POST UTME ESUT 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the value of \sum_{n=1}^{5} n^2.
A. \boxed{55}
B. 50
C. 60
D. 70
Question 2
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. \frac{-2x}{\( x^2 + 1 \)^2}
B. \frac{2x}{\( x^2 + 1 \)^2}
C. \frac{-2}{\( x^2 + 1 \)^2}
D. \frac{2}{\( x^2 + 1 \)^2}
Question 3
Solve the system of linear equations \( egin{cases} x + 2y = 3 \ 2x - y = 1 \end{cases} \).
A. \left\{ \begin{array}{c} x = 1 \ y = 1 \end{array}\right.
B. \left\{ \begin{array}{c} x = 2 \ y = 1 \end{array}\right.
C. \left\{ \begin{array}{c} x = 1 \ y = 2 \end{array}\right.
D. \left\{ \begin{array}{c} x = 2 \ y = 2 \end{array}\right.
Question 4
Find the equation of the circle with center \( -2, 3 \) and radius 4.
A. \( x + 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 2 \)^2 + \( y + 3 \)^2 = 16
C. \( x + 2 \)^2 + \( y + 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
Question 5
Find the derivative of the function ( f(x) = x^3 - 2x^2 + x - 1 ).
A. 3x^2 - 4x + 1
B. 3x^2 - 4x - 1
C. 3x^2 + 4x + 1
D. 3x^2 + 4x - 1
Question 6
Find the equation of the line pas\sing through the points (2, 3) and (4, 5).
A. y = 2x - 1
B. y = 2x + 1
C. y = x - 2
D. y = x + 2
Question 7
Find the equation of the circle with center \( -2, 3 \) and radius 4.
A. \boxed{\( x + 2 \)^2 + \( y - 3 \)^2 = 16}
B. \( x - 2 \)^2 + \( y + 3 \)^2 = 16
C. \( x + 2 \)^2 + \( y + 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
Question 8
Find the volume of the frustum of a cone with a height of 10 cm, a lower base radius of 4 cm, and an upper base radius of 2 cm.
A. 100\pi cm^3
B. 150\pi cm^3
C. 200\pi cm^3
D. 250\pi cm^3
Question 9
A set of 4 numbers has a median of 10. Find the sum of the numbers.
A. \boxed{40}
B. 30
C. 50
D. 60
Question 10
Solve the inequality x^2 - 4x - 5 > 0.
A. x < -1 \text{ or } x > 5
B. x < 1 \text{ or } x > 5
C. x < -1 \text{ or } x < 5
D. x > 1 \text{ or } x < 5
Question 11
A sequence is defined by the recurrence relation a_n = 2a_\( n-1 \) + 1, with a_1 = 3. Find the value of a_5.
A. 33
B. 35
C. 37
D. 39
Question 12
A set of data is given as: 2, 4, 6, 8, 10. Find the mean of the data.
A. ( 5 )
B. ( 6 )
C. ( 7 )
D. ( 8 )
Question 13
Determine the value of x in the equation \( \frac{1}{2}x^2 + 5x - 3 = 0 \)
A. 2
B. -3
C. 4
D. -2
Question 14
A histogram of exam scores has a mean of 80 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected student scored above 90?
A. 0.1587
B. 0.3413
C. 0.4772
D. 0.6745
Question 15
A sequence is defined by the formula \( a_n = 2n + 1 \). Find the sum of the first 5 terms of the sequence.
A. 15
B. 20
C. 25
D. 30

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