POST UTME UNIPORT 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A circle passes through the points (2, 3), (4, 1), and (6, 5). Find the equation of the circle.
A. x^2 + y^2 - 4x - 2y - 5 = 0
B. x^2 + y^2 + 4x + 2y - 5 = 0
C. x^2 + y^2 - 6x - 4y + 11 = 0
D. x^2 + y^2 + 6x + 4y - 11 = 0
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 \( \text{proj}_mathbf{a}mathbf{b} = \frac{mathbf{a} cdot mathbf{b}}{|mathbf{a}|^2} mathbf{a} \).
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{2}{13} \end{pmatrix}
Question 3
Solve for ( x ) in the equation \( \log_{10} \( x^2 \ \) = 4 ).
A. \( x = 10^4 \)
B. \( x = 10^2 \)
C. \( x = 10^{-2} \)
D. \( x = 10^{-4} \)
Question 4
A geometric progression is defined as \( a_n = 2a_{n-1} + 1 \) for \( n = 2, 3, 4, ldots \) with \( a_1 = 2 \). Find the sum of the first five terms of this progression.
A. 63
B. 62
C. 61
D. 60
Question 5
A random variable X has a probability distribution given by ( P(X) = egin{cases} 0.2 & \text{if } X = 1 \ 0.3 & \text{if } X = 2 \ 0.5 & \text{if } X = 3 \end{cases} ). Find the expected value of X.
A. 1.5
B. 2
C. 2.5
D. 3
Question 6
Find the determinant of the matrix \( egin{bmatrix} 2 & 1 & 3 \ 4 & 2 & 5 \ 6 & 3 & 7 \end{bmatrix} \).
A. -1
B. 0
C. 1
D. 2
Question 7
Solve the system of equations \( egin{cases} x + y = 4 \ 2x - 3y = -2 \end{cases} \).
A. \( x = 2, y = 2 \)
B. \( x = 3, y = 1 \)
C. \( x = 4, y = 0 \)
D. \( x = 5, y = -1 \)
Question 8
Find the equation of the circle with center ( (2, 3) ) and radius ( 4 ).
A. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )
B. \( x - 3 \ \)^2 + \( y - 2 \)^2 = 16 )
C. \( x - 4 \ \)^2 + \( y - 3 \)^2 = 16 )
D. \( x - 2 \ \)^2 + \( y - 4 \)^2 = 16 )
Question 9
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 10
Find the area under the curve \( y = \frac{1}{x^2} \) from \( x = 1 \) to \( x = 2 \).
A. \( \frac{1}{2} \)
B. \( \frac{1}{3} \)
C. \( \frac{1}{4} \)
D. \( \frac{1}{5} \)
Question 11
In the diagram below, the line $AB$ has a slope of $2$ and passes through the point $(1,3)$. Find the equation of the line in the form $y = mx + c$.
A. y = 2x + 1
B. y = 2x - 1
C. y = 2x + 2
D. y = 2x - 2
Question 12
A sequence is defined by the recurrence relation \( a_n = 2a_{n-1} + 1 \) with initial term \( a_1 = 3 \). Find the 5th term of the sequence.
A. 31
B. 33
C. 35
D. 37
Question 13
Find the equation of the circle with center ( (2, 3) ) and radius 4.
A. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )
B. \( x - 3 \ \)^2 + \( y - 2 \)^2 = 16 )
C. \( x - 4 \ \)^2 + \( y - 3 \)^2 = 16 )
D. \( x - 2 \ \)^2 + \( y - 4 \)^2 = 16 )
Question 14
Solve for x in the equation \( 2^x + 2^{x+2} = 3 cdot 2^{x+1} \).
A. \( x = -1 \)
B. \( x = 0 \)
C. \( x = 1 \)
D. \( x = 2 \)
Question 15
Find the volume of the frustum of a cone with height 6 cm, lower base radius 4 cm, and upper base radius 2 cm.
A. 48\pi cm^3
B. 64\pi cm^3
C. 80\pi cm^3
D. 96\pi cm^3

Master the Exam!

You've seen a preview, but there are thousands more questions plus AI tutor to break down complex solutions.

Unlock Full Access Available for Android & Windows
Help others prepare! Share this practice hub: