POST UTME OSUSTECH 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
A car travels from city A to city B at an average speed of 60 km/h. On the return trip, the average speed is 40 km/h. What is the average speed for the entire trip?
A. 40
B. 50
C. 60
D. 70
Question 2
Find the area under the curve \( y = x^2 + 2x + 1 \) from \( x = 0 \) to \( x = 2 \).
A. ( 10 )
B. ( 12 )
C. ( 14 )
D. ( 16 )
Question 3
Find the sum of the first 10 terms of the geometric sequence ( 2, 6, 18, ldots ).
A. 1950
B. 1960
C. 1970
D. 1980
Question 4
Solve the inequality |x - 2| > 3.
A. x < -1 or x > 5
B. x < -1 or x > 4
C. x < 1 or x > 5
D. x < 1 or x > 4
Question 5
A histogram is shown below. What is the mode of the data set?
A. A
B. B
C. C
D. D
Question 6
Find the volume of the solid formed by revolving the region bounded by y = x^2, y = 0, and x = 2 about the x-axis.
A. 64\pi
B. 128\pi
C. 256\pi
D. 512\pi
Question 7
Determine the mean of the following data set: 2, 4, 6, 8, 10. If the mean is increased by 2, what is the new mean?
A. 6
B. 8
C. 10
D. 12
Question 8
Find the sum of the first $n$ terms of the geometric series $1 + 2 + 4 + 8 + ldots$.
A. \( 2^n - 1 \)
B. \( 2^n + 1 \)
C. \( 2^n - 2 \)
D. \( 2^n + 2 \)
Question 9
Solve the system of equations \( egin{cases} x + y = 4 \ 2x - y = 3 \end{cases} \).
A. \( x = 1, y = 3 \)
B. \( x = 2, y = 2 \)
C. \( x = 3, y = 1 \)
D. \( x = 4, y = 0 \)
Question 10
Solve the matrix equation \( egin{pmatrix} 2 & 1 \ 1 & 2 \end{pmatrix} mathbf{x} = egin{pmatrix} 3 \ 4 \end{pmatrix} \) for ( mathbf{x} ).
A. \( egin{pmatrix} 1 \ 2 \end{pmatrix} \)
B. \( egin{pmatrix} 2 \ 1 \end{pmatrix} \)
C. \( egin{pmatrix} 3 \ 4 \end{pmatrix} \)
D. \( egin{pmatrix} 4 \ 3 \end{pmatrix} \)
Question 11
Given that \( mathbf{a} = egin{pmatrix} 2 \ 3 \end{pmatrix} \) and \( mathbf{b} = egin{pmatrix} -1 \ 4 \end{pmatrix} \), find the vector ( mathbf{c} ) such that ( mathbf{c} ) is perp\endicular to both ( mathbf{a} ) and ( mathbf{b} ).
A. \( egin{pmatrix} 7 \ -6 \end{pmatrix} \)
B. \( egin{pmatrix} 6 \ -7 \end{pmatrix} \)
C. \( egin{pmatrix} -6 \ 7 \end{pmatrix} \)
D. \( egin{pmatrix} 7 \ 6 \end{pmatrix} \)
Question 12
Find the surface area of the solid formed by revolving the region bounded by y = x^2, y = 0, and x = 2 about the x-axis.
A. 64\pi
B. 128\pi
C. 256\pi
D. 512\pi
Question 13
In the number system with base 7, what is the value of the digit $x$ such that $xoverline{3} = 5overline{4}$?
A. 2
B. 3
C. 4
D. 5
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. \( x-4 \ \)^2 + \( y-2 \)^2 = 16 )
Question 15
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 )

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