POST UTME EKSU 2017 Mathematics | Objective

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Question 1
A vector ( vec{a} ) has magnitude 5 and direction \( 30^circ \) from the positive x-axis. Find the vector ( vec{a} ) in component form.
A. \( vec{a} = 5 \cos 30^circ hat{i} + 5 \sin 30^circ hat{j} \)
B. \( vec{a} = 5 \sin 30^circ hat{i} + 5 \cos 30^circ hat{j} \)
C. \( vec{a} = 5 \cos 30^circ hat{j} + 5 \sin 30^circ hat{i} \)
D. \( vec{a} = 5 \sin 30^circ hat{j} + 5 \cos 30^circ hat{i} \)
Question 2
Find the equation of the circle with center at (2,3) and radius 4 in the form \( x - h \ \)^2 + \( y - k \)^2 = r^2).
A. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )
B. \( x - 3 \ \)^2 + \( y - 2 \)^2 = 16 )
C. \( x - 2 \ \)^2 + \( y - 2 \)^2 = 16 )
D. \( x - 3 \ \)^2 + \( y - 3 \)^2 = 16 )
Question 3
Solve the inequality \( |x - 2| > 3 \).
A. \( x < -1 \text{ or } x > 5 \)
B. \( x < 1 \text{ or } x > 5 \)
C. \( x < -1 \text{ or } x > 2 \)
D. \( x < 1 \text{ or } x > 2 \)
Question 4
Solve for (x) in the equation \( \log_{10} \( x^2 \ \) = 4).
A. \( x = 10^4 \)
B. \( x = 10^2 \)
C. \( x = 10^8 \)
D. \( x = 10^6 \)
Question 5
Solve the inequality $\frac{x-2}{x+1} > 0$.
A. x > 1
B. x < -1
C. x > -1
D. x < 1
Question 6
Solve the system of equations \( egin{cases} x + y = 4 \ 2x - y = 3 \end{cases} \).
A. (1, 3)
B. (2, 2)
C. (3, 1)
D. (4, 0)
Question 7
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. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \)
C. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 \)
D. \( \frac{1}{2} \times 4^2 + 3 \times \frac{4^2}{2} - 2 \times 4 \)
Question 8
A set of 5 numbers has a mean of 10 and a median of 8. If the largest number is 15, find the sum of the remaining 3 numbers.
A. ( 24 )
B. ( 26 )
C. ( 28 )
D. ( 30 )
Question 9
Find the derivative of the function \( y = \sin^2 x \) u\sing the chain rule.
A. \( y' = 2 \sin x \cos x \)
B. \( y' = \sin x \cos x \)
C. \( y' = 2 \cos x \)
D. \( y' = \sin x \)
Question 10
A binary operation ( ast ) is defined as \( a ast b = a^2 + b^2 \). Find the value of ( 2 ast 3 ).
A. \( 2 ast 3 = 2^2 + 3^2 = 13 \)
B. \( 2 ast 3 = 2^2 - 3^2 = -5 \)
C. \( 2 ast 3 = 2^2 + 3^2 + 2 \times 2 \times 3 = 25 \)
D. \( 2 ast 3 = 2^2 + 3^2 - 2 \times 2 \times 3 = 1 \)
Question 11
Solve the quadratic equation $x^2 + 4x + 4 = 0$.
A. x = -2
B. x = 2
C. x = -1
D. x = 1
Question 12
A set of 4 numbers has a mean of 12 and a range of 8. If the largest number is 18, find the sum of the remaining 3 numbers.
A. ( 36 )
B. ( 38 )
C. ( 40 )
D. ( 42 )
Question 13
Determine the value of $x$ in the equation $2^x + 5^x = 7^x$.
A. 1
B. 2
C. 3
D. 4
Question 14
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, -1 \) ∪ (1, ∞)
D. \( -∞, 1 \) ∪ (3, ∞)
Question 15
Find the value of (x) in the equation \( 2^x = 16 \).
A. ( 2 )
B. ( 3 )
C. ( 4 )
D. ( 5 )

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