POST UTME FUTA 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the value of [ \tan(2x) \] given that [ \tan(x) = \frac{1}{2} \].
A. \tan(x)
B. \sin(x)
C. \cos(x)
D. \tan(2x)
Question 2
Find the area under the curve y = 2x^2 + 3x - 4 from x = 0 to x = 2.
A. 12
B. 16
C. 20
D. 24
Question 3
Find the value of [ \sin(2x) \] given that [ \sin(x) = \frac{1}{3} \].
A. \cos(x)
B. \sin(x)
C. \cos(2x)
D. \sin(2x)
Question 4
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 = 16
C. \( x - 2 \)^2 + \( y + 3 \)^2 = 16
D. \( x + 2 \)^2 + \( y - 3 \)^2 = 16
Question 5
Determine the value of $\int_{0}^{\pi} \frac{1}{1+\sin^2(x)} dx$.
A. \frac{\pi}{2}
B. \frac{\pi}{4}
C. \frac{\pi}{3}
D. \frac{\pi}{6}
Question 6
The quadratic equation $x^2 + bx + c = 0$ has roots $x = 1$ and $x = -2$. Find the value of $b$.
A. -3
B. -2
C. -1
D. 1
Question 7
Find the sum of the first 5 terms of the geometric sequence \( a_n = 2 \cdot 3^{n-1} \).
A. \( 2 \cdot 3^0 + 2 \cdot 3^1 + 2 \cdot 3^2 + 2 \cdot 3^3 + 2 \cdot 3^4 \)
B. \( 2 \cdot 3^1 + 2 \cdot 3^2 + 2 \cdot 3^3 + 2 \cdot 3^4 + 2 \cdot 3^5 \)
C. \( 2 \cdot 3^0 + 2 \cdot 3^1 + 2 \cdot 3^2 + 2 \cdot 3^3 + 2 \cdot 3^4 \)
D. \( 2 \cdot 3^1 + 2 \cdot 3^2 + 2 \cdot 3^3 + 2 \cdot 3^4 + 2 \cdot 3^5 \)
Question 8
Let $S$ be the set of all positive integers $n$ such that $n$ is a multiple of $3$ and $n$ is a power of $2$. Which of the following is the smallest element of $S$?
A. 1
B. 2
C. 4
D. 8
Question 9
Find the equation of the line pas\sing through the points (2, 3) and (4, 5).
A. y = \frac{2}{2}x + \frac{1}{2}
B. y = \frac{2}{2}x + \frac{3}{2}
C. y = \frac{2}{2}x + \frac{5}{2}
D. y = \frac{2}{2}x + \frac{7}{2}
Question 10
Solve the equation [ x^2 + 4x + 4 = 0 ].
A. x = -2
B. x = 2
C. x = -1
D. x = 1
Question 11
Find the value of [ \cos(2x) \] given that [ \cos(x) = \frac{1}{2} \].
A. \cos(x)
B. \sin(x)
C. \cos(2x)
D. \sin(2x)
Question 12
Solve the system of equations \( \begin{cases} x + y = 2 \ x - 2y = -3 \end{cases} \).
A. \( \begin{cases} x = 1 \ y = 1 \end{cases} \)
B. \( \begin{cases} x = -1 \ y = 3 \end{cases} \)
C. \( \begin{cases} x = 2 \ y = 0 \end{cases} \)
D. \( \begin{cases} x = 0 \ y = 2 \end{cases} \)
Question 13
Find the area of the triangle with vertices (A(0, 0)), (B(3, 0)), and (C(0, 2)).
A. \( \frac{1}{2} \cdot 3 \cdot 2 \)
B. \( \frac{1}{2} \cdot 3 \cdot 3 \)
C. \( \frac{1}{2} \cdot 3 \cdot 4 \)
D. \( \frac{1}{2} \cdot 3 \cdot 5 \)
Question 14
Solve the inequality [ 2x - 5 > 3 ].
A. x > \frac{8}{2}
B. x < \frac{8}{2}
C. x > \frac{8}{2}
D. x < \frac{8}{2}
Question 15
Two events $A$ and $B$ are indep\endent. If $P(A) = 0.4$ and $P(B) = 0.6$, what is the probability that both events occur?
A. 0.2
B. 0.4
C. 0.6
D. 0.8

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