POST UTME LEAD CITY UNIVERSITY 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A circle has equation \( x - 2 \ \)^2 + \( y - 3 \)^2 = 4 ). Find the equation of the \tangent line at the point ( (3, 1) ).
A. \( y = -x + 5 \)
B. \( y = x + 1 \)
C. \( y = -x - 1 \)
D. \( y = x - 3 \)
Question 2
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 3
A curve is defined by the equation \( y = \frac{1}{x} \). Find the equation of the \tangent line to the curve at the point (1, 1).
A. \( y = x - 1 \)
B. \( y = x + 1 \)
C. \( y = -x + 1 \)
D. \( y = x - 2 \)
Question 4
Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 1 \ -2 \end{pmatrix} \). Find the vector \( mathbf{a} \times mathbf{b} \) u\sing the determinant method.
A. \( egin{pmatrix} 8 \ -4 \end{pmatrix} \)
B. \( egin{pmatrix} -8 \ 4 \end{pmatrix} \)
C. \( egin{pmatrix} 4 \ -2 \end{pmatrix} \)
D. \( egin{pmatrix} -4 \ 2 \end{pmatrix} \)
Question 5
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 6
A random variable ( X ) has probability density function ( f(x) = egin{cases} 2x & 0 leq x leq 1 \ 0 & \text{otherwise} \end{cases} ). Find ( P(0.5 leq X leq 0.8) ).
A. ( 0.4 )
B. ( 0.6 )
C. ( 0.8 )
D. ( 1.0 )
Question 7
Simplify the expression: \( \frac{2x^2 + 5x - 3}{x + 3} \)
A. 2x - 1
B. 2x + 1
C. x + 2
D. x - 2
Question 8
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 9
A set 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 10
Find the area under the curve y = 2x^2 + 3x - 1 from x = 0 to x = 2.
A. 14
B. 16
C. 18
D. 20
Question 11
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 12
Solve for x in the equation \( 2^x + 2^{x+1} = 3 cdot 2^{x+1} \).
A. -1
B. 0
C. 1
D. 2
Question 13
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 14
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -1 \) or \( x > \frac{3}{2} \)
B. \( x < -1 \) or \( x < \frac{3}{2} \)
C. \( x > -1 \) or \( x > \frac{3}{2} \)
D. \( x > -1 \) or \( x < \frac{3}{2} \)
Question 15
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 4 \).
A. 64
B. 32
C. 16
D. 8

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