POST UTME FUTA 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the equation of the circle with center \( C\( -2, 3 \ \)) and radius \( r = 4 \).
A. \( \left\( x + 2\right \ \)^2 + \left\( y - 3\right \)^2 = 16)
B. \( \left\( x - 2\right \ \)^2 + \left\( y + 3\right \)^2 = 16)
C. \( \left\( x + 2\right \ \)^2 + \left\( y + 3\right \)^2 = 16)
D. \( \left\( x - 2\right \ \)^2 + \left\( y - 3\right \)^2 = 16)
Question 2
Find the sum of the infinite geometric series \sum_{n=1}^\infty \frac{1}{2^n}.
A. 1
B. \frac{1}{2}
C. \frac{2}{3}
D. \frac{3}{4}
Question 3
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 4
Solve the inequality [ 3x + 2 > 7 ].
A. x > \frac{5}{3}
B. x < \frac{5}{3}
C. x > \frac{5}{3}
D. x < \frac{5}{3}
Question 5
Find the area of the triangle with vertices (2, 3), (4, 5), and (6, 7).
Question 6
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 7
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 8
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
Question 9
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 10
Solve for $x$: $\tan(x) = \sqrt{3}$.
A. \frac{\pi}{3}
B. \frac{\pi}{6}
C. \frac{\pi}{2}
D. \frac{\pi}{4}
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
A vector $\vec{a}$ has components $a_x = 3$ and $a_y = 4$. Find the magnitude of $\vec{a}$.
A. 5
B. \sqrt{5}
C. \sqrt{25}
D. \sqrt{50}
Question 13
Solve the equation [ x^2 + 4x + 4 = 0 ].
A. x = -2
B. x = 2
C. x = -1
D. x = 1
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
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

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