POST UTME IMS U 2022 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
If \( \sin^2 x + \cos^2 x = 1 \), find \( \tan^2 x \).
A. 1
B. 0
C. -1
D. \frac{1}{2}
Question 2
Let \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} 1 \ -2 \end{pmatrix} \). Find the projection of ( mathbf{b} ) onto ( mathbf{a} ) u\sing the formula \( mathrm{proj}_{mathbf{a}} mathbf{b} = \frac{mathbf{a} cdot mathbf{b}}{|mathbf{a}|^2} mathbf{a} \).
A. 0.8
B. 1.2
C. 1.5
D. 2.0
Question 3
Solve the trigonometric equation \( \sin^2 x + \cos^2 x = 1 \).
A. x = 0
B. x = 90
C. x = 180
D. x = 270
Question 4
Let ( f(x) = \frac{x^2 - 4}{x^2 - 2x + 1} ). Find the vertical asymptote of ( f(x) ).
A. x = 2
B. x = 1
C. x = -1
D. x = -2
Question 5
Find the derivative of the function ( f(x) = x^3 - 2x^2 + x - 1 ) u\sing the power rule.
A. f'(x) = 3x^2 - 4x + 1
B. f'(x) = 3x^2 - 4x - 1
C. f'(x) = 3x^2 + 4x - 1
D. f'(x) = 3x^2 + 4x + 1
Question 6
Let X be a random variable with probability density function ( f(x) = egin{cases} 2x, & 0 leq x leq 1 \ 0, & \text{otherwise} \end{cases} ). Find the probability that X is greater than 0.5.
A. \( \frac{1}{2} \)
B. \( \frac{3}{4} \)
C. \( \frac{5}{8} \)
D. \( \frac{7}{16} \)
Question 7
Solve the inequality \( \frac{x}{x-1} > 0 \) for ( x in mathbb{R} setminus {1} ).
A. \( -\infty, 0 \) \cup \( 1, \infty \)
B. \( -\infty, 1 \) \cup \( 1, \infty \)
C. \( -\infty, 0 \) \cup \( 1, \infty \)
D. \( -\infty, 0 \) \cup (0, 1)
Question 8
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 - 2
Question 9
Solve the system of equations \( x + y = 2 \) and \( xy = 1 \).
A. (1, 1)
B. \( 1, -1 \)
C. \( -1, 1 \)
D. \( -1, -1 \)
Question 10
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 = 16
C. \( x + 3 \)^2 + \( y - 2 \)^2 = 16
D. \( x - 3 \)^2 + \( y + 2 \)^2 = 16
Question 11
A random variable X has a probability distribution given by P\( X = 1 \) = 0.4, P\( X = 2 \) = 0.3, P\( X = 3 \) = 0.2, and P\( X = 4 \) = 0.1. If two indep\endent random variables X and Y have the same probability distribution, what is the probability that X + Y = 5?
A. 0.1
B. 0.2
C. 0.3
D. 0.4
Question 12
Find the area under the curve \( y = \frac{1}{x^2} \) from \( x = 1 \) to \( x = 2 \).
A. 0.5
B. 1
C. 1.5
D. 2
Question 13
A die is rolled twice. What is the probability that the sum of the two numbers is 7?
A. \( \frac{1}{6} \)
B. \( \frac{1}{3} \)
C. \( \frac{1}{2} \)
D. \( \frac{2}{3} \)
Question 14
Find the sum of the infinite geometric series \sum_{n=1}^\infty \frac{2}{3^n}.
A. 1
B. 2
C. 3
D. 4
Question 15
Find the derivative of the function ( f(x) = x^3 - 2x^2 + 3x - 1 ).
A. 3x^2 - 4x + 3
B. 3x^2 - 4x + 1
C. 3x^2 - 4x - 1
D. 3x^2 - 4x - 3

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