POST UTME VERITAS UNIVERSITY 2025 Mathematics | Objective

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Question 1
A polynomial function ( f(x) ) is defined by ( f(x) = x^3 - 2x^2 + 3x - 1 ). Find the value of ( f(2) ).
A. ( f(2) = 1 )
B. ( f(2) = 3 )
C. ( f(2) = 5 )
D. ( f(2) = 7 )
Question 2
Find the derivative of the function ( f(x) = 3x^2 + 2x - 5 ) u\sing the power rule.
A. 6x + 2
B. 6x^2 + 2
C. 6x^2 + 2x
D. 6x^2 - 2x
Question 3
Solve the inequality \( x^2 - 4x + 3 > 0 \).
A. \( -∞, 1 \) ∪ (3, ∞)
B. \( -∞, 3 \) ∪ (1, ∞)
C. \( -∞, 1 \) ∩ (3, ∞)
D. \( -∞, 3 \) ∩ (1, ∞)
Question 4
A polynomial function has a degree of 4 and a leading coefficient of 2. If the function has roots \( x = 1 \), \( x = 2 \), \( x = 3 \), and \( x = 4 \), find the equation of the polynomial in factored form.
A. y = 2\( x - 1 \)\( x - 2 \)\( x - 3 \)\( x - 4 \)
B. y = 2\( x - 2 \)\( x - 3 \)\( x - 4 \)\( x - 1 \)
C. y = 2\( x - 1 \)\( x - 3 \)\( x - 4 \)\( x - 2 \)
D. y = 2\( x - 2 \)\( x - 4 \)\( x - 1 \)\( x - 3 \)
Question 5
A sequence is given by the formula: \[ a_n = 2n^2 + 3n - 1 \]. Find the value of the 6th term.
A. 109
B. 119
C. 129
D. 139
Question 6
A circle has a radius of 4 cm. Find the area of the circle u\sing the formula A = πr^2.
A. 16\pi
B. 32\pi
C. 64\pi
D. 128\pi
Question 7
Find the equation of the circle with center ( (2, 3) ) and radius ( 4 ).
A. \left\( x - 2 \right \)^2 + \left\( y - 3 \right \)^2 = 16
B. \left\( x - 3 \right \)^2 + \left\( y - 2 \right \)^2 = 16
C. \left\( x - 4 \right \)^2 + \left\( y - 3 \right \)^2 = 16
D. \left\( x - 2 \right \)^2 + \left\( y - 4 \right \)^2 = 16
Question 8
Solve for ( x ) in the equation \( 2^x + 3^x = 5^x \).
A. \( x = 2 \)
B. \( x = 3 \)
C. \( x = 4 \)
D. \( x = 5 \)
Question 9
A right-angled triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. Find the length of the other leg.
A. 8 cm
B. 6 cm
C. 10 cm
D. 12 cm
Question 10
A histogram of exam scores has a mean of 75 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score will be between 60 and 90?
A. 0.6827
B. 0.3413
C. 0.8413
D. 0.1587
Question 11
A quadratic equation has roots \( x = 2 \) and \( x = 3 \). Find the equation of the quadratic in factored form.
A. y = \( x - 2 \)\( x - 3 \)
B. y = \( x - 3 \)\( x - 2 \)
C. y = \( x - 2 \)\( x + 3 \)
D. y = \( x - 3 \)\( x + 2 \)
Question 12
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. If the scores are normally distributed, what is the probability that a randomly selected score is between 50 and 70?
A. 0.135
B. 0.341
C. 0.691
D. 0.841
Question 13
Solve the system of equations \begin{align*} x + y &= 4 \ 2x - 3y &= 5 \end{align*}.
A. \begin{pmatrix} 2 \ 2 \end{pmatrix}
B. \begin{pmatrix} 1 \ 3 \end{pmatrix}
C. \begin{pmatrix} 3 \ 1 \end{pmatrix}
D. \begin{pmatrix} 4 \ 0 \end{pmatrix}
Question 14
Find the sum of the first 8 terms of the arithmetic series with first term 2 and common difference 3.
A. 64
B. 72
C. 80
D. 88
Question 15
Find the sum of the first 10 terms of the geometric series with first term 3 and common ratio 2.
A. 1215
B. 2047
C. 4095
D. 8191

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