POST UTME GREENFIELD UNIVERSITY 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).
A. 0
B. 1
C. -1
D. 2
Question 2
Solve the inequality \( 2x^2 + 5x - 3 > 0 \) u\sing the quadratic formula.
A. \[ x < -1 \]
B. \[ x > 3 \]
C. \[ x < 3 \]
D. \[ x > -3 \]
Question 3
Find the equation of the line pas\sing through the points ( (2,3) ) and ( (4,5) ).
A. \( y = \frac{1}{2}x + 1 \)
B. \( y = \frac{1}{2}x - 1 \)
C. \( y = 2x + 1 \)
D. \( y = 2x - 1 \)
Question 4
Solve the inequality \( 2x^2 + 3x - 1 > 0 \).
A. \( x < -\frac{1}{2} \) or \( x > \frac{1}{2} \)
B. \( x < -\frac{1}{2} \) or \( x < \frac{1}{2} \)
C. \( x > -\frac{1}{2} \) or \( x < \frac{1}{2} \)
D. \( x > -\frac{1}{2} \) or \( x > \frac{1}{2} \)
Question 5
Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 1 \ -2 \end{pmatrix} \). Find the vector ( mathbf{c} ) such that ( mathbf{c} ) is perp\endicular to both ( mathbf{a} ) and ( mathbf{b} ).
A. \( egin{pmatrix} 3 \ -2 \end{pmatrix} \)
B. \( egin{pmatrix} -3 \ 2 \end{pmatrix} \)
C. \( egin{pmatrix} 1 \ 1 \end{pmatrix} \)
D. \( egin{pmatrix} -1 \ -1 \end{pmatrix} \)
Question 6
The mean of a set of numbers is 25. If one of the numbers is 30, what is the sum of the remaining numbers?
A. Sum of remaining numbers = 25*4 - 30
B. Sum of remaining numbers = 25*5 - 30
C. Sum of remaining numbers = 25*6 - 30
D. Sum of remaining numbers = 25*7 - 30
Question 7
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{x}} ) u\sing the chain rule.
A. f'(x) = -\frac{1}{2x^{3/2}}
B. f'(x) = \frac{1}{2x^{3/2}}
C. f'(x) = -\frac{1}{x^{3/2}}
D. f'(x) = \frac{1}{x^{3/2}}
Question 8
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 9
In a random sample of 100 students, the mean height is 175 cm with a s\tandard deviation of 5 cm. If the sample is normally distributed, what is the probability that a randomly selected student will have a height greater than 180 cm?
A. 0.1587
B. 0.3085
C. 0.4772
D. 0.6915
Question 10
Simplify the expression \( \sqrt{16} + \sqrt{9} \).
A. 5
B. 7
C. 9
D. 11
Question 11
A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?
A. P\( X > 4 \) = \frac{1}{6}
B. P\( X > 4 \) = \frac{2}{6}
C. P\( X > 4 \) = \frac{3}{6}
D. P\( X > 4 \) = \frac{4}{6}
Question 12
Find the value of ( x ) that satisfies the equation \( x^3 - 6x^2 + 11x - 6 = 0 \).
A. \( x = 1 \)
B. \( x = 2 \)
C. \( x = 3 \)
D. \( x = 4 \)
Question 13
In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the acute angles is 30°. Find the length of the side opposite the 30° angle.
A. \( 5 \text{ cm} \)
B. \( 7.5 \text{ cm} \)
C. \( 10 \text{ cm} \)
D. \( 12.5 \text{ cm} \)
Question 14
A sequence is defined by the recurrence relation \( a_n = 2a_{n-1} + 1 \), with initial term \( a_1 = 3 \). Find the value of \( a_{10} \).
A. 1023
B. 1024
C. 1025
D. 1026
Question 15
A rec\tangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. Determine the volume of the prism in cubic centimeters.
A. 72
B. 80
C. 90
D. 100

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