POST UTME COVENANT UNIVERSITY 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
In a geometric sequence with first term $a$ and common ratio $r$, find the sum of the first 5 terms if $a=2$ and $r=3$.
A. \( 2\( 3^0+3^1+3^2+3^3+3^4 \ \) )
B. \( 2\( 1+3+9+27+81 \ \) )
C. \( 2\( 1+3+9+27+81 \ \) )
D. \( 2\( 1+3+9+27+81 \ \) )
Question 2
Find the area under the curve \( y = \frac{1}{2}x^2 + 2x - 3 \) from \( x = 0 \) to \( x = 4 \).
A. 24
B. 36
C. 48
D. 60
Question 3
Solve the equation $\frac{dy}{dx} = \frac{x^2 + 1}{x^2 - 1}$ for $y$.
A. y = \frac{1}{2} \log \( x^2 - 1 \) + C
B. y = \frac{1}{2} \log \( x^2 + 1 \) + C
C. y = \frac{1}{2} \log \( x^2 - 1 \) - C
D. y = \frac{1}{2} \log \( x^2 + 1 \) - C
Question 4
In a circle of radius 8cm, a chord of length 12cm subt\ends an angle of 60° at the centre. Find the area of the sector formed by the chord and the radii to the \ends of the chord.
A. 48π cm^2
B. 60π cm^2
C. 72π cm^2
D. 80π cm^2
Question 5
Find the derivative of the function f(x) = 3x^2 + 2x - 5.
A. 6x + 2
B. 3x + 1
C. 2x - 3
D. x^2 + 1
Question 6
The sequence $\{a_n\}$ is defined by $a_n = 2n + 1$ for $n = 1, 2, 3, \dots$. Find the sum of the first five terms of the sequence.
A. 30
B. 35
C. 40
D. 45
Question 7
Find the value of $x$ in the equation $\log_{10} \( x^2 \) = 4$.
A. 2
B. 4
C. 8
D. 16
Question 8
Solve the equation \( x^2 + 4x + 4 = 0 \) u\sing the quadratic formula.
A. \frac{-4 \pm \sqrt{16 - 16}}{2}
B. \frac{-4 \pm \sqrt{16 + 16}}{2}
C. \frac{-4 \pm \sqrt{16 - 4}}{2}
D. \frac{-4 \pm \sqrt{16 + 4}}{2}
Question 9
Solve the system of linear equations u\sing matrices: \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 7 \ 10 \end{bmatrix} \).
A. [1, 2]
B. [2, 3]
C. [3, 4]
D. [4, 5]
Question 10
Find the sum of the infinite geometric series \( 1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + ldots \).
A. 2
B. 3
C. 4
D. 5
Question 11
Simplify the expression \( \sqrt{16}+\sqrt{25}+\sqrt{36} \).
A. \( 4+5+6 \)
B. \( 4+5+6 \)
C. \( 4+5+6 \)
D. \( 4+5+6 \)
Question 12
Let A be a 3x3 matrix with determinant 6. If A is multiplied by a scalar k, what is the determinant of kA?
A. 6k^3
B. 6k
C. 6
D. 6k^2
Question 13
Find the equation of the line pas\sing through the points ( (2, 3) ) and ( (4, 5) ).
A. y = 2x - 1
B. y = 2x + 1
C. y = 3x - 2
D. y = 3x + 2
Question 14
A set $S$ contains the elements $\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$. If $T$ is a subset of $S$ such that $T$ contains the elements of $S$ that are greater than $5$, what is the number of elements in $T$?
A. 5
B. 6
C. 7
D. 8
Question 15
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 40
B. 50
C. 60
D. 70

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