POST UTME LAUTECH 2023 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Solve the inequality \( 2x - 5 > 3 \).
A. x > 4
B. x < 4
C. x > 2
D. x < 2
Question 2
A right circular cone has a height of 8 cm and a base radius of 5 cm. Find the volume of the cone.
A. ( 100pi ) cm$^3$
B. ( 200pi ) cm$^3$
C. ( 300pi ) cm$^3$
D. ( 400pi ) cm$^3$
Question 3
Find the value of y in the equation \( y = \frac{1}{2} \( 3x + 5 \ \) ) when x = 4.
A. 8
B. 9
C. 10
D. 11
Question 4
Find the value of \( \sin 2\theta \) given that \( \sin \theta = \frac{3}{5} \) and \( \cos \theta = \frac{4}{5} \).
A. \( \frac{24}{25} \)
B. \( \frac{16}{25} \)
C. \( \frac{20}{25} \)
D. \( \frac{12}{25} \)
Question 5
Find the equation of the circle pas\sing through the points (2, 3), (4, 5), and (6, 7).
A. \( x^2 + y^2 - 4x - 6y + 9 = 0 \)
B. \( x^2 + y^2 - 6x - 4y + 9 = 0 \)
C. \( x^2 + y^2 - 2x - 3y + 9 = 0 \)
D. \( x^2 + y^2 - 8x - 12y + 9 = 0 \)
Question 6
Find the volume of the solid formed by revolving the region bounded by the curve $y = \frac{1}{2}x^2 + 1$, the $x$-axis, and the line $x = 2$ about the $x$-axis.
A. \( \frac{8pi}{3} \)
B. \( \frac{16pi}{3} \)
C. \( \frac{32pi}{3} \)
D. \( \frac{64pi}{3} \)
Question 7
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( x < -\frac{3}{2} \) or \( x > \frac{1}{2} \)
B. \( x < -\frac{3}{2} \) or \( x < \frac{1}{2} \)
C. \( x > -\frac{3}{2} \) or \( x > \frac{1}{2} \)
D. \( x > -\frac{3}{2} \) or \( x < \frac{1}{2} \)
Question 8
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
B. 5√3
C. 10√3
D. 10√2
Question 9
In the diagram below, the equation of the circle is given by \( x - 2 \ \)^2 + \( y - 3 \)^2 = 4 ). Find the equation of the \tangent line to the circle at the point ( (5, 7) ).
A. y = -x + 12
B. y = x - 1
C. y = -x + 11
D. y = x + 1
Question 10
Solve the inequality \( 2x^2 - 5x - 3 > 0 \).
A. \( x < -1 \) or \( x > \frac{3}{2} \)
B. \( x < -1 \) or \( x < \frac{3}{2} \)
C. \( x > -1 \) or \( x < \frac{3}{2} \)
D. \( x > -1 \) or \( x > \frac{3}{2} \)
Question 11
A set of 5 consecutive integers has a median of 10. If the sum of the integers is 50, find the integers.
A. {8, 9, 10, 11, 12}
B. {7, 8, 9, 10, 11}
C. {6, 7, 8, 9, 10}
D. {5, 6, 7, 8, 9}
Question 12
Solve the system of equations \( egin{cases} x^2 + y^2 = 4 \ x - 2y = -1 \end{cases} \).
A. \( x = 1, y = 1 \)
B. \( x = 2, y = 1 \)
C. \( x = 1, y = 2 \)
D. \( x = 2, y = 2 \)
Question 13
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 = 16
C. \( x + 2 \)² + \( y + 3 \)² = 16
D. \( x - 2 \)² + \( y - 3 \)² = 16
Question 14
A random variable ( X ) has a probability distribution given by \( P\( X = x \ \) = egin{cases} 0.2 & \text{if } x = 1 \ 0.3 & \text{if } x = 2 \ 0.5 & \text{if } x = 3 \end{cases} ). Find the probability that ( X ) takes on a value greater than 2.
A. 0.4
B. 0.5
C. 0.6
D. 0.7
Question 15
A sequence is defined by the formula \( a_n = 2n + 1 \). Find the 5th term of the sequence.
A. 9
B. 11
C. 13
D. 15

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