POST UTME KSU 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A vector \( vec{a} = egin{pmatrix} 2 \ 3 \ 1 \end{pmatrix} \) is given. Find the magnitude of the vector.
A. \( |vec{a}| = 4 \)
B. \( |vec{a}| = 5 \)
C. \( |vec{a}| = 6 \)
D. \( |vec{a}| = 7 \)
Question 2
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \)
A. -2
B. -1
C. 1
D. 2
Question 3
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. 1.1
B. 1.3
C. 1.5
D. 1.7
Question 4
A histogram is a graphical representation of a frequency distribution. What is the shape of a histogram that represents the distribution of exam scores?
A. Symmetric
B. Skewed
C. Bell-shaped
D. Uniform
Question 5
Find the mean of the data set: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20.
A. 10
B. 12
C. 14
D. 16
Question 6
Solve the equation \( x^2 + 5x + 6 = 0 \).
A. x = -2, x = -3
B. x = 2, x = 3
C. x = -1, x = -6
D. x = 1, x = 6
Question 7
Find the equation of the line pas\sing through the points (2, 3) and (4, 1).
A. y = -x + 5
B. y = x - 1
C. y = 2x - 1
D. y = -2x + 5
Question 8
Let {a_n} be a sequence defined by a_n = 2n + 1. Find the sum of the first 5 terms of the sequence.
A. 10
B. 12
C. 15
D. 18
Question 9
Solve for x in the equation \( \frac{1}{x+2} + \frac{1}{x-3} = \frac{3}{2} \).
A. x = 5
B. x = 2
C. x = -1
D. x = 3
Question 10
A set of numbers is defined as {2, 4, 6, 8, 10}. Find the union of this set with the set {1, 3, 5, 7, 9}.
A. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
B. {2, 4, 6, 8, 10}
C. {1, 3, 5, 7, 9}
D. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}
Question 11
Solve for x in the equation \( \frac{1}{x+2} + \frac{1}{x-3} = \frac{3}{2} \).
A. x = 5
B. x = 2
C. x = -1
D. x = 3
Question 12
A line passes through the points (2, 3) and (4, 5). What is the slope of the line?
A. 1
B. 2
C. 3
D. 4
Question 13
Find the equation of the circle pas\sing through the points (2, 3), (4, 1), and (6, 5).
A. x^2 + y^2 - 10x - 2y + 28 = 0
B. x^2 + y^2 - 8x - 4y + 16 = 0
C. x^2 + y^2 - 12x - 6y + 36 = 0
D. x^2 + y^2 - 14x - 8y + 56 = 0
Question 14
Find the sum of the first 10 terms of the geometric sequence with first term \( a = 2 \) and common ratio \( r = 3 \).
A. 2 + 6 + 18 + 54 + 162 + 486 + 1458 + 4374 + 13122 + 39366
B. 2 + 6 + 18 + 54 + 162 + 486 + 1458 + 4374 + 13122 + 39366 + 118098
C. 2 + 6 + 18 + 54 + 162 + 486 + 1458 + 4374 + 13122 + 39366 + 118098 + 354294
D. 2 + 6 + 18 + 54 + 162 + 486 + 1458 + 4374 + 13122 + 39366 + 118098 + 354294 + 1062882
Question 15
Find the equation of the circle with center \( 3, -2 \ \) ) and radius ( 4 ).
A. \( x - 3 \)^2 + \( y + 2 \)^2 = 16
B. \( x + 3 \)^2 + \( y - 2 \)^2 = 16
C. \( x - 3 \)^2 + \( y + 2 \)^2 = 9
D. \( x + 3 \)^2 + \( y - 2 \)^2 = 9

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