POST UTME REDEEMERS UNIVERSITY 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the area under the curve \( y = x^2 - 2x + 1 \) from \( x = 0 \) to \( x = 2 \) u\sing integration.
A. \frac{1}{3}
B. \frac{2}{3}
C. \frac{4}{3}
D. \frac{5}{3}
Question 2
Find the determinant of the matrix \( egin{bmatrix} 2 & 1 \ 4 & 3 \end{bmatrix} \).
A. 1
B. 2
C. 3
D. 4
Question 3
Solve the inequality $|x - 2| > 3$.
A. $x < -1$ or $x > 5$
B. $x < -1$ or $x > 2$
C. $x < 2$ or $x > 5$
D. $x < 1$ or $x > 5$
Question 4
Solve for x in the equation \( 2^x + 2^x = 128 \).
A. 4
B. 5
C. 6
D. 7
Question 5
A set of numbers has a mean of 20 and a s\tandard deviation of 5. If the set contains 10 numbers, what is the sum of the numbers?
A. 200
B. 250
C. 300
D. 350
Question 6
In the diagram below, $ABCD$ is a rec\tangle, $E$ is the midpoint of $AB$, and $F$ is the midpoint of $CD$. If $AB = 6$ and $CD = 8$, find the area of the shaded region.
A. 12
B. 16
C. 20
D. 24
Question 7
Find the equation of the circle with centre at ((2,3)) and radius (5).
A. \( x-2 \ \)^2 + \( y-3 \)^2 = 25 )
B. \( x-3 \ \)^2 + \( y-2 \)^2 = 25 )
C. \( x-5 \ \)^2 + \( y-2 \)^2 = 9 )
D. \( x-2 \ \)^2 + \( y-5 \)^2 = 9 )
Question 8
A sequence is defined by the recurrence relation \( a_n = 2a_{n-1} + 3 \), with initial term \( a_1 = 2 \). Find the sum of the first five terms of the sequence.
A. \( 2 + 7 + 17 + 37 + 79 \)
B. \( 2 + 5 + 13 + 29 + 61 \)
C. \( 2 + 4 + 12 + 28 + 60 \)
D. \( 2 + 6 + 16 + 34 + 70 \)
Question 9
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 = 20$
C. $\( x - 2 \)^2 + \( y - 3 \)^2 = 24$
D. $\( x - 2 \)^2 + \( y - 3 \)^2 = 28$
Question 10
A circle with center ( C(2, 3) ) and radius \( r = 4 \) is drawn on a coordinate plane. What is the equation of the circle?
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 11
A car travels from city A to city B at an average speed of 60 km/h and returns from city B to city A at an average speed of 40 km/h. What is the average speed of the car for the entire trip?
A. 48 km/h
B. 52 km/h
C. 56 km/h
D. 60 km/h
Question 12
Solve the inequality \( 2x^2 + 5x - 3 > 0 \).
A. x < -1 or x > 3/2
B. x < -1 or x < 3/2
C. x > -1 or x > 3/2
D. x > -1 or x < 3/2
Question 13
Solve for y in the equation \( y = \frac{1}{2} \log_{10} \( x^2 \ \) + 3 ).
A. \frac{1}{2} \log_{10} \( x^2 \) + 3
B. \frac{1}{2} \log_{10} \( x^2 \) - 3
C. \frac{1}{2} \log_{10} \( x^2 \) + 5
D. \frac{1}{2} \log_{10} \( x^2 \) - 5
Question 14
Find the value of x in the equation \( x^2 + 4x + 4 = 0 \).
A. -2
B. 2
C. 4
D. 6
Question 15
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. 40
B. 50
C. 60
D. 70

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