POST UTME AAUA 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the sum of the first 10 terms of the arithmetic progression 2, 5, 8, ...
A. 50
B. 55
C. 60
D. 65
Question 2
Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).
A. ( 0 )
B. ( 1 )
C. ( 2 )
D. ( 3 )
Question 3
A sequence is defined by \( a_n = \frac{2n + 1}{n^2 + 1} \). Find the sum of the first 5 terms.
A. 1.2
B. 1.5
C. 1.8
D. 2.0
Question 4
Solve the system of equations u\sing matrices:\n\n2x + 3y = 7\n\nx - 2y = -3
A. x = 1, y = 2
B. x = 2, y = 1
C. x = 3, y = 4
D. x = 4, y = 3
Question 5
Solve the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 6
Find the determinant of the matrix \( egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} \).
A. 1
B. -1
C. 2
D. 3
Question 7
Find the equation of the line pas\sing through the points ( (2, 3) ) and ( (4, 5) ).
A. y = 2x + 1
B. y = 2x - 1
C. y = x + 1
D. y = x - 1
Question 8
Solve the system of equations $\begin{align*} x + y + z &= 6 \ x + 2y + 3z &= 11 \ x + 3y + 6z &= 16 \end{align*}$.
A. [1, 2, 3]
B. [2, 3, 1]
C. [3, 1, 2]
D. [1, 3, 2]
Question 9
A random variable $X$ has a probability distribution given by $P\( X = x \) = \frac{1}{x^2}$ for $x = 1, 2, 3, \dots$. Find the probability that $X$ is greater than 2.
A. 0.25
B. 0.5
C. 0.75
D. 1
Question 10
A histogram of exam scores is shown below. What is the mean score?
A. ( 50 )
B. ( 60 )
C. ( 70 )
D. ( 80 )
Question 11
A solid is formed by revolving the region bounded by \( y = x^2 \) and \( y = 2x \) about the x-axis. Find the volume of the solid.
A. 16π
B. 32π
C. 64π
D. 128π
Question 12
Find the derivative of the function ( f(x) = \frac{x^2}{x^2 + 1} \) u\sing the chain rule.
A. \frac{2x}{\( x^2 + 1 \)^2}
B. \frac{2x^2}{\( x^2 + 1 \)^2}
C. \frac{2x^3}{\( x^2 + 1 \)^2}
D. \frac{2x^4}{\( x^2 + 1 \)^2}
Question 13
Solve the equation \( x^2 + 4x + 4 = 0 \ \) u\sing the quadratic formula.
A. x = -2
B. x = -1
C. x = 0
D. x = 1
Question 14
Find the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 15
A vector ( mathbf{a} ) is given by \( mathbf{a} = 2mathbf{i} + 3mathbf{j} \). Find the magnitude of ( mathbf{a} ).
A. 1
B. √5
C. 2√5
D. 5

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