POST UTME ABU 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the system of equations \begin{align*} x + y &= 4 \ x - y &= 2 \end{align*}.
A. \begin{pmatrix} 1 \ 3 \end{pmatrix}
B. \begin{pmatrix} 2 \ 2 \end{pmatrix}
C. \begin{pmatrix} 3 \ 1 \end{pmatrix}
D. \begin{pmatrix} 4 \ 0 \end{pmatrix}
Question 2
Find the volume of the solid formed by revolving the region bounded by $y = x^2$, $y = 0$, and $x = 1$ about the $x$-axis.
A. \frac{1}{3}\pi
B. \frac{2}{3}\pi
C. \frac{4}{3}\pi
D. \frac{5}{3}\pi
Question 3
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \) u\sing the quadratic formula.
A. x = -2
B. x = -1
C. x = 0
D. x = 2
Question 4
A sequence is defined by the recurrence relation \( a_n = 2a_{n-1} + 3 \). If \( a_1 = 2 \), find the value of \( a_{10} \).
A. 1023
B. 1024
C. 1025
D. 1026
Question 5
A surd is given by \( \sqrt{2} + \sqrt{3} \). Find the value of \( \sqrt{2} + \sqrt{3} \ \)^2 ).
A. 5 + 2\sqrt{6}
B. 5 - 2\sqrt{6}
C. 7 + 2\sqrt{6}
D. 7 - 2\sqrt{6}
Question 6
A binary operation ( odot ) is defined as \( a odot b = ab^2 \). Find the value of ( 2 odot 3 ).
A. 18
B. 24
C. 36
D. 48
Question 7
Find the equation of the \tangent line to the curve y = x^2 + 2x - 3 at the point (1, 2).
A. y = 4x - 1
B. y = 4x + 1
C. y = 4x - 3
D. y = 4x + 3
Question 8
A probability experiment consists of rolling two fair six-sided dice. What is the probability that the sum of the numbers on the dice is 7?
A. 1/6
B. 1/12
C. 1/18
D. 1/36
Question 9
Find the volume of the solid formed by revolving the region bounded by the curve \( y = x^2 \) and the line \( x = 2 \) about the x-axis.
A. \( \frac{4}{3} pi \times 2^3 \)
B. \( \frac{4}{3} pi \times 2^2 \)
C. \( \frac{4}{3} pi \times 2 \)
D. \( \frac{4}{3} pi \times 2^2 \times 2 \)
Question 10
Let $X$ and $Y$ be indep\endent random variables with probability density functions $f_X(x) = egin{cases} 2x & 0 leq x leq 1 \ 0 & \text{otherwise} \end{cases}$ and $f_Y(y) = egin{cases} 3y^2 & 0 leq y leq 1 \ 0 & \text{otherwise} \end{cases}$. Find the probability that $X+Y leq 1$.
A. \frac{1}{2}
B. \frac{1}{3}
C. \frac{2}{3}
D. \frac{3}{4}
Question 11
Solve for x in the equation \( \frac{1}{x} + 2 = \frac{3}{x} \).
A. -1
B. 1
C. 2
D. 3
Question 12
Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 48\pi cm^3
B. 64\pi cm^3
C. 96\pi cm^3
D. 128\pi cm^3
Question 13
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 14
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 \)
B. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \)
C. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4^2 \)
D. \( \frac{1}{2} \times 4^2 + 3 \times 4^3 - 2 \times 4 \)
Question 15
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. x < -1
B. x > 1
C. x < 3
D. x > -3

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