POST UTME KSU 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A random experiment consists of rolling a fair six-sided die. Find the probability that the sum of the numbers on the two dice is 7.
A. \( \frac{1}{6} \)
B. \( \frac{1}{3} \)
C. \( \frac{1}{2} \)
D. \( \frac{2}{3} \)
Question 2
Determine the volume of the solid formed by revolving the region bounded by the curves y = x^2, y = 0, and x = 2 about the x-axis.
A. \frac{32\pi}{3}
B. \frac{64\pi}{3}
C. \frac{128\pi}{3}
D. \frac{256\pi}{3}
Question 3
Find the area of the triangle with vertices ( A(0, 0), B(3, 0), C(0, 4) ).
A. ( 6 )
B. ( 12 )
C. ( 18 )
D. ( 24 )
Question 4
Solve the system of equations \( egin{cases} x + y = 2 \ 2x - 3y = -1 \end{cases} \) u\sing matrices.
A. \( x = \frac{5}{7}, y = \frac{4}{7} \)
B. \( x = \frac{3}{5}, y = \frac{2}{5} \)
C. \( x = \frac{2}{3}, y = \frac{1}{3} \)
D. \( x = \frac{4}{5}, y = \frac{1}{5} \)
Question 5
Solve the equation \log_{10} \( x^2 \) = 4.
A. 10
B. 20
C. 40
D. 80
Question 6
Solve the equation x^4 - 6x^3 + 11x^2 - 6x - 12 = 0.
A. \( x + 1 \)\( x - 2 \)\( x^2 - 3x + 6 \) = 0
B. \( x - 1 \)\( x + 2 \)\( x^2 - 3x + 6 \) = 0
C. \( x + 2 \)\( x - 2 \)\( x^2 - 3x + 6 \) = 0
D. \( x - 2 \)\( x + 1 \)\( x^2 - 3x + 6 \) = 0
Question 7
A binary operation * on the set of real numbers is defined as follows: a * b = ab + 2. Find the value of \( 2 * 3 \) * 4.
A. 40
B. 42
C. 44
D. 46
Question 8
Find the area under the curve y = x^2 + 2x - 3 from x = 0 to x = 4.
A. 64
B. 80
C. 96
D. 112
Question 9
Solve the equation \sin^2 x + \cos^2 x = 1 for x.
A. \sin x = \cos x
B. \sin x = -\cos x
C. \cos x = \sin x
D. \cos x = -\sin x
Question 10
Find the derivative of ( f(x) = \frac{1}{\sqrt{1 - x^2}} ) u\sing the chain rule.
A. ( f'(x) = \frac{2x}{\( 1 - x^2 \)^{3/2}} )
B. ( f'(x) = \frac{-2x}{\( 1 - x^2 \)^{3/2}} )
C. ( f'(x) = \frac{2x}{\( 1 - x^2 \)^{1/2}} )
D. ( f'(x) = \frac{-2x}{\( 1 - x^2 \)^{1/2}} )
Question 11
Solve the matrix equation \begin{bmatrix} 2 & 1 \\ 1 & 2 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 3 \\ 4 \end{bmatrix}.
A. \begin{bmatrix} 1 \\ 2 \end{bmatrix}
B. \begin{bmatrix} 2 \\ 1 \end{bmatrix}
C. \begin{bmatrix} 3 \\ 4 \end{bmatrix}
D. \begin{bmatrix} 4 \\ 3 \end{bmatrix}
Question 12
In a circle with center O and radius 6 cm, chord AB = 8 cm. Find the length of the perp\endicular from O to AB.
A. 4 cm
B. 5 cm
C. 6 cm
D. 7 cm
Question 13
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. What is the probability that a randomly selected score is between 50 and 70?
A. ( 0.5 )
B. ( 0.6 )
C. ( 0.7 )
D. ( 0.8 )
Question 14
Solve the system of equations u\sing matrices:\( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 3 \ 7 \end{bmatrix} \).
A. \( x = 1, y = 2 \)
B. \( x = 2, y = 1 \)
C. \( x = 3, y = 4 \)
D. \( x = 4, y = 3 \)
Question 15
Determine the value of x in the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ) if \( \sin\( x \ \) = \frac{3}{5} ).
A. \( x = \frac{pi}{4} \)
B. \( x = \frac{3pi}{4} \)
C. \( x = \frac{5pi}{4} \)
D. \( x = \frac{7pi}{4} \)

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