POST UTME OSUSTECH 2018 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
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 2
Find the area under the curve \( y = \frac{1}{2}x^2 + 3x - 2 \) from \( x = 0 \) to \( x = 4 \).
A. \( \frac{1}{2}\left\( \frac{4^3}{3} + 3\cdot 4^2 - 2\cdot 4\right \ \) - \frac{1}{2}\left\( 0^3 + 3\cdot 0^2 - 2\cdot 0\right)\ \)
B. \( \frac{1}{2}\left\( \frac{4^3}{3} + 3\cdot 4^2 - 2\cdot 4\right \ \) + \frac{1}{2}\left\( 0^3 + 3\cdot 0^2 - 2\cdot 0\right)\ \)
C. \( \frac{1}{2}\left\( \frac{4^3}{3} + 3\cdot 4^2 - 2\cdot 4\right \ \) - \frac{1}{2}\left\( 0^3 + 3\cdot 0^2 - 2\cdot 0\right)\ \)
D. \( \frac{1}{2}\left\( \frac{4^3}{3} + 3\cdot 4^2 - 2\cdot 4\right \ \) + \frac{1}{2}\left\( 0^3 + 3\cdot 0^2 - 2\cdot 0\right)\ \)
Question 3
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 4
A bakery sells 250 loaves of bread per day. If they make a profit of ₦5 per loaf, what is their total daily profit?
A. ₦1250
B. ₦12500
C. ₦125000
D. ₦1250000
Question 5
Find the area of the region bounded by the curves y = x^2 and y = 2x.
A. 4/3
B. 8/3
C. 16/3
D. 32/3
Question 6
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 7
The mean of a set of numbers is 25. If the largest number is 50, and the smallest number is 10, what is the sum of the remaining 7 numbers?
A. 150
B. 170
C. 190
D. 210
Question 8
A set of 5 cards is drawn from a deck of 52 cards. What is the probability that the set contains at least one ace?
A. 1/52
B. 1/26
C. 1/13
D. 1/4
Question 9
A circle has a radius of 5 cm. Find the area of the circle.
A. 25π
B. 50π
C. 75π
D. 100π
Question 10
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 11
Find the equation of the line pas\sing through the points (A(1, 2)) and (B(3, 4)).
A. \( y - 2 = \frac{2}{2}\( x - 1)\ \ \)
B. \( y - 2 = \frac{2}{2}\( x - 1)\ \ \)
C. \( y - 2 = \frac{2}{2}\( x - 1)\ \ \)
D. \( y - 2 = \frac{2}{2}\( x - 1)\ \ \)
Question 12
Solve the inequality \( \frac{x}{x-1} > 2 \) for \( x > 1 \).
A. \( x > 3 \)
B. \( x < 3 \)
C. \( x > 5 \)
D. \( x < 5 \)
Question 13
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 14
A quadratic equation has the form \( ax^2 + bx + c = 0 \). If the equation has two real roots, which of the following is true?
A. The equation has no real roots.
B. The equation has one real root.
C. The equation has two real roots.
D. The equation has no real roots, but has complex roots.
Question 15
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. \( egin{pmatrix} 4 \ 3 \end{pmatrix} \)

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