POST UTME GREENFIELD UNIVERSITY 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A sequence is defined as \( a_n = 2n + 1 \) for \( n = 1, 2, 3, ldots \). Determine the sum of the first 5 terms of the sequence.
A. 15
B. 20
C. 25
D. 30
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
Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 4 \ 5 \end{pmatrix} \). Find the vector \( mathbf{a} \times mathbf{b} \) u\sing the cross product formula.
A. \begin{pmatrix} -13 \ 8 \end{pmatrix}
B. \begin{pmatrix} 13 \ -8 \end{pmatrix}
C. \begin{pmatrix} 8 \ -13 \end{pmatrix}
D. \begin{pmatrix} -8 \ 13 \end{pmatrix}
Question 4
Solve the system of equations \( \begin{cases} x + 2y = 4 \ 3x - 2y = 5 \end{cases} \) u\sing matrices.
A. \[ \begin{pmatrix} 2 \ 1 \end{pmatrix} \]
B. \[ \begin{pmatrix} 1 \ 2 \end{pmatrix} \]
C. \[ \begin{pmatrix} 3 \ -1 \end{pmatrix} \]
D. \[ \begin{pmatrix} -1 \ 3 \end{pmatrix} \]
Question 5
Determine the value of $\frac{d}{dx}\left\( \frac{1}{x^2}\right \)$ u\sing the chain rule.
A. \frac{2}{x^3}
B. -\frac{2}{x^3}
C. \frac{1}{x^3}
D. -\frac{1}{x^3}
Question 6
A set of 5 cards numbered 1 to 5 is randomly drawn from a deck of 20 cards numbered 1 to 20. If the sum of the numbers on the 5 cards is 25, what is the probability that the number 5 is among the 5 cards drawn?
A. 1/6
B. 1/5
C. 1/4
D. 1/3
Question 7
A histogram is shown below. What is the value of the area of the shaded region?
A. 10
B. 20
C. 30
D. 40
Question 8
Consider the sequence \( a_n = 2n^2 + 3n - 1 \). Find the sum of the first 5 terms of the sequence.
A. 120
B. 130
C. 140
D. 150
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
Determine the sum of the first 5 terms of the geometric series \( 2 + 6 + 18 + \cdots \).
A. 124
B. 126
C. 128
D. 130
Question 11
Find the sum of the first 10 terms of the arithmetic progression 2, 5, 8, ...
A. Sum = \frac{10}{2}[2 + 19]
B. Sum = \frac{10}{2}[2 + 18]
C. Sum = \frac{10}{2}[2 + 17]
D. Sum = \frac{10}{2}[2 + 16]
Question 12
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 13
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 14
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 15
Solve the inequality \( \log_{10} \( x^2 \ \) > 4 ).
A. \( x > 10 \)
B. \( x < -10 \)
C. \( x > 100 \)
D. \( x < -100 \)

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