POST UTME ELIZADE UNIVERSITY 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \) for ( x ) in the interval ( [0, 2pi] ).
A. \( x = \frac{pi}{4}, \frac{3pi}{4}, \frac{5pi}{4}, \frac{7pi}{4} \)
B. \( x = \frac{pi}{2}, \frac{3pi}{2} \)
C. \( x = \frac{pi}{4}, \frac{3pi}{4} \)
D. \( x = \frac{pi}{2}, \frac{3pi}{2}, \frac{5pi}{4}, \frac{7pi}{4} \)
Question 2
Determine the value of x in the equation \( \frac{1}{2}x + 5 = \frac{3}{4}x - 3 \) u\sing the method of substitution.
A. \( x = -24 \)
B. \( x = 12 \)
C. \( x = -12 \)
D. \( x = 24 \)
Question 3
Solve the equation \( 2x^2 + 5x - 3 = 0 \) u\sing the quadratic formula.
A. \( x = \frac{-5 \pm \sqrt{109}}{4} \)
B. \( x = \frac{-5 \pm \sqrt{121}}{4} \)
C. \( x = \frac{-5 \pm \sqrt{169}}{4} \)
D. \( x = \frac{-5 \pm \sqrt{225}}{4} \)
Question 4
Determine the value of x in the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ) if \( \tan\( x \ \) = \frac{3}{4} ).
A. \( \frac{pi}{4} \)
B. \( \frac{3pi}{4} \)
C. \( \frac{5pi}{4} \)
D. \( \frac{7pi}{4} \)
Question 5
A random sample of 25 students from a university had a mean height of 175.5 cm with a s\tandard deviation of 5.2 cm. If the population s\tandard deviation is 6.1 cm, calculate the 95% confidence interval for the population mean.
A. 168.3 cm, 182.7 cm
B. 170.1 cm, 180.9 cm
C. 172.9 cm, 178.1 cm
D. 169.5 cm, 181.5 cm
Question 6
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 64
B. 80
C. 96
D. 112
Question 7
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
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 8
Solve the system of equations \( \begin{cases} 2x + 3y = 7 \ 4x - 2y = -3 \end{cases} \) u\sing matrices.
A. \( x = 1, y = 2 \)
B. \( x = 2, y = 1 \)
C. \( x = 3, y = 4 \)
D. \( x = 4, y = 3 \)
Question 9
Find the equation of the circle with center (2, 3) and radius 4.
A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16 \)
B. \( x - 3 \)^2 + \( y - 2 \)^2 = 16 \)
C. \( x - 4 \)^2 + \( y - 3 \)^2 = 16 \)
D. \( x - 2 \)^2 + \( y - 4 \)^2 = 16 \)
Question 10
Find the volume 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. \( \frac{32\pi}{5} \)
B. \( \frac{64\pi}{5} \)
C. \( \frac{128\pi}{5} \)
D. \( \frac{256\pi}{5} \)
Question 11
Simplify the expression \( \frac{2^3 \cdot 3^2}{2^2 \cdot 3^4} \).
A. \frac{1}{12}
B. \frac{1}{6}
C. \frac{1}{4}
D. \frac{1}{3}
Question 12
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. x < -1
B. x > -1
C. x < 3
D. x > 3
Question 13
Find the equation of the circle with center ( (3, 4) ) and radius ( 5 ).
A. \( x - 3 \)^2 + \( y - 4 \)^2 = 25
B. \( x - 4 \)^2 + \( y - 3 \)^2 = 25
C. \( x - 3 \)^2 + \( y - 4 \)^2 = 30
D. \( x - 4 \)^2 + \( y - 3 \)^2 = 30
Question 14
A sequence is defined as \( a_n = 2n + 1 \). Find the sum of the first 5 terms of the sequence.
A. 15
B. 20
C. 25
D. 30
Question 15
Find the equation of the circle pas\sing through the points (2,3), (4,5), and \( -1,2 \).
A. \( x^2 + y^2 + 4x - 6y + 5 = 0 \)
B. \( x^2 + y^2 - 4x + 6y + 5 = 0 \)
C. \( x^2 + y^2 + 2x - 6y + 5 = 0 \)
D. \( x^2 + y^2 - 2x + 6y + 5 = 0 \)

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