POST UTME CALEB UNIVERSITY 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
The sum of the first 10 terms of the arithmetic progression ( 1, 3, 5, ldots ) is ( 100 ). Find the first term.
A. ( 1 )
B. ( 2 )
C. ( 3 )
D. ( 4 )
Question 2
A vector ( vec{a} ) has a magnitude of 5 units and makes an angle of 60° with the positive x-axis. Find the x-component of the vector.
A. 2.5
B. 3.5
C. 4.5
D. 5.5
Question 3
If \overrightarrow{a} = \begin{pmatrix} 2 \ 3 \ 4 \end{pmatrix} and \overrightarrow{b} = \begin{pmatrix} -1 \ 2 \ 1 \end{pmatrix}, find the cross product \overrightarrow{a} \times \overrightarrow{b}.
A. \begin{pmatrix} 5 \ -11 \ -1 \end{pmatrix}
B. \begin{pmatrix} -5 \ 11 \ 1 \end{pmatrix}
C. \begin{pmatrix} 5 \ 11 \ 1 \end{pmatrix}
D. \begin{pmatrix} -5 \ -11 \ 1 \end{pmatrix}
Question 4
Simplify \( \frac{3x^2 + 2x - 1}{2x^2 - 5x + 1} \).
A. \( \frac{3x + 1}{2x - 1} \)
B. \( \frac{3x - 1}{2x + 1} \)
C. \( \frac{3x + 1}{2x + 1} \)
D. \( \frac{3x - 1}{2x - 1} \)
Question 5
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. 64\pi
B. 96\pi
C. 128\pi
D. 192\pi
Question 6
Solve for ( x ) in the equation \( 2^x + 3^x = 5^x \).
A. \( x = 1 \)
B. \( x = 2 \)
C. \( x = 3 \)
D. \( x = 4 \)
Question 7
Find the determinant of the matrix \( egin{bmatrix} 2 & 1 \ 4 & 3 \end{bmatrix} \).
A. 1
B. 2
C. 3
D. 4
Question 8
Let \( A = { 1, 2, 3, 4, 5 } \) and \( B = { 2, 4, 6, 8, 10 } \). Find ( A cap B ).
A. ( { 1, 2, 3, 4, 5 } )
B. ( { 2, 4, 6, 8, 10 } )
C. ( { 1, 2, 3, 4, 5, 6, 8, 10 } )
D. ( { 2, 4 } )
Question 9
Find the area under the curve y = x^2 from x = 0 to x = 4.
A. 64
B. 128
C. 192
D. 256
Question 10
Solve the inequality \( 2x^2 + 5x - 3 \geq 0 \) u\sing the quadratic formula and graphing.
A. \[ x \leq -1 \text{ or } x \geq \frac{3}{2} \]
B. \[ x \leq -1 \text{ or } x \leq \frac{3}{2} \]
C. \[ x \geq -1 \text{ or } x \geq \frac{3}{2} \]
D. \[ x \geq -1 \text{ or } x \leq \frac{3}{2} \]
Question 11
Solve for x in the equation \( 2x^2 + 5x - 3 = 0 \).
A. \( x = -1 \)
B. \( x = 2 \)
C. \( x = -3 \)
D. \( x = 1 \)
Question 12
Solve \( \log_{10} \( x^2 \ \) = 4 ).
A. \( x = 10^2 \)
B. \( x = 10^4 \)
C. \( x = 10^{-2} \)
D. \( x = 10^{-4} \)
Question 13
Solve the equation \( x^2 - 6x + 8 = 0 \).
A. (2, 4)
B. (3, 2)
C. (4, 3)
D. (2, 2)
Question 14
Find the sum of the first 10 terms of the geometric series \( 2 + 6 + 18 + ldots \).
A. 1950
B. 1960
C. 1970
D. 1980
Question 15
Solve the inequality $\left| x - 2 \right| \geq 3$.
A. $x \leq -1$ or $x \geq 5$
B. $x \leq 1$ or $x \geq 5$
C. $x \leq -1$ or $x \geq 2$
D. $x \leq 1$ or $x \geq 2$

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: