POST UTME LEAD CITY UNIVERSITY 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the determinant of the matrix [ egin{pmatrix} 2 & 3 & 1 \ 4 & 2 & 3 \ 1 & 2 & 4 \end{pmatrix} ].
A. 4
B. -2
C. 6
D. 8
Question 2
A random experiment consists of rolling a fair six-sided die. If the number rolled is even, the experiment is repeated. If the number rolled is odd, the experiment \ends. Find the probability that the experiment will \end on the third roll.
A. \( \frac{1}{2} \)
B. \( \frac{1}{4} \)
C. \( \frac{1}{6} \)
D. \( \frac{1}{8} \)
Question 3
Find the sum of the first 10 terms of the geometric series \( 2x^2 + 4x^3 + 8x^4 + ldots \).
A. \( 2048x^{20} \)
B. \( 1024x^{20} \)
C. \( 512x^{20} \)
D. \( 256x^{20} \)
Question 4
A set of exam scores has a mean of 75 and a s\tandard deviation of 10. Find the z-score of a score of 90.
A. \( \frac{90 - 75}{10} \)
B. \( \frac{75 - 90}{10} \)
C. \( \frac{90 - 75}{10} + 1 \)
D. \( \frac{75 - 90}{10} - 1 \)
Question 5
Find the derivative of the function ( f(x) = 3x^2 \sin x ) u\sing the product rule.
A. \( 6x \sin x + 3x^2 \cos x \)
B. \( 3x^2 \cos x + 6x \sin x \)
C. \( 6x^2 \sin x + 3x \cos x \)
D. \( 3x^2 \sin x + 6x \cos x \)
Question 6
Find the area of the triangle with vertices ( A(1,2) ), ( B(3,4) ), and ( C(2,1) ).
A. ( 5 )
B. ( 10 )
C. ( 15 )
D. ( 20 )
Question 7
A rec\tangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. Find the volume of the prism.
A. \( 6 \times 4 \times 3 \)
B. \( 6 + 4 + 3 \)
C. \( 6 \times 4 + 6 \times 3 + 4 \times 3 \)
D. \( 6 \times 4 \times 3 \)
Question 8
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 4 \) from \( x = 0 \) to \( x = 2 \).
A. 10
B. 12
C. 14
D. 16
Question 9
Find the equation of the circle with centre at ((2,3)) and radius (5).
A. \( x-2 \ \)^2 + \( y-3 \)^2 = 25 )
B. \( x+2 \ \)^2 + \( y-3 \)^2 = 25 )
C. \( x-2 \ \)^2 + \( y+3 \)^2 = 25 )
D. \( x+2 \ \)^2 + \( y+3 \)^2 = 25 )
Question 10
If \( y = \frac{1}{x} \), find \( \frac{dy}{dx} \) at \( x = 2 \).
A. \( -\frac{1}{4} \)
B. \( \frac{1}{4} \)
C. \( -\frac{1}{2} \)
D. \( \frac{1}{2} \)
Question 11
Solve the system of equations u\sing matrices: [ egin{cases} 2x + 3y = 7 \ x - 2y = -3 \end{cases} ]
A. \( x = 1, y = 2 \)
B. \( x = 2, y = 1 \)
C. \( x = 3, y = 4 \)
D. \( x = 4, y = 3 \)
Question 12
A matrix A has the following form: [ A = egin{bmatrix} 2 & 1 & 3 \ 4 & 3 & 5 \ 6 & 2 & 1 \end{bmatrix} ]. Find the determinant of A.
A. 0
B. 1
C. 2
D. 3
Question 13
Find the derivative of the function ( f(x) = 3x^2 + 2x - 5 ).
A. 6x + 2
B. 3x^2 + 2
C. 6x - 2
D. 3x^2 - 2
Question 14
A fair six-sided die is rolled. What is the probability that the number rolled is greater than 4?
A. \( \frac{1}{6} \)
B. \( \frac{1}{3} \)
C. \( \frac{2}{3} \)
D. \( \frac{5}{6} \)
Question 15
A coin is tossed three times. What is the probability that at least two of the tosses result in heads?
A. 1/4
B. 1/2
C. 3/4
D. 7/8

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