POST UTME LEAD CITY UNIVERSITY 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \).
A. \( x = 0 \)
B. \( x = \frac{pi}{2} \)
C. \( x = \frac{pi}{4} \)
D. \( x = \frac{3pi}{4} \)
Question 2
Find the value of x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 3
A random variable ( X ) has a probability distribution given by ( P(X) = egin{cases} 0.2 & \text{if } X = 1 \ 0.3 & \text{if } X = 2 \ 0.5 & \text{if } X = 3 \end{cases} ). Find the expected value of ( X ).
A. \( 1 \times 0.2 + 2 \times 0.3 + 3 \times 0.5 \)
B. \( 1 \times 0.3 + 2 \times 0.2 + 3 \times 0.5 \)
C. \( 1 \times 0.5 + 2 \times 0.3 + 3 \times 0.2 \)
D. \( 1 \times 0.5 + 2 \times 0.2 + 3 \times 0.3 \)
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 = 4
C. \( x - 2 \)^2 + \( y - 3 \)^2 = 9
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 25
Question 5
A matrix ( A ) is given by \( A = egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} \). Find the determinant of ( A ).
A. \( 1 \times 4 - 2 \times 3 \)
B. \( 1 \times 3 - 2 \times 4 \)
C. \( 2 \times 4 - 1 \times 3 \)
D. \( 2 \times 3 - 1 \times 4 \)
Question 6
Find the equation of the circle with center (2, 3) and radius 4.
A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 3 \)^2 + \( y - 2 \)^2 = 16
C. \( x - 4 \)^2 + \( y - 3 \)^2 = 16
D. \( x - 3 \)^2 + \( y - 4 \)^2 = 16
Question 7
Find the determinant of the matrix \[\begin{bmatrix} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{bmatrix}\].
A. 0
B. 1
C. -1
D. 2
Question 8
Find the derivative of ( 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 9
A right triangle has a hypotenuse of 10 cm and one leg of 6 cm. Find the length of the other leg.
A. 8
B. 6
C. 4
D. 2
Question 10
A rec\tangular box has dimensions (x), (2x), and (3x). Find the volume of the box.
A. \( 6x^3 \)
B. \( 12x^3 \)
C. \( 18x^3 \)
D. \( 24x^3 \)
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
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. x = -2
B. x = -1
C. x = 0
D. x = 1
Question 13
Solve the system of linear equations u\sing matrices:
A. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 3 \ 2 \end{bmatrix}
B. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 2 \ 3 \end{bmatrix}
C. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 1 \ 4 \end{bmatrix}
D. \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 4 \ 1 \end{bmatrix}
Question 14
Solve for y in the equation \( y = \frac{1}{2} \left\( \frac{1}{3} \right \ \)^x ).
A. 3
B. 6
C. 9
D. 12
Question 15
Find the area of the triangle with vertices ( A(1, 2) ), ( B(3, 4) ), and ( C(2, 1) ).
A. 5
B. 6
C. 7
D. 8

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