POST UTME UI 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A probability experiment consists of rolling a fair six-sided die. Find the probability that the number rolled is greater than 4.
A. 1/3
B. 1/2
C. 2/3
D. 3/4
Question 2
Solve for ( x ) in the equation \( 2x^2 + 5x - 3 = 0 \).
A. \( x = \frac{-5 pm \sqrt{25 + 24}}{4} \)
B. \( x = \frac{-5 pm \sqrt{25 - 24}}{4} \)
C. \( x = \frac{-5 pm \sqrt{25 + 24}}{2} \)
D. \( x = \frac{-5 pm \sqrt{25 - 24}}{2} \)
Question 3
In a binomial distribution with parameters \( n = 5 \) and \( p = 0.4 \), find the probability that exactly \( k = 2 \) successes occur.
A. 0.328
B. 0.328
C. 0.328
D. 0.328
Question 4
Find the area of the triangle with vertices ( (0, 0) ), ( (3, 0) ), and ( (0, 4) ).
A. ( 6 )
B. ( 12 )
C. ( 18 )
D. ( 24 )
Question 5
Find the sum of the first 10 terms of the geometric sequence with first term \( a = 2 \) and common ratio \( r = 3 \).
A. \( 2\( 3^{10} - 1 \ \) )
B. \( 2\( 3^{11} - 1 \ \) )
C. \( 2\( 3^{12} - 1 \ \) )
D. \( 2\( 3^{13} - 1 \ \) )
Question 6
A circle has equation $x^2+y^2=16$. Find the equation of the \tangent line at the point $(4,0)$.
A. y = -x + 4
B. y = x + 4
C. y = -x - 4
D. y = x - 4
Question 7
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 8
If \( \sin \theta = \frac{3}{5} \) and \( \cos \theta = \frac{4}{5} \), find the value of \( \tan \theta \).
A. \frac{3}{4}
B. \frac{4}{3}
C. \frac{3}{4}
D. \frac{4}{3}
Question 9
A circle has an equation of the form x^2 + y^2 + 2gx + 2fy + c = 0. Find the center of the circle.
A. \( -g, -f \)
B. (g, f)
C. \( -f, -g \)
D. (f, g)
Question 10
Find the volume of the solid formed by revolving the region bounded by the curve y = x^2, the x-axis, and the line x = 2 about the x-axis.
A. \frac{32\pi}{5}
B. \frac{64\pi}{5}
C. \frac{128\pi}{5}
D. \frac{256\pi}{5}
Question 11
Find the value of $\lim_{x\to\infty} \left\( \frac{\ln x}{x}\right \)$.
A. 0
B. 1
C. ∞
D. -∞
Question 12
A random variable (X) has a probability distribution given by [ P\( X = x \) = egin{cases} 0.2 & \text{if } x = 1 \ 0.3 & \text{if } x = 2 \ 0.5 & \text{if } x = 3 \ 0.1 & \text{if } x = 4 \end{cases} ]. Find the expected value of (X).
A. 1.5
B. 2.5
C. 3.5
D. 4.5
Question 13
Solve the inequality \( \frac{x^2 - 4}{x^2 - 9} > 0 \).
A. \( x in \( -infty, -3 \ \) cup (3, infty) )
B. \( x in \( -infty, -3 \ \) cup (3, 4) cup (4, infty) )
C. \( x in \( -infty, -3 \ \) cup (3, 4) )
D. \( x in \( -infty, -3 \ \) cup (4, infty) )
Question 14
Find the area of the triangle with vertices ( (0, 0), (1, 0), ) and ( (0, 1) ) u\sing the formula for the area of a triangle.
A. \frac{1}{2}
B. \frac{1}{3}
C. \frac{1}{4}
D. \frac{1}{6}
Question 15
In a right-angled triangle, the length of the hypotenuse is 10 units and one of the acute angles is 30°. Find the length of the side opposite the 30° angle.
A. 5.773
B. 6.928
C. 7.071
D. 8.062

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