POST UTME NILE UNIVERSITY 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality \( \frac{x}{x-1} > 2 \) for \( x > 1 \).
A. \( x > 3 \)
B. \( x < 3 \)
C. \( x > 1 \) and \( x < 3 \)
D. \( x > 3 \) and \( x < 5 \)
Question 2
A binary number 1011 is converted to decimal. What is the decimal equivalent?
A. 11
B. 11
C. 11
D. 11
Question 3
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. \( x = -2 \)
B. \( x = -1 \)
C. \( x = 0 \)
D. \( x = 1 \)
Question 4
A sequence is defined by the formula $a_n = 2n + 1$. Find the sum of the first 5 terms.
A. 15
B. 20
C. 25
D. 30
Question 5
Let \( A = egin{pmatrix} 1 & 2 \ 3 & 4 \end{pmatrix} \). Find the determinant of ( A ).
A. ( det(A) = 5 )
B. ( det(A) = 7 )
C. ( det(A) = 9 )
D. ( det(A) = 11 )
Question 6
Find the value of \( \tan 2\theta \) given that \( \sin \theta = \frac{3}{5} \) and \( \cos \theta = \frac{4}{5} \).
A. \( \frac{24}{25} \)
B. \( \frac{25}{24} \)
C. \( \frac{24}{25} \)
D. \( \frac{25}{24} \)
Question 7
Find the derivative of ( f(x) = \frac{1}{\sqrt{1-x^2}} ) u\sing the chain rule.
A. ( f'(x) = \frac{x}{\( 1-x^2 \)^{3/2}} )
B. ( f'(x) = \frac{-x}{\( 1-x^2 \)^{3/2}} )
C. ( f'(x) = \frac{1}{\( 1-x^2 \)^{3/2}} )
D. ( f'(x) = \frac{x^2}{\( 1-x^2 \)^{3/2}} )
Question 8
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{64}{3} \)
B. \( \frac{32}{3} \)
C. \( \frac{16}{3} \)
D. \( \frac{8}{3} \)
Question 9
A geometric sequence has first term 2 and common ratio 3. Find the sum of the first 5 terms of the sequence.
A. 325
B. 327
C. 329
D. 331
Question 10
Find the area under the curve y = 2x^2 + 3x - 4 from x = 0 to x = 2.
A. 14
B. 14
C. 14
D. 14
Question 11
A histogram of exam scores is shown. Find the mean score.
A. ( 60 )
B. ( 70 )
C. ( 80 )
D. ( 90 )
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
A vector →A = 2→i + 3→j + 4→k is given. What is the magnitude of the vector?
A. 5
B. 5
C. 5
D. 5
Question 14
Solve the inequality \( 2x^2 - 5x - 3 > 0 \) u\sing the quadratic formula.
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 15
Solve the equation \( x^3 - 6x^2 + 11x - 6 = 0 \).
A. \( x = 1 \)
B. \( x = 2 \)
C. \( x = 3 \)
D. \( x = 4 \)

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