POST UTME NOUN 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Determine the value of ( x ) in the equation \( 2^x + 5^x = 3^x \).
A. 1
B. 2
C. 3
D. 4
Question 2
The mean of 5 numbers is 12. If one of the numbers is 15, what is the mean of the remaining 4 numbers?
A. \( 10 \)
B. \( 11 \)
C. \( 12 \)
D. \( 13 \)
Question 3
A vector →A = 3→i + 4→j. Find the magnitude of the vector.
A. 5
B. 10
C. 15
D. 20
Question 4
Solve the inequality $|x-2| \geq 3$.
A. x \leq -1 \text{ or } x \geq 5
B. x \leq 1 \text{ or } x \geq 5
C. x \leq -1 \text{ or } x \geq 4
D. x \leq 1 \text{ or } x \geq 4
Question 5
A circle has a radius of 4 cm. What is the area of the circle?
A. 50.24 cm²
B. 62.83 cm²
C. 75.40 cm²
D. 100.53 cm²
Question 6
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. \( -\frac{2x}{\( x^2 + 1 \ \)^2} )
B. \( \frac{2x}{\( x^2 + 1 \ \)^2} )
C. \( -\frac{2}{\( x^2 + 1 \ \)^2} )
D. \( \frac{2}{\( x^2 + 1 \ \)^2} )
Question 7
A function f(x) = 2x^2 + 3x - 1 has a local maximum at x = -1. Find the value of the function at this point.
A. -3
B. -1
C. 1
D. 3
Question 8
Find the derivative of the function $f(x) = \frac{1}{x^2+1}$ u\sing the chain rule.
A. -\frac{2x}{\( x^2+1 \)^2}
B. \frac{2x}{\( x^2+1 \)^2}
C. -\frac{1}{\( x^2+1 \)^2}
D. \frac{1}{\( x^2+1 \)^2}
Question 9
In a random sample of 100 students, the mean height is 175 cm with a s\tandard deviation of 5 cm. If the mean height of the entire population is 180 cm, what is the s\tandard error of the mean?
A. 2.5 cm
B. 5 cm
C. 10 cm
D. 15 cm
Question 10
Solve the system of equations \( egin{cases} x + y = 4 \ x - y = 2 \end{cases} \).
A. \( x = 3, y = 1 \)
B. \( x = 1, y = 3 \)
C. \( x = 2, y = 2 \)
D. \( x = 4, y = 0 \)
Question 11
Find the area of the triangle with vertices ( (0, 0), (3, 0), ) and ( (0, 2) ).
A. \( 6 \)
B. \( 8 \)
C. \( 10 \)
D. \( 12 \)
Question 12
In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the other sides is 6 cm. Find the length of the third side u\sing the Pythagorean theorem.
A. 8 cm
B. 12 cm
C. 16 cm
D. 20 cm
Question 13
Solve the quadratic equation \( x^2 + 5x + 6 = 0 \).
A. -2
B. -3
C. -4
D. -5
Question 14
Determine the volume of the frustum of a cone with height $h$ and radii $r_1$ and $r_2$, where $r_1 > r_2$.
A. \frac{1}{3}\pi h\( r_1^2+r_2^2+r_1r_2 \)
B. \frac{1}{3}\pi h\( r_1^2-r_2^2 \)
C. \frac{1}{3}\pi h\( r_1^2+r_2^2-r_1r_2 \)
D. \frac{1}{3}\pi h\( r_1^2-r_2^2+r_1r_2 \)
Question 15
Find the equation of the circle with center ( (2, 3) ) and radius 4.
A. \( x-2 \)^2 + \( y-3 \)^2 = 16 \)
B. \( x-2 \)^2 + \( y-3 \)^2 = 20 \)
C. \( x-2 \)^2 + \( y-3 \)^2 = 24 \)
D. \( x-2 \)^2 + \( y-3 \)^2 = 28 \)

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