POST UTME LEAD CITY UNIVERSITY 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Determine the value of k in the polynomial equation \( x^3 + 2x^2 - 7x - 12 = k\( x + 3 \)\( x - 1 \ \) ).
A. -3
B. -1
C. 1
D. 3
Question 2
Find the area under the curve \( y = \frac{1}{2}x^2 + 2x - 3 \) from \( x = 0 \) to \( x = 4 \).
A. 32
B. 40
C. 48
D. 56
Question 3
Let ( S ) be the set of all ordered pairs ( (x, y) ) such that \( x^2 + y^2 leq 4 \). Find the number of elements in the set ( S ).
A. 4
B. 6
C. 8
D. 10
Question 4
Solve the inequality 2x^2 + 5x - 3 > 0.
A. x < -1 or x > 3/2
B. x > -1 or x < 3/2
C. x < 3/2 or x > -1
D. x > 3/2 or x < -1
Question 5
Solve the system of equations x + y = 4 and x - y = 2.
A. x = 3, y = 1
B. x = 1, y = 3
C. x = 2, y = 2
D. x = 4, y = 0
Question 6
A line passes through the points ( (1, 2) ) and ( (3, 4) ). Find the equation of the line in slope-intercept form.
A. \( y = x + 1 \)
B. \( y = x - 1 \)
C. \( y = -x + 3 \)
D. \( y = x - 3 \)
Question 7
Solve the equation \( x^2 + 4x + 4 = 0 \) u\sing the quadratic formula.
A. \( x = -2 \pm 2i \)
B. \( x = -1 \pm i \)
C. \( x = -2 \pm i \)
D. \( x = -1 \pm 2i \)
Question 8
A polynomial ( p(x) ) is defined by ( p(x) = x^3 + 2x^2 - 5x + 1 ). Find the value of \( p\( -1 \ \) ).
A. -3
B. -2
C. -1
D. 0
Question 9
Solve the inequality: \( 2x - 5 > 3x + 2 \).
A. \( x < -\frac{7}{2} \)
B. \( x > -\frac{7}{2} \)
C. \( x < \frac{7}{2} \)
D. \( x > \frac{7}{2} \)
Question 10
A histogram is shown below. What is the mean of the data set?
A. 10
B. 15
C. 20
D. 25
Question 11
Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 4 \ 5 \end{pmatrix} \). Find the magnitude of the vector \( mathbf{a} + mathbf{b} \).
A. 5
B. 6
C. 7
D. 8
Question 12
A histogram of exam scores has a mean of 70 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 80?
A. 0.135
B. 0.25
C. 0.5
D. 0.75
Question 13
Simplify the expression: \( \frac{2x^2 + 5x - 3}{x + 3} \)
A. 2x - 1
B. 2x + 1
C. x + 2
D. x - 2
Question 14
A sequence is defined by \( a_n = \frac{1}{n} + \frac{1}{n+1} \) for ( n geq 1 ). Find the sum of the first 5 terms of the sequence.
A. 1.5
B. 2.5
C. 3.5
D. 4.5
Question 15
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 = 25 \)
C. \( x - 2 \)^2 + \( y - 3 \)^2 = 36 \)
D. \( x - 2 \)^2 + \( y - 3 \)^2 = 49 \)

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