POST UTME BSU 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A fair six-sided die is rolled twice. What is the probability that the sum of the two rolls is 7?
A. \( \frac{1}{6} \)
B. \( \frac{1}{3} \)
C. \( \frac{1}{2} \)
D. \( \frac{2}{3} \)
Question 2
Solve for x in the equation \( \frac{1}{2}x^2 + 5x - 3 = 0 \) u\sing the quadratic formula.
A. x = -10 ± √\( 100 - 24 \)
B. x = 10 ± √\( 100 - 24 \)
C. x = -5 ± √\( 25 - 12 \)
D. x = 5 ± √\( 25 - 12 \)
Question 3
Find the equation of the line pas\sing through the points (2, 3) and (4, 5).
A. y = 2x - 1
B. y = 2x + 1
C. y = x - 1
D. y = x + 1
Question 4
Solve the equation \( \frac{x}{2} + \frac{1}{x} = 3 \).
A. \( x = 2 \)
B. \( x = 4 \)
C. \( x = 6 \)
D. \( x = 8 \)
Question 5
A company produces two products, A and B. The profit from producing x units of product A and y units of product B is given by the function ( P(x,y) = 2x + 3y - xy - 10 ). Find the values of x and y that maximize the profit.
A. \( x = 5, y = 3 \)
B. \( x = 3, y = 5 \)
C. \( x = 10, y = 2 \)
D. \( x = 2, y = 10 \)
Question 6
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{1}{2} \times 4^3 + 3 \times \frac{4^2}{2} - 2 \times 4 \)
B. \( \frac{1}{2} \times 4^3 + 3 \times \frac{4^2}{2} - 2 \times 4 + \frac{1}{2} \)
C. \( \frac{1}{2} \times 4^3 + 3 \times \frac{4^2}{2} - 2 \times 4 - \frac{1}{2} \)
D. \( \frac{1}{2} \times 4^3 + 3 \times \frac{4^2}{2} - 2 \times 4 \)
Question 7
Find the value of \( \log_{10} \( x^2 \ \) ) given that \( \log_{10} \( x \ \) = 2 ).
A. ( 4 )
B. ( 8 )
C. ( 16 )
D. ( 32 )
Question 8
A circle has a diameter of 10 cm. Find the area of the circle.
A. 25π cm^2
B. 50π cm^2
C. 75π cm^2
D. 100π cm^2
Question 9
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. x < -1 or x > 3
B. x < 1 or x > 3
C. x < -3 or x > 1
D. x < -3 or x > 3
Question 10
Evaluate the definite integral \( int_{0}^{1} x^2 \sqrt{1-x^2} dx \).
A. \( \frac{1}{3} \)
B. \( \frac{2}{3} \)
C. \( \frac{1}{2} \)
D. \( \frac{1}{4} \)
Question 11
Find the value of \( \tan left\( \frac{pi}{4} \right \ \) ).
A. ( 1 )
B. \( -1 \)
C. \( \sqrt{2} \)
D. \( -\sqrt{2} \)
Question 12
Find the value of \( int_{0}^{2} \( x^2 + 2x - 1 \ \) dx ).
A. \( \frac{8}{3} \)
B. \( \frac{16}{3} \)
C. \( \frac{24}{3} \)
D. \( \frac{32}{3} \)
Question 13
Solve the equation \( x^2 + 4x + 4 = 0 \).
A. \( x = -2 \)
B. \( x = 2 \)
C. \( x = -1 \)
D. \( x = 1 \)
Question 14
Find the volume of the solid formed by revolving the region bounded by the parabola \( y = x^2 \) and the line \( y = 2x \) about the x-axis.
A. \( \frac{8}{15} pi \)
B. \( \frac{16}{15} pi \)
C. \( \frac{32}{15} pi \)
D. \( \frac{64}{15} pi \)
Question 15
Find the equation of the circle pas\sing through the points (2,3), (4,5), and \( -1,2 \).
A. \( x^2 + y^2 + 4x - 6y - 3 = 0 \)
B. \( x^2 + y^2 - 4x + 6y - 3 = 0 \)
C. \( x^2 + y^2 + 2x - 4y - 3 = 0 \)
D. \( x^2 + y^2 - 2x + 4y - 3 = 0 \)

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