POST UTME CRAWFORD UNIVERSITY 2017 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the derivative of the function ( f(x) = \frac{x^2}{x^2 + 1} ) u\sing the quotient rule.
A. 2x\( x^2 + 1 \) - 2x^2
B. 2x\( x^2 + 1 \) + 2x^2
C. 2x\( x^2 + 1 \) - x^2
D. 2x\( x^2 + 1 \) + x^2
Question 2
Solve the equation \( 2^x = 32 \) for x.
A. 5
B. 6
C. 7
D. 8
Question 3
A particle moves in a plane with position vector \( \vec{r}\( t \ \) = 2\cos t\hat{i} + 3\sin t\hat{j}). Find the velocity vector at time t = π/2.
A. \hat{i} + 3\hat{j}
B. -\hat{i} + 3\hat{j}
C. -\hat{i} - 3\hat{j}
D. \hat{i} - 3\hat{j}
Question 4
A vector A has a magnitude of 5 units and makes an angle of 30° with the positive x-axis. Find the x and y components of vector A.
A. 4.33, 2.5
B. 4.5, 2.5
C. 4.33, 2.33
D. 4.5, 2.33
Question 5
Find the derivative of the function \( y = 3x^2 + 2x - 5 \).
A. 6x + 2
B. 3x + 1
C. 2x - 3
D. x - 2
Question 6
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 40
B. 50
C. 60
D. 70
Question 7
Find the mean of the data set: 2, 4, 6, 8, 10.
A. 6
B. 7
C. 8
D. 9
Question 8
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 4 \) from \( x = 0 \) to \( x = 2 \).
A. \( \frac{1}{2} \)
B. ( 3 )
C. ( 4 )
D. ( 5 )
Question 9
Find the derivative of the function ( f(x) = \sin^2(x) ) u\sing the chain rule.
A. 2\sin\( x)\cos(x \)
B. -2\sin\( x)\cos(x \)
C. 2\sin^2\( x)\cos(x \)
D. -2\sin^2\( x)\cos(x \)
Question 10
Solve the equation 2x^2 + 5x - 3 = 0 u\sing the quadratic formula.
A. 1
B. -1
C. 2
D. -2
Question 11
Solve the system of equations \( x + y = 2, x - 2y = -3 \).
A. x = 1, y = 1
B. x = 1, y = -1
C. x = -1, y = 1
D. x = -1, y = -1
Question 12
Solve the inequality \( \frac{x}{x-2} > 2 \) for \( x > 2 \).
A. x > 4
B. x > 6
C. x > 8
D. x > 10
Question 13
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 40
B. 50
C. 60
D. 70
Question 14
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, -3 \) ∪ \( -1, ∞ \)
D. \( -∞, -1 \) ∪ (1, ∞)
Question 15
A set of exam scores has a mean of 75 and a s\tandard deviation of 10. What is the z-score of a score of 85?
A. 0.5
B. 1
C. 1.5
D. 2

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