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Algebra II/Trig A Final Review 2005
Algebra II Trig A
Fall 2008
In reviewing for the final, consider the following sources: 1. Your notebook. Many of you took very good notes, go
over them. 2. Homework. We did over 1000 homework problems. You knew how to do it at one time. Review
your own work. 3. Unit review packets. Before each test you were given a review packet (sometimes two). Redo
those reviews. Finally, there are 64 questions that follow this outline. Complete the packet as your last homework
assignment. Don’t wait until the last minute to start studying!!!
The final will be a multiple choice final covering the following California standards. The number of questions
on the test from each standard is in parenthesis.
1.0 Students solve equations and inequalities involving absolute value. (4 Questions)
2.0 Students solve systems of linear equations and inequalities (in two or three variables) by substitution, with
graphs, or with matrices. (8 Questions)
3.0 Students are adept at operations on polynomials, including long division. (4 Questions)
4.0 Students factor polynomials representing the difference of squares, perfect square trinomials, and the sum and
difference of two cubes. (6 Questions)
5.0 Students demonstrate knowledge of how real and complex numbers are related both arithmetically and
graphically. In particular, they can plot complex numbers as points in the plane.
6.0 Students add, subtract, multiply, and divide complex numbers. (5 Questions)
7.0 Students add, subtract, multiply, divide, reduce, and evaluate rational expressions with monomial and
polynomial denominators and simplify complicated rational expressions, including those with negative exponents in
the denominator. (5 Questions)
8.0 Students solve and graph quadratic equations by factoring, completing the square, or using the quadratic
formula. Students apply these techniques in solving word problems. They also solve quadratic equations in the
complex number system. (4 Questions)
9.0 Students demonstrate and explain the effect that changing a coefficient has on the graph of quadratic functions;
2
that is, students can determine how the graph of a parabola changes as a, b, and c vary in the equation y = a(x-b) +
c. (1 Question)
10.0 Students graph quadratic functions and determine the maxima, minima, and zeros of the function. (2 Questions)
12.0 Students know the laws of fractional exponents, understand exponential functions, and use these functions in
problems involving exponential growth and decay. (3 Questions)
16.0 Students demonstrate and explain how the geometry of the graph of a conic section (e.g., asymptotes, foci,
eccentricity) depends on the coefficients of the quadratic equation representing it. (3 Questions)
2
2
17.0 Given a quadratic equation of the form ax + by + cx + dy + e = 0, students can use the method for completing
the square to put the equation into standard form and can recognize whether the graph of the equation is a circle,
ellipse, parabola, or hyperbola. Students can then graph the equation. (4 Questions)
24.0 Students solve problems involving functional concepts, such as composition, defining the inverse function and
performing arithmetic operations on functions. (8 Questions)
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Algebra II/Trig A Final Review 2005
State the name of the conic section and give all the required information. Be able to graph.
x2 y2
1.
2. y 2  121  x 2

1
64 49
2
2
4. 6 x  16 y  96
2
3. y  2( x  2)  1
State the name of the conic section and give all the required information. Be able to graph.
2
2
2
5. x  2 x  y  8  0
6. x  2 x  y  4 y  7
2
2
7. x  4 y  2 x  24 y  33  0
8.
x2  y2  x  2
For the next 10 problems, f(x) = x2 –x + 3; g(x) = x + 8; h(x) = 3x2 + 1
9. Find f(x) + g(x)
10. Find f(x) – h(x)
11. Find f(g(x))
12. Find f(h(x))
13. Find g(f(x))
14. Find h(f(x))
15. Find h(g(x))
16. Find f(-3)
17. Find h(f(4))
18. Find g(h(2))
Find the inverse of the following problems
19. f(x) = 4x +5
20. g(x) = 3x2 –12
Determine whether the pair of functions are inverses
21. f(x) = 1/2 x + 2
g(x) = 2x – 4
22. f(x) = 3x –9
g(x) = -3x + 9
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Algebra II/Trig A Final Review 2005
Find the inverse of the relationship and determine whether its inverse is a function
23. [(1,3)(1, -1)(1, -3)(1, 1)]
24. Simplify
x 2  4 x  4 3x 2  x  10

x2  x  6
x2  9
b 3 2a 2 b 2
 2  2
a
25. Simplify 4 b
26. Simplify
7
3
 2
2 x  2 y x  2 xy  y 2
x2  4
x2  2x  1
x2
x 1
27. Simplify
28. Solve: 2 4 x  2 1  9
29. Solve: 3 x  1  12
30. Find f(-5) if f(x) = 4x3 – x + 1
31. (8x3 + 2x2 + 3x) ÷ (2x + 3)
32.
36 x6 y10
6 xy 6
33. Factor: 27a3 + 125b3
34. Factor: 9x2 – 12x + 4
35. Factor: 7y – 12x + 4xy – 21
36. Factor: 15a3b – 5a2b2 – 10ab3
37. Simplify:
3
64a5b3
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Algebra II/Trig A Final Review 2005
1
5
38. Simplify:  9a  a
4
5
39. Simplify: 5( 3 27a )( 3 64a 7 )
1
40. Solve: a 5  2  0
41. Solve: x2 + 441 = 0
42. (9 – 3i) – (3 + 5i)
43. (5 + 4i)(3 – 7i)
44.
5
7i
45. (7 – 3i)(7 + 3i)
46. i10i21i30
47.
4i 7
4i 7
48. Solve: x2 + 5x + 13 = 0
49. Solve: 6x2 + 7x = 3
50. Solve: 2x2 + 3x – 13 = 0
51. A man throws a ball in the air. The equation of the distance of the ball with respect to time
is h(t) = -16t2 + 10t + 50 with time in seconds and height in feet. How high was the ball after 1
second? How long did it take for the ball to reach the ground?
52. (4b4 + 6b2 - 3b + 5) – (2b3 + 3b - 2)
53. (y + 2)(y2 – 4y + 1)
54. (2x3 – 3x2 + 4x – 5) ÷ (x – 2)
55. Factor: 64x2y2 – 25z2
56. Find the zeros of the quadratic equation y = 3x2 + 5x + 2
57. Find the maximum or minimum of the quadratic equation in #56.
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Algebra II/Trig A Final Review 2005
58. Solve the following systems of equations by graphing :
x y 2
x  3y  6
59. You want to eliminate y by the addition method in the system 3x - 5y = 6
2x + 7y = 12.
If you multiply each side of the top equations by 7, by which number would you multiply
each of the bottom equation?
60. To solve the system of equations 7x + 3y = -1 and 2x – y = 9, what expression would be
substituted for y into the first equation? What is the solution?
61. Solve.
x y
  4
2 3
x y
 1
5 6
x 1
62. Is (1,2) a solution to the following system of inequalities?
y3
y  2x 1
63. How many solutions does the following system have?
2 x  4 y  6
4 x  8 y  12
64. Solve.
2x - y - z = -4
2x + y - 5z = -16
x + 3y - 4z = -9
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