POST UTME IMS U 2025 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{1}{2} \)
B. ( 3 )
C. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \)
D. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 + \frac{1}{2} \)
Question 2
Find the mean of the data set ( { 2, 4, 6, 8, 10 } ).
A. 5
B. 6
C. 7
D. 8
Question 3
Find the value of \sin 75^\circ.
A. \frac{\sqrt{3}}{2}
B. \frac{\sqrt{5}}{2}
C. \frac{\sqrt{6}}{2}
D. \frac{\sqrt{10}}{2}
Question 4
Let ( f(x) = x^2 - 4x + 3 ). Find the equation of the \tangent line to the graph of ( f(x) ) at the point ( (1, f(1)) ).
A. y - 1 = 2\( x - 1 \)
B. y - 1 = -2\( x - 1 \)
C. y - 1 = x - 1
D. y - 1 = -x + 1
Question 5
In the diagram below, find the equation of the circle with center ( C ) and radius ( 4 ) units.
A. \( x^2 + y^2 = 16 \)
B. \( x^2 + y^2 = 4 \)
C. \( x^2 + y^2 = 8 \)
D. \( x^2 + y^2 = 2 \)
Question 6
Let X be a random variable with probability density function f(x) = \( \frac{1}{2}e^{-|x|} \) for -∞ < x < ∞. Find the probability that X is greater than 1.
A. 0.5
B. 0.6
C. 0.7
D. 0.8
Question 7
A sequence is defined by the recurrence relation \( a_n = 2a_{n-1} + 1 \) with initial term \( a_1 = 3 \). Find the value of \( a_{10} \).
A. 1023
B. 1024
C. 1025
D. 1026
Question 8
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 2 \) u\sing integration.
A. 4
B. 6
C. 8
D. 10
Question 9
Find the volume of the frustum of a cone with height 8 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 64\pi\text{ cm}^3
B. 128\pi\text{ cm}^3
C. 192\pi\text{ cm}^3
D. 256\pi\text{ cm}^3
Question 10
Solve the quadratic equation \( x^2 + 5x + 6 = 0 \).
A. \( x = -2 \) or \( x = -3 \)
B. \( x = -1 \) or \( x = -6 \)
C. \( x = 2 \) or \( x = 3 \)
D. \( x = 1 \) or \( x = 4 \)
Question 11
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. \begin{pmatrix} \frac{7}{13} \\ \frac{12}{13} \end{pmatrix}
B. \begin{pmatrix} \frac{1}{13} \\ \frac{2}{13} \end{pmatrix}
C. \begin{pmatrix} \frac{2}{13} \\ \frac{3}{13} \end{pmatrix}
D. \begin{pmatrix} \frac{3}{13} \\ \frac{4}{13} \end{pmatrix}
Question 12
Find the derivative of the function ( f(x) = \frac{1}{x^2 + 1} ) u\sing the chain rule.
A. \( \frac{-2x}{\( x^2 + 1 \ \)^2} )
B. \( \frac{2x}{\( x^2 + 1 \ \)^2} )
C. \( \frac{2}{\( x^2 + 1 \ \)^2} )
D. \( \frac{-2}{\( x^2 + 1 \ \)^2} )
Question 13
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 40
B. 42
C. 44
D. 46
Question 14
A set ( A ) contains the elements ( { 1, 2, 3, 4, 5 } ). Find the number of subsets of ( A ) that contain exactly two elements.
A. 10
B. 15
C. 20
D. 25
Question 15
Solve for x in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. 10
B. 100
C. 1000
D. 10000

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