POST UTME ESUT 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve for ( x ) in the equation \( 2^x + 3^x = 5^x \).
A. \( x = 2 \ \)
B. \( x = 3 \ \)
C. \( x = 4 \ \)
D. \( x = 5 \ \)
Question 2
Find the equation of the circle with center (1, 2) and radius 3
A. x^2 + y^2 - 2x + 4y + 5 = 0
B. x^2 + y^2 + 2x - 4y + 5 = 0
C. x^2 + y^2 - 2x - 4y + 5 = 0
D. x^2 + y^2 + 2x + 4y + 5 = 0
Question 3
Solve the system of equations: \begin{align*} x + y &= 3 \ x - y &= 1 \end{align*}
A. x = 2, y = 1
B. x = 1, y = 2
C. x = 2, y = 2
D. x = 1, y = 1
Question 4
Find the surface area of the solid formed by revolving the region bounded by the parabola y = x^2, the x-axis, and the line x = 2 about the x-axis.
A. 64\pi
B. 128\pi
C. 256\pi
D. 512\pi
Question 5
A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?
A. \( \frac{1}{2} \ \)
B. \( \frac{2}{3} \ \)
C. \( \frac{3}{4} \ \)
D. \( \frac{5}{6} \ \)
Question 6
A circle has a radius of 5 cm. Find the area of the circle.
A. \pi r^2
B. 2\pi r
C. \pi r
D. \pi r^2 + 2\pi r
Question 7
Find the value of x in the equation 2^x + 2^x = 128.
A. 5
B. 6
C. 7
D. 8
Question 8
Solve the inequality \( x^2 - 4x + 3 > 0 \).
A. \( -\infty, 1 \) \cup \( 3, \infty \)
B. \( -\infty, 3 \) \cup \( 1, \infty \)
C. (1, 3)
D. \( -\infty, 1 \) \cup \( 3, \infty \)
Question 9
Find the value of \( \log_{10} \left\( \frac{1}{2} \right \ \) given that \( \log_{10} 2 = \frac{3}{5} \ \).
A. \( -\frac{3}{5} \ \)
B. \( -\frac{1}{5} \ \)
C. \( \frac{1}{5} \ \)
D. \( \frac{3}{5} \ \)
Question 10
Find the value of ( x ) in the equation \( x^3 - 6x^2 + 11x - 6 = 0 \).
A. 1
B. 2
C. 3
D. 4
Question 11
Find the area under the curve y = x^3 - 6x^2 + 9x + 2 from x = 0 to x = 4.
A. 64
B. 128
C. 256
D. 512
Question 12
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. x < -1
B. x > -1
C. x < 1
D. x > 1
Question 13
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. 24π cm³
B. 48π cm³
C. 96π cm³
D. 192π cm³
Question 14
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. x < -1 or x > 3/2
B. x < 1 or x > -3/2
C. x < -3/2 or x > 1
D. x < 3/2 or x > -1
Question 15
A fair six-sided die is rolled twice. What is the probability that the sum of the two rolls is 7?
A. 1/6
B. 1/12
C. 1/18
D. 1/36

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