POST UTME SKYLINE UNIVERSITY 2021 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Find the area under the curve \( y = \frac{1}{x^2 + 1} \) from \( x = 0 \) to \( x = 1 \).
A. \( \frac{pi}{4} - 1 \)
B. \( \frac{pi}{4} \)
C. \( \frac{pi}{4} + 1 \)
D. \( \frac{pi}{4} - 2 \)
Question 2
A polynomial f(x) has degree 3 and has roots 1, 2, and 3. Find the polynomial.
A. f(x) = \( x - 1 \)\( x - 2 \)\( x - 3 \)
B. f(x) = \( x - 1 \)\( x - 2 \)\( x - 3 \) + 1
C. f(x) = \( x - 1 \)\( x - 2 \)\( x - 3 \) - 1
D. f(x) = \( x - 1 \)\( x - 2 \)\( x - 3 \) + 2
Question 3
A rec\tangular prism has a length of 10 cm, a width of 5 cm, and a height of 8 cm. Calculate its volume and surface area.
A. 400 cm^3, 240 cm^2
B. 500 cm^3, 240 cm^2
C. 600 cm^3, 240 cm^2
D. 800 cm^3, 240 cm^2
Question 4
Find the sum of the first 10 terms of the arithmetic sequence with first term 3 and common difference 2.
A. \( 3 + 5\( 10 \ \) )
B. \( 3 + 5\( 9 \ \) )
C. \( 3 + 5\( 11 \ \) )
D. \( 3 + 5\( 12 \ \) )
Question 5
Find the determinant of the matrix \begin{pmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{pmatrix}.
A. 0
B. 1
C. 2
D. 3
Question 6
Determine the value of x in the equation \( \frac{1}{2}x + 5 = \frac{3}{4}x - 3 \) in base 8.
A. 10
B. 12
C. 14
D. 16
Question 7
Find the equation of the line pas\sing through the points (2, 3) and (4, 5) in the coordinate plane.
A. y = 2x - 1
B. y = 2x + 1
C. y = -2x + 1
D. y = -2x - 1
Question 8
Find the mean of the data set ( { 2, 4, 6, 8, 10 } ).
A. ( 6 )
B. ( 7 )
C. ( 8 )
D. ( 9 )
Question 9
In the diagram below, the circle with center A has radius 4cm. The circle with center B has radius 3cm. If the two circles intersect at points C and D, what is the length of CD?
A. \( 4 - 3 \)
B. \( 4 + 3 \)
C. \( 4 \times 3 \)
D. \( 4 - 3 \)
Question 10
Two events A and B are indep\endent. If P(A) = 0.4 and P(B) = 0.6, find P\( A \cap B \).
A. 0.12
B. 0.24
C. 0.36
D. 0.48
Question 11
Solve the system of equations \( x + y = 4 \) and \( xy = 5 \).
A. \( x = 1, y = 3 \)
B. \( x = 3, y = 1 \)
C. \( x = 2, y = 2 \)
D. \( x = 4, y = 0 \)
Question 12
Find the area under the curve \( y = x^2 \) from \( x = 0 \) to \( x = 2 \) u\sing integration.
A. \( \frac{8}{3} \)
B. \( \frac{16}{3} \)
C. \( \frac{32}{3} \)
D. \( \frac{64}{3} \)
Question 13
Solve the inequality \( \frac{x}{x-2} > 2 \) for \( x > 2 \).
A. \( x > 4 \)
B. \( x < 4 \)
C. \( x > 2 \)
D. \( x < 2 \)
Question 14
A circle has a radius of 4 cm. Calculate its area.
A. 50.24 cm^2
B. 100.48 cm^2
C. 150.72 cm^2
D. 200.96 cm^2
Question 15
In the diagram below, the line AB has a slope of 2. If the line passes through the point (3, 4), what is the equation of the line?
A. \( y = 2x - 1 \)
B. \( y = 2x + 1 \)
C. \( y = 2x - 2 \)
D. \( y = 2x + 2 \)

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