POST UTME LEAD CITY UNIVERSITY 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the sum of the first 10 terms of the geometric series with first term 2 and common ratio 3/2.
A. 2 + 3 + 9/2 + 27/4 + 81/8 + 243/16 + 729/32 + 2187/64 + 6561/128 + 19683/256
B. 2 + 3 + 9/2 + 27/4 + 81/8 + 243/16 + 729/32 + 2187/64 + 6561/128 + 19683/256 + 59049/512
C. 2 + 3 + 9/2 + 27/4 + 81/8 + 243/16 + 729/32 + 2187/64 + 6561/128 + 19683/256 + 177147/1024
D. 2 + 3 + 9/2 + 27/4 + 81/8 + 243/16 + 729/32 + 2187/64 + 6561/128 + 19683/256 + 531441/2048
Question 2
A quadratic equation \( ax^2 + bx + c = 0 \) has roots \( x = 1 \) and \( x = 2 \). Find the value of ( a ).
A. 1
B. 2
C. 3
D. 4
Question 3
Solve the inequality \( \frac{x}{x-2} > 1 \) for \( x > 2 \).
A. \( x > 4 \)
B. \( x < 4 \)
C. \( x = 4 \)
D. ( x leq 4 )
Question 4
A die is rolled 5 times. What is the probability that the sum of the 5 rolls is 20?
A. \frac{1}{6}
B. \frac{1}{12}
C. \frac{1}{24}
D. \frac{1}{36}
Question 5
Solve for x in the equation \( \sin^2 x + \cos^2 x = 1 \) u\sing the identity \( \sin^2 x + \cos^2 x = 1 \).
A. \( x = \frac{pi}{2} \)
B. \( x = \frac{pi}{4} \)
C. \( x = \frac{3pi}{4} \)
D. \( x = \frac{5pi}{4} \)
Question 6
Solve the equation \frac{x}{2} + 3 = 7.
A. 4
B. 6
C. 8
D. 10
Question 7
Solve the polynomial equation \( x^3 - 2x^2 + 3x - 4 = 0 \) u\sing synthetic division.
A. \( x = 1 \)
B. \( x = 2 \)
C. \( x = 3 \)
D. \( x = 4 \)
Question 8
Find the equation of the line pas\sing through the points (2, 3) and (4, 5).
Question 9
In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the acute angles is 30°. Find the length of the side opposite the 30° angle.
A. 5 cm
B. 7.07 cm
C. 10 cm
D. 15 cm
Question 10
Find the determinant of the matrix \( egin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} \).
A. ( 0 )
B. ( 1 )
C. ( 2 )
D. ( 3 )
Question 11
A polynomial ( p(x) ) is defined by ( p(x) = x^3 - 6x^2 + 11x - 6 ). Find the value of ( p(2) ).
A. 0
B. 1
C. 2
D. 3
Question 12
A bakery sells 250 loaves of bread per day. If they make a profit of ₦5 per loaf, how much profit do they make in a day?
A. ₦1250
B. ₦12500
C. ₦125000
D. ₦1250000
Question 13
Find the area of the triangle with vertices (0, 0), (3, 0), and (0, 4).
A. 6
B. 12
C. 18
D. 24
Question 14
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000
Question 15
Find the area under the curve \( y = \frac{1}{x^2} \) from \( x = 1 \) to \( x = 2 \).
A. 0.083
B. 0.0833
C. 0.08333
D. 0.083333

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