POST UTME GREENFIELD UNIVERSITY 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Determine the value of x in the equation \( egin{bmatrix} 2 & 1 \ 3 & 2 \end{bmatrix} egin{bmatrix} x \ 1 \end{bmatrix} = egin{bmatrix} 4 \ 8 \end{bmatrix} \).
A. 1
B. 2
C. 3
D. 4
Question 2
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -∞, -1 \) ∪ (3, ∞)
B. \( -∞, -3 \) ∪ (1, ∞)
C. \( -∞, -1 \) ∪ (1, ∞)
D. \( -∞, 1 \) ∪ (3, ∞)
Question 3
In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the other sides is 6 cm. Find the length of the third side u\sing the Pythagorean theorem.
A. 8 cm
B. 12 cm
C. 14 cm
D. 16 cm
Question 4
Solve the equation \( \frac{1}{2}x^2 + \frac{3}{4}x - 2 = 0 \) for x.
A. 4
B. -4
C. 2
D. -2
Question 5
A circle has a radius of 5 cm. Find the area of the circle.
A. 25π
B. 50π
C. 100π
D. 200π
Question 6
A polynomial function has roots at \( x = -2, 0, 3 \). Find the polynomial function in factored form.
A. f(x) = \( x + 2 \)\( x)\( x - 3 \ \)
B. f(x) = \( x - 2 \)\( x)\( x + 3 \ \)
C. f(x) = \( x + 2 \)\( x)\( x - 2 \ \)
D. f(x) = \( x - 2 \)\( x)\( x + 3 \ \)
Question 7
Find the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 8
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 9
Solve the system of equations \( x + y = 4 \) and \( 2x - 3y = -2 \).
A. (1, 3)
B. (2, 2)
C. (3, 1)
D. (4, 0)
Question 10
Solve the equation \( \sin^2 x + \cos^2 x = 1 \) for ( x ) in the interval ( [0, 2pi] ).
A. \( x = \frac{pi}{2} \)
B. \( x = \frac{pi}{4} \)
C. \( x = \frac{3pi}{4} \)
D. \( x = \frac{5pi}{4} \)
Question 11
A circle with center (2, 3) and radius 4 passes through the point (6, 7). Find the equation of the circle.
A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 2 \)^2 + \( y - 3 \)^2 = 25
C. \( x - 2 \)^2 + \( y - 3 \)^2 = 36
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 49
Question 12
Find the value of \( sum_{n=1}^{10} \frac{1}{n^2} \)
A. 1.6449340668482264
B. 1.6449340668482265
C. 1.6449340668482266
D. 1.6449340668482267
Question 13
A set $A$ contains $5$ elements, and a set $B$ contains $3$ elements. If $A \cap B = \emptyset$, what is the number of elements in $A \cup B$?
A. 8
B. 7
C. 6
D. 5
Question 14
Solve for ( x ) in the equation \( 2x^2 + 5x - 3 = 0 \)
A. -1.5
B. 1.5
C. -1
D. 2
Question 15
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -infty, -1 \) cup (3, infty)
B. \( -infty, -3 \) cup (1, infty)
C. \( -infty, -3 \) cup \( -1, infty \)
D. \( -infty, 1 \) cup (3, infty)

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