POST UTME UNILORIN 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 64
B. 80
C. 96
D. 112
Question 2
Find the value of x in the equation \( \frac{x}{2} + \frac{3}{4} = \frac{5}{6} \).
A. 1
B. 2
C. 3
D. 4
Question 3
Find the derivative of \( y = \frac{1}{x^2 + 1} \ \) u\sing the chain rule.
A. \frac{-2x}{\( x^2 + 1 \)^2}
B. \frac{2x}{\( x^2 + 1 \)^2}
C. \frac{1}{\( x^2 + 1 \)^2}
D. \frac{-1}{\( x^2 + 1 \)^2}
Question 4
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. \( y = -2x + 1 \)
D. \( y = -2x - 1 \)
Question 5
Find the derivative of the function ( f(x) = x^3 - 2x^2 + 5x - 1 ) u\sing the power rule.
A. 3x^2 - 4x + 5
B. 3x^2 - 4x + 5
C. 3x^2 - 4x + 6
D. 3x^2 - 4x + 7
Question 6
A geometric sequence is defined as \( a_n = 2^n \). Find the sum of the first five terms of the sequence.
A. ( 63 )
B. ( 127 )
C. ( 255 )
D. ( 511 )
Question 7
Solve the system of linear equations \( egin{cases} x + y = 2 \ 2x - 3y = - 1 \end{cases} \) u\sing substitution.
A. x = 1, y = 1
B. x = 1, y = 2
C. x = 2, y = 1
D. x = 2, y = 2
Question 8
Find the determinant of the matrix \( \begin{bmatrix} 2 & 3 \ 4 & 5 \end{bmatrix} \).
A. 1
B. 2
C. 3
D. 4
Question 9
A binary operation ( ast ) is defined as \( a ast b = a^2 + b^2 \). Find the value of ( 2 ast 3 ).
A. ( 4 )
B. ( 5 )
C. ( 6 )
D. ( 7 )
Question 10
Find the area under the curve \( y = x^2 - 4x + 3 \) from \( x = 0 \) to \( x = 2 \).
A. \frac{1}{3}x^3 - 2x^2 + 3x \Big|_0^2 = \frac{1}{3}\( 8 - 8 + 6 \) = 2
B. \frac{1}{3}x^3 - 2x^2 + 3x \Big|_0^2 = \frac{1}{3}\( 8 - 8 + 6 \) = 4
C. \frac{1}{3}x^3 - 2x^2 + 3x \Big|_0^2 = \frac{1}{3}\( 8 - 8 + 6 \) = 6
D. \frac{1}{3}x^3 - 2x^2 + 3x \Big|_0^2 = \frac{1}{3}\( 8 - 8 + 6 \) = 8
Question 11
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 40
B. 50
C. 60
D. 70
Question 12
A random variable ( X ) has a probability distribution given by \( P\( X = x \ \) = \frac{1}{2} \) for \( x = 1, 2, 3 \). Find the expected value of ( X ).
A. 2
B. 3
C. 4
D. 5
Question 13
A fair six-sided die is rolled. What is the probability that the sum of the numbers on the two dice is 7?
A. 1/6
B. 1/3
C. 1/2
D. 2/3
Question 14
Solve the system of linear equations u\sing matrices: \( \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 7 \end{bmatrix} \).
A. \begin{bmatrix} 1 \ 2 \end{bmatrix}
B. \begin{bmatrix} 2 \ 1 \end{bmatrix}
C. \begin{bmatrix} -1 \ 3 \end{bmatrix}
D. \begin{bmatrix} 3 \ -1 \end{bmatrix}
Question 15
A sequence is defined as \( a_n = 2n + 1 \). Find the sum of the first five terms of the sequence.
A. ( 15 )
B. ( 25 )
C. ( 35 )
D. ( 45 )

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