POST UTME NOUN 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the area under the curve \( y = x^2 + 2x - 3 \) from \( x = 1 \) to \( x = 3 \).
A. \( 14 \)
B. \( 16 \)
C. \( 18 \)
D. \( 20 \)
Question 2
A set ( A ) is defined as \( A = \{ 1, 2, 3, 4, 5 \} \). Find the number of subsets of ( A ) that contain exactly 3 elements.
A. 10
B. 15
C. 20
D. 25
Question 3
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 4
A histogram is constructed from the following data: 2, 4, 5, 6, 8, 9, 10, 12, 15, 18. What is the mean of the data?
A. 8
B. 9
C. 10
D. 11
Question 5
Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 1 \ -2 \end{pmatrix} \). Find the projection of ( mathbf{b} ) onto ( mathbf{a} ) u\sing the formula \( \text{proj}_{mathbf{a}}\( mathbf{b} \ \) = \frac{mathbf{a} cdot mathbf{b}}{|mathbf{a}|^2} mathbf{a} ).
A. 0
B. \begin{pmatrix} \frac{4}{13} \\ \frac{6}{13} \end{pmatrix}
C. \begin{pmatrix} \frac{2}{13} \\ \frac{-3}{13} \end{pmatrix}
D. \begin{pmatrix} \frac{1}{13} \\ \frac{-2}{13} \end{pmatrix}
Question 6
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 7
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 8
Determine the value of ( x ) in the equation \( 2^x + 5^x = 3^x \).
A. 1
B. 2
C. 3
D. 4
Question 9
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 10
Find the sum of the first $n$ terms of the geometric series $\sum_{k=1}^{n} \frac{1}{2^k}$.
A. 1-\frac{1}{2^n}
B. 1-\frac{1}{2^{n+1}}
C. 1-\frac{2}{2^n}
D. 1-\frac{2}{2^{n+1}}
Question 11
Find the equation of the line pas\sing through the points ( (1, 2) ) and ( (3, 4) ).
A. \( y = 2x - 1 \)
B. \( y = 2x + 1 \)
C. \( y = 2x - 2 \)
D. \( y = 2x + 2 \)
Question 12
Solve the quadratic equation \( x^2 + 5x + 6 = 0 \).
A. -2
B. -3
C. -4
D. -5
Question 13
Solve the inequality \( |x - 2| > 3 \).
A. \( x < -1 \text{ or } x > 5 \)
B. \( x < -1 \text{ or } x > 2 \)
C. \( x < 2 \text{ or } x > 5 \)
D. \( x < 1 \text{ or } x > 5 \)
Question 14
Let X be a random variable with probability density function ( f(x) = egin{cases} 2x & 0 leq x leq 1 \ 0 & \text{otherwise} \end{cases} ). Find the probability that X is greater than 0.5.
A. \( \frac{1}{2} \)
B. \( \frac{1}{4} \)
C. \( \frac{3}{4} \)
D. \( \frac{1}{3} \)
Question 15
If the mean of the numbers 2, 4, 6, 8, 10 is 7, what is the median?
A. 6
B. 7
C. 8
D. 9

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