POST UTME CALEB UNIVERSITY 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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. \( egin{pmatrix} 6 \ -2 \end{pmatrix} \)
B. \( egin{pmatrix} -6 \ 2 \end{pmatrix} \)
C. \( egin{pmatrix} 0 \ 0 \end{pmatrix} \)
D. \( egin{pmatrix} 3 \ -6 \end{pmatrix} \)
Question 2
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 3
Find the equation of the circle with center ( C(2, 3) ) and radius ( 4 ).
A. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )
B. \( x + 2 \ \)^2 + \( y - 3 \)^2 = 16 )
C. \( x - 2 \ \)^2 + \( y + 3 \)^2 = 16 )
D. \( x + 2 \ \)^2 + \( y + 3 \)^2 = 16 )
Question 4
Solve the equation \frac{x^2-4x+4}{x^2-4x+3}=1.
A. x=1
B. x=2
C. x=3
D. x=4
Question 5
Find the volume of the solid formed by revolving the region bounded by the parabola \( y = x^2 \) and the line \( y = 4 \) about the x-axis.
A. \( \frac{32}{3} pi \)
B. \( \frac{64}{3} pi \)
C. \( \frac{128}{3} pi \)
D. \( \frac{256}{3} pi \)
Question 6
A sequence is defined by \( a_n = \frac{1}{n} + \frac{1}{n+1} \) for ( n in mathbb{N} ). Find the sum of the first 5 terms.
A. 1
B. 2
C. 3
D. 4
Question 7
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4 \)
B. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \)
C. \( \frac{1}{2} \times 4^3 + 3 \times 4^2 - 2 \times 4^2 \)
D. \( \frac{1}{2} \times 4^2 + 3 \times 4 - 2 \times 4 \)
Question 8
Find the determinant of the matrix \begin{bmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{bmatrix} u\sing the cofactor expansion method.
A. 0
B. 1
C. -1
D. 2
Question 9
A die is rolled twice. What is the probability that the sum of the two numbers shown is 7?
A. \frac{1}{6}
B. \frac{1}{3}
C. \frac{1}{2}
D. \frac{2}{3}
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=4
C. \( x-2 \)^2+\( y-3 \)^2=9
D. \( x-2 \)^2+\( y-3 \)^2=25
Question 11
Solve the system of equations \\begin{align*} x + y &= 2 \\ x - y &= 1 \\end{align*} u\sing matrices.
A. x = 1, y = 1
B. x = 2, y = 0
C. x = 0, y = 2
D. x = 1, y = 2
Question 12
A binary number 1011 is converted to decimal. What is the decimal equivalent?
A. 10
B. 11
C. 12
D. 13
Question 13
A quadratic equation is given by \[x^2 + 4x + 4 = 0\]. Solve for x.
A. \[x = -2\]
B. \[x = -1\]
C. \[x = 0\]
D. \[x = 1\]
Question 14
A particle moves along the curve y=x^2+2x+1. Find the equation of the \tangent line at the point where x=1.
A. y=x+3
B. y=x+2
C. y=x-1
D. y=x-2
Question 15
A vector ( mathbf{a} ) has magnitude 5 and direction \( 60^circ \) counterclockwise from the positive x-axis. Find the vector ( mathbf{a} ).
A. \( 5mathbf{i} + 5mathbf{j} \)
B. \( 5mathbf{i} - 5mathbf{j} \)
C. \( -5mathbf{i} + 5mathbf{j} \)
D. \( -5mathbf{i} - 5mathbf{j} \)

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: