POST UTME RSU 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A histogram of exam scores has a mean of 60 and a s\tandard deviation of 10. Find the probability that a randomly selected score is between 50 and 70.
A. ( 0.5 )
B. ( 0.6 )
C. ( 0.7 )
D. ( 0.8 )
Question 2
Find the area under the curve y = \sin^2 x from x = 0 to x = \frac{\pi}{2}.
A. \frac{\pi}{4}
B. \frac{\pi}{2}
C. \frac{\pi}{3}
D. \frac{2\pi}{3}
Question 3
A right-angled triangle has a hypotenuse of length 10 cm and one leg of length 6 cm. Find the length of the other leg.
A. 8\sqrt{3}
B. 6\sqrt{3}
C. 8\sqrt{2}
D. 6\sqrt{2}
Question 4
A right circular cone has a height of 10 cm and a base radius of 4 cm. Find the volume of the cone.
A. \frac{160\pi}{3}
B. \frac{320\pi}{3}
C. \frac{80\pi}{3}
D. \frac{40\pi}{3}
Question 5
A rec\tangular prism has a length of 6 cm, a width of 4 cm, and a height of 8 cm. What is the volume of the prism?
A. 192
B. 192
C. 192
D. 192
Question 6
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. \( -\infty, -1 \) \cup \( 3, \infty \)
B. \( -\infty, -3 \) \cup \( 1, \infty \)
C. \( -\infty, 1 \) \cup \( 3, \infty \)
D. \( -\infty, -3 \) \cup \( 1, \infty \)
Question 7
Find the equation of the circle pas\sing through the points $(2, 3)$ and $\( -1, 4 \)$.
A. $x^2 + y^2 - 5x + 7y + 12 = 0$
B. $x^2 + y^2 + 5x - 7y + 12 = 0$
C. $x^2 + y^2 - 5x - 7y + 12 = 0$
D. $x^2 + y^2 + 5x + 7y + 12 = 0$
Question 8
Find the surface area of the sphere with radius 6cm.
A. 288\pi cm^2
B. 576\pi cm^2
C. 864\pi cm^2
D. 1152\pi cm^2
Question 9
Find the area under the curve y = x^3 - 6x^2 + 9x + 2 from x = 0 to x = 4.
A. 120
B. 150
C. 180
D. 200
Question 10
Find the derivative of the function f(x) = 3x^2 - 2x + 1.
A. 6x - 2
B. 3x^2 - 2
C. 6x + 2
D. 3x^2 + 2
Question 11
Find the determinant of the matrix [ egin{bmatrix} 2 & 3 & 4 \ 5 & 6 & 7 \ 8 & 9 & 10 \end{bmatrix} ].
A. 0
B. 1
C. 2
D. 3
Question 12
A sequence is defined by the formula \( a_n = 2n + 1 \). Find the sum of the first 5 terms of the sequence.
A. 15
B. 25
C. 35
D. 45
Question 13
A particle moves in a straight line with its position given by the equation s(t) = 2t^3 - 5t^2 + 3t + 1. Find the velocity of the particle at time t = 2.
A. 4
B. 6
C. 8
D. 10
Question 14
Find the equation of the circle with center (2, 3) and radius 4.
A. \( x - 2 \)^2 + \( y - 3 \)^2 = 16
B. \( x - 3 \)^2 + \( y - 2 \)^2 = 16
C. \( x + 2 \)^2 + \( y + 3 \)^2 = 16
D. \( x - 2 \)^2 + \( y + 3 \)^2 = 16
Question 15
Solve the system of linear equations u\sing matrices:\n\n\begin{align*}\n2x + 3y &= 7 \\n4x - 2y &= -3\n\end{align*}
A. x = 1, y = 2
B. x = 2, y = 1
C. x = 3, y = 4
D. x = 4, y = 3

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