POST UTME JOSEPH AYO BABALOLA UNIVERSITY 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the derivative of the function \( y = 2x^3 - 5x^2 + x - 1 \) u\sing the chain rule.
A. \( 6x^2 - 10x + 1 \)
B. \( 6x^2 - 10x + 2 \)
C. \( 6x^2 - 10x - 1 \)
D. \( 6x^2 - 10x - 2 \)
Question 2
A line passes through the points ( (2, 3) ) and ( (4, 5) ). Find the equation of the line in slope-intercept form.
A. \( y = x + 1 \)
B. \( y = x - 1 \)
C. \( y = x + 2 \)
D. \( y = x - 2 \)
Question 3
A circle has a radius of 5 cm. Find the area of the circle.
A. \( 50 \pi \)
B. \( 100 \pi \)
C. \( 150 \pi \)
D. \( 200 \pi \)
Question 4
Find the value of \( \sin \( 2 \theta \ \) ) given that \( \sin \( \theta \ \) = \frac{3}{5} ) and \( \cos \( \theta \ \) = \frac{4}{5} ).
A. √2
B. √6
C. √10
D. √14
Question 5
Solve the equation \( x^2 + 4x - 5 = 0 \) u\sing the quadratic formula.
A. x = 1 or x = -5
B. x = 2 or x = -3
C. x = 3 or x = -2
D. x = 4 or x = -1
Question 6
Let ( f(x) = x^2 + 2x + 1 ). Find the equation of the \tangent line to the curve at the point where \( x = 1 \).
A. y = 3x - 2
B. y = 3x + 2
C. y = 3x - 1
D. y = 3x + 1
Question 7
Solve the inequality \( 2x^2 + 5x - 3 > 0 \) u\sing the quadratic formula.
A. x < -1 or x > 3/2
B. x < -3/2 or x > 1
C. x < 1 or x > -3/2
D. x < 3/2 or x > -1
Question 8
A right-angled triangle has a hypotenuse of length 10 cm and one of its acute angles is 30°. Find the length of the side opposite the 30° angle.
A. 5
B. 7.07
C. 10
D. 15
Question 9
In a histogram with 5 classes, the class width is 2 units. If the total frequency is 20, find the frequency of each class.
A. 2
B. 4
C. 6
D. 8
Question 10
A random experiment has two indep\endent events ( A ) and ( B ) with probabilities ( P(A) = 0.4 ) and ( P(B) = 0.6 ). Find the probability that both events occur.
A. ( 0.24 )
B. ( 0.36 )
C. ( 0.48 )
D. ( 0.64 )
Question 11
Find the area of the triangle with vertices ( (0, 0) ), ( (2, 0) ), and ( (0, 3) ).
A. ( 6 )
B. ( 12 )
C. ( 18 )
D. ( 24 )
Question 12
Find the derivative of the function ( f(x) = \frac{x^2 + 2x - 3}{x^2 - 4} ) u\sing the quotient rule.
A. \frac{2x\( x^2 - 4 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}
B. \frac{2x\( x^2 - 4 \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}
C. \frac{2x\( x^2 - 4 \) - \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}
D. \frac{2x\( x^2 - 4 \) + \( x^2 + 2x - 3 \)(2x)}{\( x^2 - 4 \)^2}
Question 13
Solve for y in the equation \( y = \frac{1}{2} \left\( x + \frac{1}{x} \right \ \) ) given that x = 2.
A. 2
B. 3
C. 4
D. 5
Question 14
Find the area under the curve \( y = \frac{1}{2}x^2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{16}{3} \)
B. \( \frac{32}{3} \)
C. \( \frac{64}{3} \)
D. \( \frac{128}{3} \)
Question 15
A binary operation \( \ast \) on the set \( \{1, 2, 3\} \) is defined by \( 1 \ast 1 = 1, 1 \ast 2 = 2, 1 \ast 3 = 3, 2 \ast 1 = 2, 2 \ast 2 = 3, 2 \ast 3 = 1, 3 \ast 1 = 3, 3 \ast 2 = 1, 3 \ast 3 = 2 \). Find the result of \( 2 \ast 3 \).
A. 1
B. 2
C. 3
D. 4

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