POST UTME ACHIEVERS UNIVERSITY 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A sequence is defined by the recurrence relation a_n = 2a_{n-1} + 1, with a_1 = 3. Find the value of a_5.
A. 31
B. 32
C. 33
D. 34
Question 2
Solve the inequality \( x^2 - 4x + 3 > 0 \).
A. x < 1 or x > 3
B. x > 1 or x < 3
C. x < 3 or x > 1
D. x > 3 or x < 1
Question 3
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 64
B. 128
C. 256
D. 512
Question 4
Find the area under the curve \( y = \frac{1}{x^2 + 1} \) from \( x = 0 \) to \( x = 1 \).
A. \frac{π}{4}
B. \frac{π}{2}
C. \frac{π}{3}
D. \frac{π}{5}
Question 5
Solve the system of linear equations u\sing matrices:
A. x = 1, y = 2
B. x = 2, y = 1
C. x = 3, y = 4
D. x = 4, y = 3
Question 6
A histogram of exam scores is shown below. What is the mean score?
A. ( 60 )
B. ( 70 )
C. ( 80 )
D. ( 90 )
Question 7
Simplify the expression [ \sqrt[3]{64x^3y^3} ].
A. \( \sqrt[3]{64x^3y^3} = 4x^1y^1 \)
B. \( \sqrt[3]{64x^3y^3} = 4x^3y^3 \)
C. \( \sqrt[3]{64x^3y^3} = 8x^3y^3 \)
D. \( \sqrt[3]{64x^3y^3} = 2x^3y^3 \)
Question 8
Find the equation of the circle with center at $\( -2,3 \)$ and radius $4$.
A. \( x^2 + y^2 + 4x - 6y - 7 = 0 \)
B. \( x^2 + y^2 - 4x + 6y - 7 = 0 \)
C. \( x^2 + y^2 + 2x - 3y - 7 = 0 \)
D. \( x^2 + y^2 - 2x + 3y - 7 = 0 \)
Question 9
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 = 32
C. \( x + 2 \)^2 + \( y - 3 \)^2 = 16
D. \( x + 2 \)^2 + \( y - 3 \)^2 = 32
Question 10
Find the value of (x) in the equation \( 2^x + 2^x = 128 \).
A. 5
B. 6
C. 7
D. 8
Question 11
A random experiment consists of rolling a fair six-sided die. If the number rolled is even, the experiment is repeated. If the number rolled is odd, the experiment stops. Find the probability that the experiment will stop after exactly two rolls.
A. \frac{1}{6}
B. \frac{1}{3}
C. \frac{1}{2}
D. \frac{2}{3}
Question 12
A binary operation \(* \) is defined as \( a * b = ab + 2a + 2b \). Find the value of \( 2 * 3 \).
A. 20
B. 22
C. 24
D. 26
Question 13
Solve the equation \( x^2 + 4x + 4 = 0 \) u\sing the quadratic formula.
A. -2
B. -1
C. 1
D. 2
Question 14
Solve the system of equations \begin{align*} x + y &= 2 \ x - 2y &= -3 \end{align*}.
A. \begin{cases} x = -1 \ y = 3 \end{cases}
B. \begin{cases} x = 1 \ y = 1 \end{cases}
C. \begin{cases} x = -1 \ y = 1 \end{cases}
D. \begin{cases} x = 1 \ y = 3 \end{cases}
Question 15
Find the derivative of ( f(x) = \frac{x^2}{x^2 + 1} ) u\sing the chain rule.
A. ( f'(x) = \frac{2x\( x^2 + 1 \) - 2x^3}{\( x^2 + 1 \)^2} )
B. ( f'(x) = \frac{2x^2 - 2}{\( x^2 + 1 \)^2} )
C. ( f'(x) = \frac{2x^3 - 2x}{\( x^2 + 1 \)^2} )
D. ( f'(x) = \frac{2x^2 + 2}{\( x^2 + 1 \)^2} )

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