POST UTME UNIOSUN 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A random variable $X$ has a probability distribution given by $P\( X = k \) = \frac{1}{2^k}$ for $k = 1, 2, 3, dots$. Find the expected value of $X$.
A. 1
B. 2
C. 3
D. 4
Question 2
Solve the inequality 2x^2 + 5x - 3 > 0.
A. \( -\infty, -1 \) \cup \( 3, \infty \)
B. \( -\infty, -3 \) \cup \( 1, \infty \)
C. \( -\infty, -1 \) \cup \( 1, \infty \)
D. \( -\infty, 1 \) \cup \( 3, \infty \)
Question 3
A vector (mathbf{a}) has magnitude 5 and direction 30°. A vector (mathbf{b}) has magnitude 3 and direction 60°. Find the magnitude of the sum of (mathbf{a}) and (mathbf{b}).
A. 4
B. 5
C. 6
D. 7
Question 4
Find the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 5
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 6
Find the volume of the frustum of a cone with height 10cm, lower base radius 5cm, and upper base radius 3cm.
A. ( 100pi ) cm³
B. ( 150pi ) cm³
C. ( 200pi ) cm³
D. ( 250pi ) cm³
Question 7
Find the area under the curve y = x^3 - 6x^2 + 9x + 2 from x = 0 to x = 2.
A. \frac{16}{5}
B. \frac{32}{5}
C. \frac{48}{5}
D. \frac{64}{5}
Question 8
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∪ (3, ∞)
D. \( -∞, -3 \) ∪ (1, ∞)
Question 9
A binary operation \( * \) on the set of real numbers is defined as \( a * b = ab + 1 \). Find the value of \( 2 * 3 \).
A. 7
B. 8
C. 9
D. 10
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
Solve the equation \( x^3 - 6x^2 + 11x - 6 = 0 \) u\sing the factor theorem.
A. \( x - 1 \)\( x - 2 \)\( x - 3 \ \) = 0 )
B. \( x - 1 \)\( x - 2 \)\( x + 3 \ \) = 0 )
C. \( x + 1 \)\( x - 2 \)\( x - 3 \ \) = 0 )
D. \( x - 1 \)\( x + 2 \)\( x - 3 \ \) = 0 )
Question 12
Solve the inequality \( 2x^2 + 5x - 3 > 0 \) for ( x ) in the interval \( -infty, infty \ \) ).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, -1 \) ∪ (1, ∞)
D. \( -∞, 1 \) ∪ (3, ∞)
Question 13
Find the surface area of the sphere with radius 6cm.
A. ( 288pi ) cm²
B. ( 360pi ) cm²
C. ( 432pi ) cm²
D. ( 480pi ) cm²
Question 14
A sequence is defined by the formula \( a_n = 2n + 1 \). Find the 10th term of the sequence.
A. 21
B. 22
C. 23
D. 24
Question 15
Find the derivative of the function f(x) = \( \frac{1}{x^2 + 1} \) u\sing the chain rule.
A. \( \frac{-2x}{\( x^2 + 1 \ \)^2} )
B. \( \frac{2x}{\( x^2 + 1 \ \)^2} )
C. \( \frac{1}{\( x^2 + 1 \ \)^2} )
D. \( \frac{-1}{\( x^2 + 1 \ \)^2} )

Master the Exam!

You've seen a preview, but there are thousands more questions plus AI tutor to break down complex solutions.

Unlock Full Access Available for Android & Windows
Help others prepare! Share this practice hub: