POST UTME ESUT 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the area of the triangle with vertices ( (0, 0) ), ( (3, 0) ), and ( (0, 2) ).
A. \( \frac{1}{2} \times 3 \times 2 \)
B. \( \frac{1}{2} \times 3 \times 3 \)
C. \( \frac{1}{2} \times 2 \times 3 \)
D. \( \frac{1}{2} \times 2 \times 2 \)
Question 2
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 3
Find the area under the curve \( y = \sin^2 x \) from \( x = 0 \) to \( x = \frac{pi}{2} \).
A. \( \frac{pi}{4} \)
B. \( \frac{pi}{2} \)
C. \( \frac{pi}{3} \)
D. \( \frac{pi}{6} \)
Question 4
Determine the value of $\int_0^1 x^2 \sin(x) dx$.
A. -1
B. 0
C. 1
D. 2
Question 5
Solve the system of equations: $\begin{cases} x + y = 2 \ 2x - 3y = - 1 \end{cases}$
A. (x,y) = (1,1)
B. (x,y) = (2,0)
C. (x,y) = (0,2)
D. (x,y) = (1,0)
Question 6
Find the derivative of the function $f(x) = \frac{1}{x^2 + 1}$
A. f'(x) = \frac{-2x}{\( x^2 + 1 \)^2}
B. f'(x) = \frac{2x}{\( x^2 + 1 \)^2}
C. f'(x) = \frac{-2}{\( x^2 + 1 \)^2}
D. f'(x) = \frac{2}{\( x^2 + 1 \)^2}
Question 7
Solve the inequality \( 2x^2 + 5x - 3 > 0 \):
A. \( x < -1 \) or \( x > \frac{3}{2} \)
B. \( x < -1 \) or \( x < \frac{3}{2} \)
C. \( x > -1 \) or \( x > \frac{3}{2} \)
D. \( x > -1 \) or \( x < \frac{3}{2} \)
Question 8
Solve for x in the equation: \( 2^x = 16 \)
A. 2
B. 3
C. 4
D. 5
Question 9
A circle has a radius of 4 cm. Find the area of the circle.
A. \( pi \times 4^2 \)
B. \( 2 \times pi \times 4 \)
C. \( pi \times 2^2 \)
D. \( 2 \times pi \times 2 \)
Question 10
Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3:
A. \( 2\( 3^{10}-1 \ \) )
B. \( 2\( 3^{10}+1 \ \) )
C. \( 2\( 3^{10}-2 \ \) )
D. \( 2\( 3^{10}+2 \ \) )
Question 11
In the diagram below, \( AB = 5 \) cm, \( BC = 6 \) cm, and \( AC = 7 \) cm. Find the area of triangle ( ABC ).
A. ( 15 ) cm\( ^2 \)
B. ( 20 ) cm\( ^2 \)
C. ( 25 ) cm\( ^2 \)
D. ( 30 ) cm\( ^2 \)
Question 12
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 \)
B. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \)
C. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4^2 \)
D. \( \frac{1}{2} \times 4^2 + 3 \times 4^3 - 2 \)
Question 13
A random sample of 16 students from a population of 100 students has a mean height of 170 cm with a s\tandard deviation of 5 cm. Calculate the s\tandard error of the mean.
A. 2.5 cm
B. 3.5 cm
C. 4.5 cm
D. 5.5 cm
Question 14
Solve for x in the equation \( \frac{x}{2} + 5 = 11 \):
A. 6
B. 7
C. 8
D. 9
Question 15
Solve for ( x ) in the equation \( 2^x + 3^x = 5^x \).
A. \( x = 2 \)
B. \( x = 3 \)
C. \( x = 4 \)
D. \( x = 5 \)

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