2014 Final Exam Review Packet:
Name
List of final exam topics
1. Solve system of equations using the graphing method
2. Solve system of equations using the substitution method
3. Solve system of equations using the elimination method
4. Solve a word problem by setting up and solving a system of equations
5. Simplify square root of a non-perfect square
6. Add/Subtract radical expression (where the radicals are already simplified)
7. Add/Subtract radical expression (simplify radicals first, then combine like radicals
8. Multiply radical expressions
9. Multiply radicals using FOIL
10. Divide radicals (rationalize the denominator)
11. Divide radicals (use the conjugate)
12. 13.14. Simplify cube, fourth, fifth roots
15. Convert from rational exponent form to radical form
16. Convert from radical form to rational exponent form
17. Solve a radical equation (square, cube, fourth, or fifth root)
18. Solve a rational exponent equation
19.20.21. Simplify the square roots of negative numbers
22. Add/Subtract complex numbers
23. Multiply complex numbers, remember i2 = -1
24. Simplify powers of i
( i0 = 1
i 1 = i i2 =- 1
i3 = -i )
25. Classify polynomials (is it a monomial, binomial, trinomial, etc.)
26. What makes an expression not a polynomial?
27. Subtract polynomials (all of the like terms line up)
28. Add polynomials (the terms in the polynomials do not line up)
29. Multiply polynomials (FOIL)
30. Find the square of a sum
31. Multiply a binomial and a trinomial
32. Factor a polynomial by factoring out the GCF
33. Factor a polynomial with 4 terms using the grouping method
34.35.36. Factor a trinomial in standard form in which a = 1 using the Guess and Check method
37.38. Factor a trinomial in standard form in which a > 1 using the AC method
39. Factor a perfect square trinomial ax2 + bx + c
40. Factor a perfect square trinomial ax2 - bx + c
41. Factor the difference of two perfect squares ax2 – c
42. Factor a trinomial by first factoring out the GCF then using the guess and check method
43. Factor a polynomial with 4 terms by first using the grouping method, then factoring the difference
of perfect squares
44. Factor a binomial by factoring the difference of perfect squares two separate times
45.46. Solve a quadratic equation by using zero product property
47.48. Solve a quadratic equation by using the square root method
49.50.51. Solve a quadratic equation using the quadratic formula
52.53.54.55.56. How can you use the discriminant to predict the number and type of solutions to a quadratic
equation? (show all four answer possibilities
57. Given a quadratic function find the axis of symmetry (use x = -b/2a)
Identify the vertex and decide if it is a maximum or minimum point
Create a table of values and graph (use a minimum of 5pts including the vertex)
Identify the domain and range
58. Graph a quadratic function in vertex form
59. Graph an absolute value function in vertex form
60. Find the x-intercepts of an absolute value function algebraically
61. Find the y-intercept of a quadratic function algebraically
Part 1: Systems of Equations and Inequalities
1. Solve by Graphing Method
y = 2x + 3
1
y = - x -7
2
2.
Solve using Substitution Method
y = -4x + 11
-5x + 2y = -4
3.
Solve using Elimination Method
2x + 3y = -7
-5x + 9y = -32
4. A youth group visits an amusement park. They took two vans. In the first van, 2
adults and 5 students paid $77 for admission. In the second van, 2 adults and 7
students paid $95 for the same tour. Find the adult price and the student price of
the tour.
Part 2: Radicals and Rational Exponents
5. Simplify:
80
7. Simplify (Add/Subtract):
8. Multiply:
6.
Simplify (Add/Subtract):
2 7 -5 10 - 6 7 + 9 10
5 2 + 18 -3 50
4 3•2 15
9. Multiply:
(3+2 3)(7 6 -5)
HINT: FOIL
10. Simplify:
HINT: (Rationalize the denominator)
5 7
3
11. Simplify:
HINT: use the conjugate
4 2
5- 3
12. Simplify:
3
64
15. Convert to radical form:
13. Simplify:
x
3
4
4
625
14. Simplify:
16. Convert to exponent form:
5
7
243
y5
Solve each equation
17.
4
3x + 4 +2 = 6
19. Simplify:
HINT:
Don’t forget i
-40
18.
20.
Simplify:
22. Add the following complex numbers:
(x +2) + 3 = 7
-10
21. Simplify:
(-5 +2i) + (-3- 6i)
23. Multiply the following complex numbers:
(4 +2i)(-3+ 6i)
1
3
HINT: remember i2 = -1
-36
24. Use the chart containing the powers of i to find the following
i1
i
i2
-1
a) Find i 13
i3
-i
i4
1
a) Find i 95
a) Find i 482
Part 3: Polynomials and Factoring
Use the polynomials below to answer the following question
27a9b
5
+ 3y - 4
y2
6x5 +3x2 +11
12m8 -5m6n3
25. Which of the expressions above is NOT a polynomial?
26. Which of the expressions above is a binomial?
Perform the indicated operation
Subtract
27.
Add
(5a - 3a - 7a) - (8a - 10a + 2a - 11)
3
2
Multiply
29.
(x - 4)(2x + 3)
3
2
28.
(6m3 - 2m + 3) + (4m3 + 5m2 - 7)
Multiply
30.
(5h + 3)2
Multiply
31.
(2x - 1)(x 2 + 8x + 5)
Factor completely using the appropriate method. You are not done factoring until
every remaining factor is prime
32. 3a2b7 -12ab11
34.
x2 +13x +30
36. m2 - m-56
33. 2ax +2bx -3a -3b
35.
a2 -14a + 40
37. 10x2 -3x - 4
38. 5x2 +29x - 6
39.
49x2 + 70x +25
40. 9y2 -24y +16
41.
x2 -100
42.
2x3 +14x2 +24x
44.
x 4 - 81
43. 3x3 + x2 -27x - 9
Part 4: Solving Polynomial Equations
Solve each quadratic equation using the method specified
Zero Product Property
45.
x2 + 9x +20 = 0
46.
25x2 -20x +11 = 7
Square Root Method
47.
x2 -50 = 0
Solve using the Quadratic Formula
49.
2x2 - 4x -3 = 0
48.
(2x + 9)
-b ± b2 - 4ac
x=
2a
2
- 49 = 0
50.
5x2 +10x -3 = 0
x=
-b ± b2 - 4ac
2a
51. A student solves a quadratic equation using the quadratic formula. Finish the
student’s work form this point...
x=
-4 ± -20
10
52. Use your knowledge of the discriminant to complete the table.
Discriminant Formula:
Discriminant
Perfect Square
b2 - 4ac
Number of Solutions
Type of Solutions
Two
One
Rational
Imaginary
Positive
Non Perfect
Square
Two
Find the discriminant for the quadratic equations below and predict the number and
type of solution each equation has
53.
55.
x2 + 6x +5 = 0
x2 +5x +2 = 0
54.
x2 -14x + 49 = 0
56.
-2x2 + 6x -5 = 0
Part 5: Graphing Quadratic Functions
Given the quadratic function…
57.
a)
f(x) =2x2 - 8x +1
Find the axis of symmetry
b) Create a table of values and graph
c) Estimate the x-intercepts
HINT: Use formula x =
-b
2a
Graph the quadratic equation below using your knowledge of vertex form
58.
f ( x) = -(x -3)2 + 4
Identify the vertex. Is it a max or min point?
Does this parabola open upwards or downwards?
Identify the x intercept(s)
Identify the y intercept
Find the domain and range
59.
f ( x) = x - 7 + 8
Identify the vertex. Is it a max or min point?
Does the graph of this function open up or down?
Identify the x intercept(s)
Identify the y intercept
Find the domain and range