POST UTME SUMMIT UNIVERSITY 2024 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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. \( \frac{pi}{6} \)
Question 2
Solve the system of equations \( egin{cases} x + y + z = 6 \ x + 2y + 3z = 13 \ x + 3y + 5z = 20 \end{cases} \).
A. \( x = 1, y = 2, z = 3 \)
B. \( x = 2, y = 3, z = 1 \)
C. \( x = 3, y = 1, z = 2 \)
D. \( x = 4, y = 2, z = 0 \)
Question 3
A random sample of 25 students from a university had a mean height of 175.5 cm with a s\tandard deviation of 5.2 cm. Calculate the coefficient of variation (CV) of the sample.
A. 12.5%
B. 15%
C. 17.5%
D. 20%
Question 4
Solve the quadratic equation \( x^2 + 4x + 4 = 0 \).
A. \( x = -2 \)
B. \( x = -1 \)
C. \( x = 1 \)
D. \( x = 2 \)
Question 5
Solve the system of equations u\sing matrices: \begin{align*} x + 2y - 3z &= 7 \ 2x - 3y + z &= -3 \ -x + y + 2z &= 2 \end{align*}
A. \begin{bmatrix} 1 \ 2 \ 3 \end{bmatrix}
B. \begin{bmatrix} 2 \ -1 \ 4 \end{bmatrix}
C. \begin{bmatrix} 3 \ 1 \ 2 \end{bmatrix}
D. \begin{bmatrix} 4 \ 2 \ 1 \end{bmatrix}
Question 6
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. \( y = x - 2 \)
D. \( y = x + 2 \)
Question 7
A sequence is defined by the recurrence relation: \begin{align*} a_1 &= 2 \ a_n &= 3a_{n-1} + 2 \end{align*} Find the first five terms of the sequence.
A. \begin{bmatrix} 2 \ 8 \ 26 \ 82 \ 250 \end{bmatrix}
B. \begin{bmatrix} 2 \ 6 \ 20 \ 62 \ 190 \end{bmatrix}
C. \begin{bmatrix} 2 \ 4 \ 14 \ 46 \ 142 \end{bmatrix}
D. \begin{bmatrix} 2 \ 2 \ 6 \ 18 \ 54 \end{bmatrix}
Question 8
A histogram is given below: \begin{align*} \text{Class} & \text{Frequency} \ 0-10 & 5 \ 10-20 & 10 \ 20-30 & 15 \ 30-40 & 20 \ 40-50 & 10 \end{align*} Find the mean of the data.
A. 20
B. 25
C. 30
D. 35
Question 9
A quadratic equation is given by: \begin{align*} x^2 + 4x + 4 &= 0 \end{align*} Solve the equation.
A. \begin{bmatrix} -2 \ -2 \end{bmatrix}
B. \begin{bmatrix} -1 \ -4 \end{bmatrix}
C. \begin{bmatrix} 1 \ 4 \end{bmatrix}
D. \begin{bmatrix} 2 \ -2 \end{bmatrix}
Question 10
Solve the inequality \( \frac{x^2 - 4x - 5}{x + 1} > 0 \) for ( x in mathbb{R} ).
A. \( x < -1 \) or \( x > 5 \)
B. \( x < -1 \) or \( x > 1 \)
C. \( x > -1 \) or \( x < 5 \)
D. \( x > 1 \) or \( x < 5 \)

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