POST UTME GREENFIELD UNIVERSITY 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the equation \( \frac{1}{2} \log_{10} \( x^2 \ \) = 4 ).
A. \( x = 10^{8} \)
B. \( x = 10^{4} \)
C. \( x = 10^{2} \)
D. \( x = 10^{6} \)
Question 2
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 3
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{-2x}{\( x^2 + 1 \)^2}
D. f'(x) = \frac{2}{\( x^2 + 1 \)^2}
Question 4
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)
Question 5
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 6
Solve the system of equations \( x + y = 2 \) and \( x - y = 1 \)
A. (1, 1)
B. (2, 0)
C. (0, 2)
D. (1, 0)
Question 7
Find the mean of the following data set: 2, 4, 6, 8, 10.
A. 5
B. 6
C. 7
D. 8
Question 8
Solve for ( x ) in the equation \( 2x^2 + 5x - 3 = 0 \)
A. -1.5
B. 1.5
C. -1
D. 2
Question 9
A circle with center $C$ and radius $r$ passes through the point $P$. What is the equation of the circle in s\tandard form?
A. \( x - h \)^2 + \( y - k \)^2 = r^2
B. x^2 + y^2 = r^2
C. x^2 + y^2 - 2gx - 2fy = 0
D. x^2 + y^2 + 2gx + 2fy = 0
Question 10
Find the area under the curve \( y = x^2 \) from x = 0 to x = 4.
A. 32
B. 64
C. 128
D. 256
Question 11
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 12
Find the equation of the circle with centre at \( left\( -2, 3 \right \ \) ) and radius ( 4 ).
A. \( x^2 + y^2 + 4x - 6y - 7 = 0 \)
B. \( x^2 + y^2 - 4x + 6y - 7 = 0 \)
C. \( x^2 + y^2 + 2x - 3y - 7 = 0 \)
D. \( x^2 + y^2 - 2x + 3y - 7 = 0 \)
Question 13
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 14
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 2 \)
A. 4
B. 2
C. 1
D. 3
Question 15
Find the vector projection of the vector \( vec{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) onto the vector \( vec{b} = egin{pmatrix} 1 \ 1 \end{pmatrix} \).
A. egin{pmatrix} 2/3 \ 2/3 \end{pmatrix}
B. egin{pmatrix} 1/3 \ 1/3 \end{pmatrix}
C. egin{pmatrix} 4/3 \ 4/3 \end{pmatrix}
D. egin{pmatrix} 5/3 \ 5/3 \end{pmatrix}

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