POST UTME MADONNA UNIVERSITY 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the sum of the infinite geometric series \sum_{n=1}^\infty \frac{2}{3^n}.
A. \frac{2}{3}
B. \frac{4}{3}
C. \frac{6}{3}
D. \frac{8}{3}
Question 2
Find the sum of the first 10 terms of the geometric series \( 2x^2 + 4x^3 + 8x^4 + ... \).
A. 2x^2\( 1 + 2 + 4 + ... + 512 \)
B. 2x^2\( 1 - 2 + 4 - ... + 512 \)
C. 2x^2\( 1 + 2 + 4 + ... + 512 \)
D. 2x^2\( 1 - 2 + 4 - ... + 512 \)
Question 3
Find the equation of the line pas\sing through the points ( (1, 2) ) and ( (3, 4) )
A. \( y = 2x - 1 \ \)
B. \( y = 2x + 1 \ \)
C. \( y = 3x - 2 \ \)
D. \( y = 3x + 2 \ \)
Question 4
A set of data has a mean of 25 and a s\tandard deviation of 3. If the data follows a normal distribution, what is the probability that a randomly selected value is between 20 and 30?
A. 0.8413
B. 0.8413
C. 0.6827
D. 0.6827
Question 5
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 40
B. 50
C. 60
D. 70
Question 6
Solve for ( x ) in the equation \( 2^x = 64 \)
A. \( x = 3 \ \)
B. \( x = 4 \ \)
C. \( x = 5 \ \)
D. \( x = 6 \ \)
Question 7
Solve the system of equations \( 2x + 3y = 7 \) and \( x - 2y = -3 \)
A. \( x = 1, y = 2 \ \)
B. \( x = 2, y = 1 \ \)
C. \( x = 3, y = 4 \ \)
D. \( x = 4, y = 3 \ \)
Question 8
Solve for ( x ) in the equation \( 2^x + 3^x = 5^x \).
A. 1
B. 2
C. 3
D. 4
Question 9
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. \( x < -\frac{5}{4} \) or \( x < \frac{3}{2} \)
D. \( x > -\frac{5}{4} \) or \( x < \frac{3}{2} \)
Question 10
A sequence is defined by \( a_n = 2n + 1 \). Find the sum of the first 5 terms of the sequence.
A. ( 15 )
B. ( 25 )
C. ( 35 )
D. ( 45 )
Question 11
Find the equation of the line pas\sing through the points ( A(2, 3) ) and ( B(4, 5) ).
A. \( y = \frac{1}{2}x + \frac{1}{2} \)
B. \( y = \frac{1}{2}x - \frac{1}{2} \)
C. \( y = 2x - 1 \)
D. \( y = 2x + 1 \)
Question 12
A random experiment has two indep\endent events, A and B. The probability of event A occurring is 0.4, and the probability of event B occurring is 0.6. What is the probability that both events A and B occur?
A. 0.24
B. 0.24
C. 0.24
D. 0.24
Question 13
A geometric sequence is defined by \( a_n = 2 \times 3^{n-1} \). Find the sum of the first 4 terms of the sequence.
A. ( 82 )
B. ( 92 )
C. ( 102 )
D. ( 112 )
Question 14
Find the equation of the circle with center \( C\( -2, 3 \ \) ) and radius \( r = 4 \).
A. \( x + 2 \ \)^2 + \( y - 3 \)^2 = 16 )
B. \( x - 2 \ \)^2 + \( y + 3 \)^2 = 16 )
C. \( x + 2 \ \)^2 + \( y + 3 \)^2 = 16 )
D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )
Question 15
Solve the inequality \( \frac{x^2 - 4}{x + 2} > 0 \) for \( x in mathbb{R} setminus { -2 } \).
A. \( -2, -∞ \) ∪ (2, ∞)
B. \( -∞, -2 \) ∪ (2, ∞)
C. \( -∞, -2 \) ∪ \( -2, 2 \) ∪ (2, ∞)
D. \( -∞, 2 \) ∪ (2, ∞)

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