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Advanced Algebra with Trigonometry
Unit 1 Take-Home Test
Name
Directions: Show all work and reasoning to receive full credit.
1) Write each expression in the standard form a  bi if z  4  3i and w  2  8i .
a) z  w
c) z  w
b) z  w
2) Solve the following equations in the complex number system.
a) x3  729  0
b) 5 x6  30 x 4  35x 2  0
c) 2x 2  3x  5  0
d) x(3x 2  5x  27)  45
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3) Solve the inequality. Express your answer using interval notation. Graph the solution set.
4 x  3
1
3
a) 9 
b)  x  3  5  2
3
2
4) Simplify each expression.
3
a) 15x
53
4 7
9x y
xy10   xy 

b)
32
 x8 y 4 
c) 6 x2 (4 x  3)5 3  9 x(4 x  3)2 3
5) Using the Pythagorean Theorem, determine whether or not the points are the vertices of a right triangle:
(-9, 7), (-3, 7), (-3, 15).
6) Determine the center (h, k) and radius r of the circle 4 x2  4 y 2 12 x  16 y  5  0 . Graph the circle.
1
1
7) Determine the general form of the equation of the circle with endpoints of a diameter at (6, -2) and (-4, 4).
For Questions 8 & 9, determine an equation, in slope-intercept form, for the line with the given properties.
8) Parallel to the line 4 x  3 y  3 ;
9) Perpendicular to the line 2 x  9 y  66 ;
containing the point (6, 0).
containing the point (6, -13).
10) Determine the equation, in general form, of the line in the graph illustrated below.
10
8
6
(5,5)
4
(5,1)
2
-10 -8 -6 -4 -2
2
4
6
8 10
-2
-4
-6
-8
-10
11) At 2:00 p.m. there was 9 feet 8 inches of snow at Breckenridge Ski Resort. By 10:00 p.m. the same night
there was 10 feet 3 inches of snow. What is the average rate of change (in inches) for the snow level?