POST UTME COVENANT UNIVERSITY 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the system of linear equations u\sing matrices:\n\n\( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 7 \ 11 \end{bmatrix} \)
A. \( x = 3, y = 2 \)
B. \( x = 2, y = 3 \)
C. \( x = 1, y = 4 \)
D. \( x = 4, y = 1 \)
Question 2
A cylindrical \tank has a height of 10m and a radius of 4m. If the \tank is filled with water to a height of 6m, find the volume of water in the \tank.
A. ( 120pi ) m³
B. ( 240pi ) m³
C. ( 480pi ) m³
D. ( 960pi ) m³
Question 3
In a circle with center $O$ and radius $5$, a chord $AB$ is drawn such that $OA = 3$. Find the length of the chord $AB$.
A. \sqrt{91}
B. \sqrt{121}
C. \sqrt{169}
D. \sqrt{289}
Question 4
A sequence is defined by the recurrence relation $a_n = 2a_{n-1} + 1$, where $a_1 = 3$. Find the value of $a_{10}$.
A. 1023
B. 1024
C. 1025
D. 1026
Question 5
A circle has a diameter of 10 cm. What is the area of the circle?
A. 50\pi
B. 75\pi
C. 100\pi
D. 125\pi
Question 6
Find the derivative of the function ( f(x) = \sin^2 x ) u\sing the chain rule.
A. ( f'(x) = 2\sin x \cos x )
B. ( f'(x) = 2\sin x )
C. ( f'(x) = 2\cos x )
D. ( f'(x) = 2\sin^2 x )
Question 7
A right-angled triangle has sides of length $3$, $4$, and $5$. Find the area of the triangle.
A. 6
B. 12
C. 18
D. 24
Question 8
Solve the equation \( x^2 + 4x + 4 = 0 \).
A. \( x = -2 \)
B. \( x = -1 \)
C. \( x = 1 \)
D. \( x = 2 \)
Question 9
A set $S$ contains the elements ${1, 2, 3, 4, 5}$. Find the number of subsets of $S$ that contain exactly two elements.
A. 5
B. 10
C. 15
D. 20
Question 10
A line passes through the points (2, 3) and (4, 5). What is the equation of the line in slope-intercept form?
A. y = x + 1
B. y = x - 1
C. y = -x + 1
D. y = x + 2
Question 11
A rec\tangular prism has a length of 6 cm, a width of 4 cm, and a height of 3 cm. Find the volume of the prism.
A. 72 cm^3
B. 96 cm^3
C. 108 cm^3
D. 120 cm^3
Question 12
Differentiate the function ( f(x) = 3x^2 + 2x - 5 ) with respect to x.
A. f'(x) = 6x + 2
B. f'(x) = 6x - 2
C. f'(x) = 3x^2 + 2
D. f'(x) = 3x^2 - 2
Question 13
Find the equation of the line pas\sing through the points ( (1, 2) ) and ( (3, 4) ).
A. \( y = 2x - 1 \)
B. \( y = 2x + 1 \)
C. \( y = 3x - 2 \)
D. \( y = 3x + 2 \)
Question 14
Find the equation of the circle with center (3, 4) and radius 5.
A. \( x - 3 \)^2 + \( y - 4 \)^2 = 25
B. \( x - 4 \)^2 + \( y - 3 \)^2 = 25
C. \( x - 3 \)^2 + \( y - 3 \)^2 = 25
D. \( x - 4 \)^2 + \( y - 4 \)^2 = 25
Question 15
Find the value of [ \log_{10} left\( \frac{1}{\sqrt{2}} \right \) ].
A. \( -\frac{1}{2} \)
B. \( -\frac{3}{2} \)
C. \( -\frac{1}{4} \)
D. \( -\frac{3}{4} \)

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