POST UTME UNIPORT 2024 Mathematics | Objective

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Question 1
Find the equation of the circle pas\sing through the points (2, 3), (4, 5), and \( -1, 1 \).
A. \left\( x - 1 \right \)^2 + \left\( y - 1 \right \)^2 = 10
B. \left\( x + 1 \right \)^2 + \left\( y - 1 \right \)^2 = 10
C. \left\( x - 1 \right \)^2 + \left\( y + 1 \right \)^2 = 10
D. \left\( x + 1 \right \)^2 + \left\( y + 1 \right \)^2 = 10
Question 2
Let $A = \begin{pmatrix} 1 & 2 \ 3 & 4 \end{pmatrix}$ and $B = \begin{pmatrix} 5 & 6 \ 7 & 8 \end{pmatrix}$. Find the product $AB$.
A. $\begin{pmatrix} 19 & 22 \ 43 & 50 \end{pmatrix}$
B. $\begin{pmatrix} 23 & 26 \ 47 & 54 \end{pmatrix}$
C. $\begin{pmatrix} 21 & 24 \ 45 & 52 \end{pmatrix}$
D. $\begin{pmatrix} 25 & 28 \ 49 & 56 \end{pmatrix}$
Question 3
A quadratic equation has roots at x = 2 and x = 4. What is the equation of the axis of symmetry?
A. x = 3
B. x = 2
C. x = 4
D. x = 1
Question 4
Find the value of $k$ such that the polynomial $x^3 + kx^2 - 2x + 1$ has a root at $x = 1$.
A. -1
B. 0
C. 1
D. 2
Question 5
Simplify the expression \( \sqrt[3]{64x^3y^3} \).
A. 4x^1y^1
B. 8x^1y^1
C. 16x^1y^1
D. 32x^1y^1
Question 6
If ( f(x) = \frac{x^2 - 4}{x - 2} ), find ( f'(x) ) u\sing the chain rule.
A. ( f'(x) = \frac{x^2 - 4}{\( x - 2 \)^2} )
B. ( f'(x) = \frac{2x}{\( x - 2 \)^2} )
C. ( f'(x) = \frac{2x - 4}{\( x - 2 \)^2} )
D. ( f'(x) = \frac{2x + 4}{\( x - 2 \)^2} )
Question 7
A rec\tangular prism has a length of 8 cm, a width of 5 cm, and a height of 3 cm. What is its surface area?
A. 120 cm²
B. 150 cm²
C. 180 cm²
D. 200 cm²
Question 8
Solve the inequality \frac{x + 2}{x - 1} > 0.
A. \text{Solution: } x < -2 \text{ or } x > 1
B. \text{Solution: } x < -2 \text{ or } x < 1
C. \text{Solution: } x > -2 \text{ or } x > 1
D. \text{Solution: } x < -2 \text{ or } x < 1
Question 9
Find the derivative of the function f(x) = 3x^2 + 2x - 5.
A. 6x + 2
B. 6x - 2
C. 3x + 2
D. 3x - 2
Question 10
Find the derivative of the function \( y = \sqrt{2x + 1} \) u\sing the chain rule.
A. 1/\( 2√\( 2x + 1 \ \))
B. 1/\( 2√\( 2x + 1 \ \)) * \( 2x + 1 \)
C. 1/\( 2√\( 2x + 1 \ \)) * \( 2x + 1 \)^2
D. 1/\( 2√\( 2x + 1 \ \)) * \( 2x + 1 \)^3
Question 11
If ( f(x) = 2x^3 - 5x^2 + x - 1 ), find the derivative of ( f(x) ) u\sing the power rule.
A. ( f'(x) = 6x^2 - 10x + 1 )
B. ( f'(x) = 6x^2 - 10x - 1 )
C. ( f'(x) = 6x^2 - 10x + 2 )
D. ( f'(x) = 6x^2 - 10x - 2 )
Question 12
A fair six-sided die is rolled. Find the probability that the number rolled is greater than 4.
A. \frac{1}{6}
B. \frac{2}{6}
C. \frac{3}{6}
D. \frac{4}{6}
Question 13
A random variable X has a probability distribution given by P\( X = 1 \) = 0.4, P\( X = 2 \) = 0.3, P\( X = 3 \) = 0.2, and P\( X = 4 \) = 0.1. What is the expected value of X?
A. 1.5
B. 2.0
C. 2.5
D. 3.0
Question 14
Determine 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 6 cm.
A. 100π cm³
B. 150π cm³
C. 200π cm³
D. 250π cm³
Question 15
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

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