POST UTME LEAD CITY UNIVERSITY 2019 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the area of the triangle with vertices ( A(1,2) ), ( B(3,4) ), and ( C(2,1) ).
A. ( 5 )
B. ( 10 )
C. ( 15 )
D. ( 20 )
Question 2
Solve the system of equations u\sing matrices: [ egin{cases} 2x + 3y = 7 \ x - 2y = -3 \end{cases} ]
A. \( x = 1, y = 2 \)
B. \( x = 2, y = 1 \)
C. \( x = 3, y = 4 \)
D. \( x = 4, y = 3 \)
Question 3
In a right-angled triangle, the length of the hypotenuse is 10 cm and one of the acute angles is 30°. Find the length of the side opposite the 30° angle.
A. 5 cm
B. 7.5 cm
C. 10 cm
D. 12.5 cm
Question 4
Solve the system of equations \n\begin{align*} \n 2x + 3y &= 7, \n 4x + 5y &= 11. \n\end{align*}
A. x = 1, y = 1
B. x = 2, y = 2
C. x = 3, y = 3
D. x = 4, y = 4
Question 5
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 4 \) from \( x = 0 \) to \( x = 2 \).
A. 10
B. 12
C. 14
D. 16
Question 6
A circle has a radius of 5 cm. Find the area of the circle.
A. ( pi (5)^2 )
B. ( 2pi (5) )
C. ( pi (5)^3 )
D. ( 2pi (5)^2 )
Question 7
Solve the system of equations u\sing matrices: \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} 5 \ 6 \end{bmatrix} \).
A. [1, 2]
B. [2, 1]
C. [3, 4]
D. [4, 3]
Question 8
Simplify the expression \( \frac{3x^2 + 2x - 1}{2x^2 - 5x + 1} \).
A. x + 1
B. x - 1
C. 3x - 2
D. 2x + 1
Question 9
If \( y = \frac{1}{x} \), find \( \frac{dy}{dx} \) at \( x = 2 \).
A. \( -\frac{1}{4} \)
B. \( \frac{1}{4} \)
C. \( -\frac{1}{2} \)
D. \( \frac{1}{2} \)
Question 10
Find the derivative of the function ( f(x) = \frac{1}{\sqrt{1 - x^2}} ) u\sing the chain rule.
A. \( \frac{-x}{\( 1 - x^2 \ \)^{3/2}} )
B. \( \frac{x}{\( 1 - x^2 \ \)^{3/2}} )
C. \( \frac{1}{\( 1 - x^2 \ \)^{3/2}} )
D. \( \frac{-1}{\( 1 - x^2 \ \)^{3/2}} )
Question 11
Let $X$ and $Y$ be indep\endent random variables with probability density functions $f_X(x) = 2x$ for $0 < x < 1$ and $f_Y(y) = 3y^2$ for $0 < y < 1$. Find the probability that $X + Y < 1$.
A. \frac{1}{2}
B. \frac{1}{3}
C. \frac{2}{3}
D. \frac{3}{4}
Question 12
A histogram represents the distribution of exam scores of 20 students. The scores are: 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 210, 220, 230. Find the mean of the scores.
A. 100
B. 110
C. 120
D. 130
Question 13
Find the sum of the first 10 terms of the geometric series \( 2x^2 + 4x^3 + 8x^4 + ldots \).
A. \( 2048x^{20} \)
B. \( 1024x^{20} \)
C. \( 512x^{20} \)
D. \( 256x^{20} \)
Question 14
Find the derivative of the function ( f(x) = 3x^2 \sin x ) u\sing the product rule.
A. \( 6x \sin x + 3x^2 \cos x \)
B. \( 3x^2 \cos x + 6x \sin x \)
C. \( 6x^2 \sin x + 3x \cos x \)
D. \( 3x^2 \sin x + 6x \cos x \)
Question 15
The equation of a circle is given by \( x^2 + y^2 = 16 \). Find the equation of the line that passes through the point ( (4, 0) ) and is perp\endicular to the given circle.
A. x + y = 4
B. x - y = 4
C. x + y = 8
D. x - y = 8

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