POST UTME FUTO 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A die is rolled. What is the probability that the number obtained is a multiple of 3?
A. \frac{1}{3}
B. \frac{1}{6}
C. \frac{1}{2}
D. \frac{2}{3}
Question 2
Find the equation of the circle pas\sing through the points (2,3), (4,5), and (6,7).
A. \( x^2 + y^2 - 14x - 2y + 20 = 0 \)
B. \( x^2 + y^2 - 12x - 4y + 16 = 0 \)
C. \( x^2 + y^2 - 16x - 6y + 24 = 0 \)
D. \( x^2 + y^2 - 18x - 8y + 32 = 0 \)
Question 3
Find the equation of the circle with center ( (3, 4) ) and radius ( 5 ).
A. \( x - 3 \ \)^2 + \( y - 4 \)^2 = 25 )
B. \( x - 4 \ \)^2 + \( y - 3 \)^2 = 25 )
C. \( x - 5 \ \)^2 + \( y - 3 \)^2 = 25 )
D. \( x - 3 \ \)^2 + \( y - 5 \)^2 = 25 )
Question 4
A bag contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?
A. 1/2
B. 1/3
C. 2/5
D. 3/8
Question 5
A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find the volume of the prism.
A. 30 cm^3
B. 40 cm^3
C. 50 cm^3
D. 60 cm^3
Question 6
Solve the trigonometric equation \( 2 \sin^2 x + 3 \cos x - 1 = 0 \).
A. \( x = \frac{\pi}{6} \ \)
B. \( x = \frac{\pi}{4} \ \)
C. \( x = \frac{\pi}{3} \ \)
D. \( x = \frac{\pi}{2} \ \)
Question 7
A binary operation $\ast$ is defined as $a \ast b = a^2 + b^2$. Find the value of $2 \ast 3$.
A. 13
B. 25
C. 37
D. 49
Question 8
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 60 and 90?
A. ( 0.9544 )
B. ( 0.9772 )
C. ( 0.9987 )
D. ( 0.9999 )
Question 9
Solve the matrix equation \( \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 7 \end{bmatrix} \).
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 10
Find the volume of the solid formed by revolving the region bounded by the curves $y = x^2$ and $y = 4 - x^2$ about the x-axis.
A. \frac{16\pi}{3}
B. \frac{32\pi}{3}
C. \frac{64\pi}{3}
D. \frac{128\pi}{3}
Question 11
Find the volume of the solid formed by revolving the region bounded by the parabola \( y = x^2 \), the line \( x = 2 \), and the x-axis about the x-axis.
A. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi
Question 12
A vector ( mathbf{a} ) has a magnitude of 5 and makes an angle of 60° with the positive x-axis. Find the unit vector in the direction of ( mathbf{a} ).
A. \begin{pmatrix} 0.5 \ 0.866 \end{pmatrix}
B. \begin{pmatrix} 0.866 \ 0.5 \end{pmatrix}
C. \begin{pmatrix} 0.5 \ -0.866 \end{pmatrix}
D. \begin{pmatrix} -0.866 \ 0.5 \end{pmatrix}
Question 13
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 14
Solve the system of linear equations u\sing the method of substitution: \begin{align*} x + y &= 4 \ 2x - 3y &= 5 \end{align*}
A. \begin{pmatrix} 2 \ 2 \end{pmatrix}
B. \begin{pmatrix} 1 \ 3 \end{pmatrix}
C. \begin{pmatrix} -1 \ -3 \end{pmatrix}
D. \begin{pmatrix} 3 \ 1 \end{pmatrix}
Question 15
A line passes through the points (2,3) and (4,5). Find the equation of the line in slope-intercept form.
A. y = 2x - 1
B. y = 2x + 1
C. y = -2x + 1
D. y = -2x - 1

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