POST UTME ACHIEVERS UNIVERSITY 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the quadratic equation $x^2 + 5x + 6 = 0$
A. \begin{cases} x = -2 \ x = -3 \end{cases}
B. \begin{cases} x = 2 \ x = 3 \end{cases}
C. \begin{cases} x = -1 \ x = -4 \end{cases}
D. \begin{cases} x = 1 \ x = 4 \end{cases}
Question 2
Find the area of the region bounded by the curves y = x^2 + 1, y = 0, and x = 2.
A. 9
B. 18
C. 27
D. 36
Question 3
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
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
Solve the equation \( \sin^2 x + \cos^2 x = 1 \) for ( x ) in the interval ( [0, 2pi] ).
A. 0
B. \frac{pi}{4}
C. \frac{pi}{2}
D. pi
Question 6
In a random sample of 100 students, the mean height is 170 cm with a s\tandard deviation of 5 cm. If the height of a student is 180 cm, what is the z-score?
A. 1.2
B. 1.5
C. 1.8
D. 2.0
Question 7
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. \( x = -2 \)
B. \( x = -1 \)
C. \( x = 0 \)
D. \( x = 1 \)
Question 8
Solve the inequality |x^2 - 4| < 5.
A. x < -1 or x > 4
B. x < 0 or x > 5
C. x < 1 or x > 6
D. x < 2 or x > 7
Question 9
A matrix ( A ) is given by \( A = egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \). Find the value of ( x ) in the equation \( A^2 = xA \).
A. 1
B. 2
C. 3
D. 4
Question 10
Find the sum of the infinite geometric series $\sum_{n=1}^\infty \frac{1}{2^n}$
A. 1
B. 2
C. 3
D. 4
Question 11
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 12
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -1 \) or \( x > \frac{3}{2} \)
B. \( x > -1 \) or \( x < \frac{3}{2} \)
C. \( x < -1 \) or \( x < \frac{3}{2} \)
D. \( x > -1 \) or \( x > \frac{3}{2} \)
Question 13
Find the value of ( x ) in the equation \( x^3 - 6x^2 + 11x - 6 = 0 \) if the sum of the roots is ( 6 ) and the product of the roots is \( -6 \).
A. 1
B. 2
C. 3
D. 4
Question 14
A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?
A. 1/2
B. 1/3
C. 2/3
D. 1/6
Question 15
Find the volume of the solid generated by revolving the region bounded by the curves y = x^2, y = 0, and x = 2 about the x-axis.
A. 32\pi
B. 64\pi
C. 128\pi
D. 256\pi

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