POST UTME SKYLINE UNIVERSITY 2021 Mathematics | Objective

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Question 1
Solve the system of equations u\sing matrices: \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 3 \\ 8 \end{bmatrix}.
A. \\begin{bmatrix} 1 \\\\ 2 \\end{bmatrix}
B. \\begin{bmatrix} 2 \\\\ 1 \\end{bmatrix}
C. \\begin{bmatrix} 3 \\\\ 4 \\end{bmatrix}
D. \\begin{bmatrix} 4 \\\\ 3 \\end{bmatrix}
Question 2
Solve for x in the equation \( \sin^2\( x \ \) + \cos^2(x) = 1 ).
A. \( x = \frac{pi}{2} \)
B. \( x = \frac{pi}{4} \)
C. \( x = \frac{3pi}{4} \)
D. \( x = \frac{5pi}{4} \)
Question 3
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 4
A random sample of 25 students from a university had a mean height of 175 cm with a s\tandard deviation of 5 cm. If the population s\tandard deviation is 6 cm, calculate the s\tandard error of the mean.
A. 2.5 cm
B. 3.0 cm
C. 3.5 cm
D. 4.0 cm
Question 5
A vector ( mathbf{a} ) has components \( a_1 = 2 \) and \( a_2 = 3 \). Find the magnitude of the vector ( mathbf{a} ).
A. \( \sqrt{13} \)
B. \( \sqrt{5} \)
C. \( \sqrt{7} \)
D. \( \sqrt{11} \)
Question 6
Find the value of \( \log_{10} \( 1000 \ \) ).
A. ( 3 )
B. ( 4 )
C. ( 5 )
D. ( 6 )
Question 7
Solve the quadratic equation \( x^2 + 5x + 6 = 0 \).
A. \( x = -2 \)
B. \( x = -3 \)
C. \( x = 2 \)
D. \( x = 3 \)
Question 8
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 9
Find the sum of the infinite geometric series \( sum_{n=1}^{infty} \frac{1}{2^n} \).
A. 1
B. 2
C. 3
D. 4
Question 10
Solve for x in the equation \( x^2 + 4x + 4 = 0 \).
A. -2
B. -1
C. 1
D. 2
Question 11
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 12
Solve the inequality \( \frac{x + 2}{x - 1} > 0 \).
A. \( x < -2 \) or \( x > 1 \)
B. \( x < -2 \) or \( x < 1 \)
C. \( x > -2 \) or \( x < 1 \)
D. \( x > -2 \) or \( x > 1 \)
Question 13
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 = 16 )
C. \( x + 2 \ \)^2 + \( y + 3 \)^2 = 16 )
D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )
Question 14
Find the mean of the data set ( { 2, 4, 6, 8, 10 } ).
A. ( 6 )
B. ( 7 )
C. ( 8 )
D. ( 9 )
Question 15
A circle with center (0, 0) and radius 4 passes through the point (3, 4). Find the equation of the circle.
A. x^2 + y^2 = 16
B. x^2 + y^2 = 20
C. x^2 + y^2 = 24
D. x^2 + y^2 = 28

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