POST UTME NILE UNIVERSITY 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the sum of the infinite geometric series \( \sum_{n=1}^\infty \frac{2}{3^n} \ \).
A. \frac{2}{3}
B. \frac{2}{3} \cdot \frac{1}{1 - \frac{1}{3}}
C. \frac{2}{3} \cdot \frac{1}{1 - \frac{1}{3}} \cdot \frac{1}{1 - \frac{1}{3}}
D. \frac{2}{3} \cdot \frac{1}{1 - \frac{1}{3}} \cdot \frac{1}{1 - \frac{1}{3}} \cdot \frac{1}{1 - \frac{1}{3}}
Question 2
Solve the inequality $\frac{x^2 - 4}{x + 2} \geq 0$.
A. \( -\infty, -2 \) \cup [0, \infty)
B. \( -\infty, -2 \) \cup \( 0, \infty \)
C. \( -\infty, -2 \) \cup [2, \infty)
D. \( -\infty, -2 \) \cup \( -2, \infty \)
Question 3
Solve the inequality \( 2x^2 - 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, 1 \) ∪ (3, ∞)
C. \( -∞, -1 \) ∪ (1, ∞)
D. \( -∞, 3 \) ∪ (5, ∞)
Question 4
Let X and Y be indep\endent random variables with probability density functions f_X(x) = 2x, 0 < x < 1, and f_Y(y) = 3y^2, 0 < y < 1. Find the probability P\( X > Y \).
A. 1/4
B. 1/2
C. 3/4
D. 1
Question 5
Solve the quadratic equation \(x^2 + 4x + 4 = 0\)
A. -2
B. 0
C. 2
D. 4
Question 6
Let $X$ and $Y$ be indep\endent random variables with probability density functions $f_X(x) = egin{cases} 2x & 0 leq x leq 1 \ 0 & \text{otherwise} \end{cases}$ and $f_Y(y) = egin{cases} 3y^2 & 0 leq y leq 1 \ 0 & \text{otherwise} \end{cases}$. Find the probability that $X + Y leq 1$.
A. \frac{1}{4}
B. \frac{1}{2}
C. \frac{3}{4}
D. \frac{5}{8}
Question 7
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 = 4
C. \( x + 2 \)^2 + \( y + 3 \)^2 = 16
D. \( x + 2 \)^2 + \( y + 3 \)^2 = 4
Question 8
Find the value of k such that the function f(x) = kx^2 + 2x - 5 has a local maximum at x = -1.
A. 3
B. 4
C. 5
D. 6
Question 9
A histogram of exam scores is shown below. What is the mean score of the exam?
A. 25
B. 30
C. 35
D. 40
Question 10
A rec\tangular garden has a length of 15 m and a width of 8 m. If a path that is 2 m wide is built around the garden, what is the area of the path?
A. 48
B. 64
C. 80
D. 96
Question 11
Solve the equation \[ 2^x + 3^x = 5^x \] for x.
A. 1
B. 2
C. 3
D. 4
Question 12
Let ( X ) be a random variable with probability density function ( f(x) = egin{cases} 2x & \text{if } 0 leq x leq 1 \ 0 & \text{otherwise} \end{cases} ). Find the probability that ( X ) takes a value between 0.5 and 1.
A. 0.25
B. 0.5
C. 0.75
D. 1
Question 13
Solve the system of equations \( x + y = 4 \) and \( xy = 5 \).
A. (1, 3)
B. (2, 2)
C. (3, 1)
D. (4, 0)
Question 14
Solve the system of equations \begin{align*} x + y + z &= 6 \ x + 2y + 3z &= 11 \ x + 3y + 6z &= 16 \end{align*} u\sing Cramer's rule.
A. \begin{pmatrix} 1 \ 2 \ 3 \end{pmatrix}
B. \begin{pmatrix} 2 \ 3 \ 4 \end{pmatrix}
C. \begin{pmatrix} 3 \ 4 \ 5 \end{pmatrix}
D. \begin{pmatrix} 4 \ 5 \ 6 \end{pmatrix}
Question 15
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 24
B. 30
C. 36
D. 40

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