POST UTME VERITAS UNIVERSITY 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the value of x in the equation \( x^3 - 6x^2 + 11x - 6 = 0 \) u\sing synthetic division.
A. 1
B. 2
C. 3
D. 4
Question 2
A vector \( \vec{a} \) has a magnitude of 5 and is directed at an angle of 60° to the x-axis. Find the x and y components of the vector.
A. 2.5, 4.33
B. 4.33, 2.5
C. 3.33, 3.33
D. 2.5, 2.5
Question 3
In a set of 5 integers, the sum of the first 3 integers is 15, and the sum of the last 2 integers is 8. Find the sum of all 5 integers.
A. 23
B. 25
C. 27
D. 29
Question 4
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 2
B. 4
C. 8
D. 16
Question 5
Find the volume of the frustum of a cone with height 10 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 100π cm³
B. 200π cm³
C. 300π cm³
D. 400π cm³
Question 6
A matrix A has elements a11 = 2, a12 = 3, a21 = 4, a22 = 5. Find the determinant of A.
A. -1
B. 1
C. 3
D. 5
Question 7
Find the surface area of the sphere with radius 5 cm.
A. 314.16
B. 314.16
C. 314.16
D. 314.16
Question 8
In a right circular cone, the radius of the base is 6 cm and the height is 8 cm. Find the volume of the cone in cubic centimeters.
A. 288\pi
B. 384\pi
C. 576\pi
D. 768\pi
Question 9
A company produces two products, A and B. The profit from product A is $10 per unit, and the profit from product B is $15 per unit. If the company produces 100 units of product A and 50 units of product B, what is the total profit?
A. $1500
B. $2000
C. $2500
D. $3000
Question 10
Find the sum of the first 10 terms of the geometric progression 3, 6, 12, 24, ...
A. 1230
B. 1240
C. 1250
D. 1260
Question 11
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 12
Find the value of x in the equation \( 2x^2 + 5x - 3 = 0 \) u\sing the quadratic formula.
A. 1
B. -1
C. 2
D. -2
Question 13
A histogram is shown below. Find the mean of the data set.
A. 10
B. 15
C. 20
D. 25
Question 14
Solve the system of equations u\sing matrices: \begin{align*} x + y + z &= 6, \ 2x - y + 3z &= 7, \ x - 2y + z &= -2 \end{align*}.
A. [1, 2, 3]
B. [2, -1, 1]
C. [3, 1, -1]
D. [1, -1, 2]
Question 15
The equation of a circle is given by \( x^2 + y^2 - 6x + 4y + 12 = 0 \). Find the center and radius of the circle.
A. \( 3, -2 \), 1
B. (3, 2), 1
C. (2, 3), 1
D. \( 2, -3 \), 1

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