POST UTME FUTO 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \left\( -\infty, -\frac{3}{2} \right \) \cup \left\( \frac{1}{2}, \infty \right \)
B. \left\( -\infty, -\frac{1}{2} \right \) \cup \left\( \frac{3}{2}, \infty \right \)
C. \left\( -\infty, \frac{1}{2} \right \) \cup \left\( -\frac{3}{2}, \infty \right \)
D. \left\( -\infty, \infty \right \)
Question 2
Solve the inequality $|x-2| > 3$.
A. \( -\infty, -1 \) \cup \( 5, \infty \)
B. \( -\infty, 1 \) \cup \( 5, \infty \)
C. \( -\infty, -1 \) \cup \( 1, \infty \)
D. \( -\infty, 1 \) \cup \( 1, \infty \)
Question 3
Find the sum of the first 10 terms of the geometric series \( 2x^2 + 5x - 3 \).
A. 2
B. 5
C. 10
D. 15
Question 4
Find the area of the triangle with vertices ( (0, 0), (3, 4), (6, 0) ).
A. 12
B. 18
C. 24
D. 30
Question 5
Find the value of $\sum_{n=1}^\infty \frac{1}{n^2}$.
A. \frac{\pi^2}{6}
B. \frac{\pi^2}{12}
C. \frac{\pi^2}{24}
D. \frac{\pi^2}{48}
Question 6
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If 80% of the scores fall below 90, what is the value of x in the equation \( P\( x < 90 \ \) = 0.8 )?
A. 70
B. 80
C. 85
D. 90
Question 7
Solve the equation \( \sin^2 x + \cos^2 x = 1 \) for x.
A. \sin x = \pm \frac{1}{\sqrt{2}}
B. \cos x = \pm \frac{1}{\sqrt{2}}
C. \tan x = \pm 1
D. \cot x = \pm 1
Question 8
Solve the matrix equation \( \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 5 \\ 6 \end{bmatrix} \) for x and y.
A. \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 1 \\ 2 \end{bmatrix}
B. \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 2 \\ 1 \end{bmatrix}
C. \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 3 \\ 4 \end{bmatrix}
D. \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 4 \\ 3 \end{bmatrix}
Question 9
Find the volume of the frustum of a cone with height 6, lower base radius 4, and upper base radius 2.
A. \frac{1}{3} \pi (6) \( 4^2 + 2^2 + 4 \cdot 2 \)
B. \frac{1}{3} \pi (6) \( 4^2 + 2^2 - 4 \cdot 2 \)
C. \frac{1}{3} \pi (6) \( 4^2 - 2^2 + 4 \cdot 2 \)
D. \frac{1}{3} \pi (6) \( 4^2 - 2^2 - 4 \cdot 2 \)
Question 10
Find the equation of the line pas\sing through the points (2, 3) and (4, 5).
A. y - 3 = \frac{2}{2}\( x - 2 \)
B. y - 3 = \frac{2}{2}\( x - 4 \)
C. y - 5 = \frac{2}{2}\( x - 2 \)
D. y - 5 = \frac{2}{2}\( x - 4 \)
Question 11
Solve the inequality \[|x - 2| > 3\].
A. \[x < -1, x > 5\]
B. \[x < 1, x > 5\]
C. \[x < -1, x < 5\]
D. \[x > 1, x > 5\]
Question 12
A set A is defined as \( A = \{ x \in \mathbb{R} : x^2 + 2x + 1 \geq 0 \} \). Find the range of A.
A. \left[ -1, \infty \right)
B. \left( -\infty, -1 \right]
C. \left( -\infty, 0 \right]
D. \left( 0, \infty \right]
Question 13
A random variable X has a probability distribution given by P(X) = \( 1/2 \)^\( X-1 \) for X = 1, 2, 3, ... . Find the expected value of X.
A. 2
B. 3
C. 4
D. \infty
Question 14
Find the value of $\int_0^1 \frac{1}{x^2+4x+5} dx$.
A. \frac{1}{2} \ln|2x+1| + \frac{1}{2} \ln|x+1| + C
B. \frac{1}{2} \ln|2x+1| - \frac{1}{2} \ln|x+1| + C
C. \frac{1}{2} \ln|2x+1| + C
D. \frac{1}{2} \ln|x+1| + C
Question 15
A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. What is the surface area of the prism?
A. 62
B. 65
C. 68
D. 70

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