POST UTME COAL CITY UNIVERSITY 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality $|x - 2| > 3$.
A. \( -∞, -1 \) ∪ (4, ∞)
B. \( -∞, 1 \) ∪ (4, ∞)
C. \( -∞, -1 \) ∪ (1, 4)
D. \( -∞, 1 \) ∪ (1, 4)
Question 2
In a geometric sequence with first term 3 and common ratio 2, find the sum of the first five terms.
A. 3 + 6 + 12 + 24 + 48
B. 3 + 6 + 12 + 24 + 40
C. 3 + 6 + 12 + 24 + 32
D. 3 + 6 + 12 + 24 + 36
Question 3
Find the determinant of the matrix \( egin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} \).
A. -1
B. 1
C. 3
D. 5
Question 4
A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?
A. 1/2
B. 1/3
C. 2/5
D. 3/8
Question 5
Solve the inequality \frac{x+2}{x-1} > 0.
A. x < -2 or x > 1
B. x > -2 or x < 1
C. x < -2 or x = 1
D. x > -2 or x = 1
Question 6
A polynomial ( P(x) ) is defined as ( P(x) = ax^3 + bx^2 + cx + d ). If ( P(1) = 4 ), ( P(2) = 12 ), and ( P(3) = 24 ), find the value of \( a + b + c + d \).
A. 10
B. 12
C. 14
D. 16
Question 7
Find the sum of the first 10 terms of the geometric series \( 2 + 6 + 18 + ldots \).
A. 1950
B. 1960
C. 1970
D. 1980
Question 8
Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 48\pi cm^3
B. 64\pi cm^3
C. 80\pi cm^3
D. 96\pi cm^3
Question 9
Solve the matrix equation $\begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 7 \end{bmatrix}$.
A. x = 1, y = 2
B. x = 2, y = 1
C. x = 1, y = 1
D. x = 2, y = 2
Question 10
A snail is at the bottom of a 20-foot well. Each day, it climbs up 3 feet, but at night, it slips back 2 feet. How many days will it take for the snail to reach the top of the well?
A. 18
B. 20
C. 22
D. 24
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
Let ( f(x) = \frac{1}{x^2 + 1} ). Find \( int_{-\frac{pi}{2}}^{\frac{pi}{2}} f\( x \ \) , dx ).
A. 0
B. 1
C. π
D. 2π
Question 13
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 14
Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3.
A. 3124
B. 3142
C. 3162
D. 3184
Question 15
A circle with center (0, 0) and radius 5 passes through the point (3, 4). Find the equation of the circle.
A. \( x^2 + y^2 = 25 \)
B. \( x^2 + y^2 = 16 \)
C. \( x^2 + y^2 = 9 \)
D. \( x^2 + y^2 = 4 \)

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