeated 10 times, what is the probability that outcome A occurs at least 4 times?
A. 0.2
B. 0.3
C. 0.4
D. 0.5
Question 13
Find the derivative of the function \( y = \sin^2\( x \ \) ) u\sing the chain rule.
A. \( 2 \sin\( x \ \) \cos(x) )
B. \( \cos^2\( x \ \) )
C. \( \sin^2\( x \ \) )
D. \( \sin\( x \ \) )
Question 14
A sequence is defined by the recurrence relation \( a_n = 2a_{n-1} + 3 \) with initial term \( a_1 = 2 \). Find the sum of the first 5 terms of the sequence.
A. \( 2 + 7 + 17 + 37 + 79 \)
B. \( 2 + 5 + 13 + 29 + 61 \)
C. \( 2 + 7 + 17 + 37 + 79 \)
D. \( 2 + 5 + 13 + 29 + 61 \)
Question 15
Find the equation of the line pas\sing through the points ( (2, 3) ) and ( (4, 5) ).
A. \( y = \frac{5 - 3}{4 - 2}x + \frac{3 \times 4 - 5 \times 2}{4 - 2} \)
B. \( y = \frac{5 - 3}{4 - 2}x + \frac{3 \times 4 - 5 \times 2}{4 - 2} \)
C. \( y = \frac{5 - 3}{4 - 2}x + \frac{3 \times 2 - 5 \times 4}{4 - 2} \)
D. \( y = \frac{5 - 3}{4 - 2}x + \frac{3 \times 2 - 5 \times 4}{4 - 2} \)

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