POST UTME RSU 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Evaluate the definite integral \( int_0^1 x^2 , dx \) u\sing the power rule.
A. \( \frac{1}{3} \)
B. \( \frac{1}{2} \)
C. \( \frac{2}{3} \)
D. \( \frac{1}{4} \)
Question 2
Find the area under the curve y = x^2 + 2x - 3 from x = 0 to x = 2.
A. 13/3
B. 14/3
C. 15/3
D. 16/3
Question 3
A vector ℓ has a magnitude of 5 and makes an angle of 60° with the positive x-axis. What is the magnitude of the vector ℓ + 3℔, where ℔ is a unit vector in the positive x-direction?
A. 5
B. 6
C. 7
D. 8
Question 4
The mean of 5 numbers is 12. If one of the numbers is 15, find the sum of the remaining 4 numbers.
A. 45
B. 48
C. 51
D. 54
Question 5
In a quadratic equation of the form \( ax^2 + bx + c = 0 \), if the discriminant \( b^2 - 4ac \) is 12, and the sum of the roots is 5, find the product of the roots.
A. 3
B. 4
C. 6
D. 12
Question 6
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -\frac{5}{4} \ \) or \( x > \frac{3}{2} \ \)
B. \( x < -\frac{3}{2} \ \) or \( x > \frac{5}{4} \ \)
C. \( x < -\frac{3}{2} \ \) or \( x > \frac{5}{4} \ \)
D. \( x < -\frac{5}{4} \ \) or \( x > \frac{3}{2} \ \)
Question 7
A box contains 5 red balls and 3 blue balls. If two balls are drawn at random, what is the probability that both balls are blue?
A. \frac{1}{14}
B. \frac{3}{14}
C. \frac{1}{7}
D. \frac{3}{7}
Question 8
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. \( 22.5 + 24 - 8 = 38.5 \)
B. \( 8 + 24 - 2 = 30 \)
C. \( 8 + 24 - 8 = 24 \)
D. \( 22.5 + 24 - 8 = 38.5 \)
Question 9
Find the sum of the first 10 terms of the geometric series 2, 6, 18, ...
A. 1023
B. 1024
C. 1025
D. 1026
Question 10
Solve for ( x ) in the equation \( 2x^2 - 5x + 3 = 0 \).
A. \( x = \frac{5 \pm \sqrt{25 - 24}}{4} = \frac{5 \pm 1}{4} \ \)
B. \( x = \frac{5 \pm \sqrt{25 + 24}}{4} = \frac{5 \pm 7}{4} \ \)
C. \( x = \frac{5 \pm \sqrt{25 - 24}}{2} = \frac{5 \pm 1}{2} \ \)
D. \( x = \frac{5 \pm \sqrt{25 + 24}}{2} = \frac{5 \pm 7}{2} \ \)
Question 11
In a geometric sequence with a common ratio of 2, the first term is 3. What is the sum of the first 5 terms?
A. 255
B. 265
C. 275
D. 285
Question 12
In a normal distribution, the mean is 10 and the s\tandard deviation is 2. What is the probability that a value is between 8 and 12?
A. 0.5
B. 0.6
C. 0.7
D. 0.8
Question 13
Determine the volume of the frustum of a cone with a height of 10 cm, a lower base radius of 4 cm, and an upper base radius of 2 cm.
A. 50\pi cm^3
B. 75\pi cm^3
C. 100\pi cm^3
D. 125\pi cm^3
Question 14
A circle with center ( O ) and radius 6 units is inscribed in a square with side length 12 units. Find the area of the shaded region.
A. 72
B. 144
C. 216
D. 288
Question 15
Solve for x in the equation \( \sin^2 x + \cos^2 x = 1 \) u\sing the identity \( \sin^2 x + \cos^2 x = 1 \).
A. \( x = \frac{pi}{2} \)
B. \( x = \frac{pi}{4} \)
C. \( x = \frac{3pi}{4} \)
D. \( x = \frac{5pi}{4} \)

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