1. Sem Exam Review Test: Solving
1) Be able to solve equations (using my notes Steps for Solving Equations).
2/5x = 4/5x
2 (3x + 5) = 4x

2. 2) Be able to solve inequalities (using my notes Steps for Solving Equations).
When do you reverse the less than / greater than sign?
-4x > (+11)
4 (2x - 5) < 3 (4x + 8)

3. 3) Be able to solve Absolute Value equations.
Know that Absolute Value has 2 answers so you need 2 equations.
What is the rule for setting up the two equations?
| 2x | = 15
| -4x | = 12

4. ( )( ) ( )( ) ( )( ) x2 + 3x - 18 = 0 x2 - 7x + 12 = 0 x2 + x - 20 = 0
4) Be able to factor x2 + bx + c = 0 quadratics.
Be able to find the values for x that make the equation true.
What is the rule for solving?
x2 + 3x - 18 = 0
x2 - 7x + 12 = 0
x2 + x - 20 = 0
( )( )
( )( )
( )( )
x = _____ , _____
x = _____ , _____
x = _____ , _____

5. -( ) ( )2 - 4( )( ) ± √ ( ) ( ) 2( ) ( ) ( ) ( ) ( ) ( ) ( )
5) Be able to solve quadratics by setting up and simplifying the Quadratic Formula.
Given the 2 solutions to a quadratic, be able to write
them in factored form (with integer coefficients).
6x2 + 7x - 20 = 0 6)
2/5 and -3/4
x =
-( ) ( )2 - 4( )( ) √
( ) ( )
2( )
( ) ( )
x =
7/3 and -4/9
( ) ( )
( ) ( )

6. 7) Be able to simplify radicals (Church of Square Root).
You must show the factoring for credit.

7. 5x2 - 8 = 12 8) Be able to solve equations that contain x2.
How do you cancel out the exponent?
When you solve for x2, how many answers do you get?
5x2 - 8 = 12

8. x2 + 6x + 8 = y x2 - 5x - 3 = y ( )2 = ( )2 = ( )2 = y ( )2 = y
9) Be able to Complete the Square. Show work.
(1/2 the number, square the number, move it on back)
x x = y
x x = y
( ) =
( ) =
( ) = y
( ) = y

9. Review Test: Finding Zeroes
10) Divide using long division. Show work.
4x2 - 3
32x x x x

10. 11) List the possible Rational Zeroes for these polynomials.
3x8 + 7x4 - 5x3 + 2x2 - 8x + 10
- 4x5 + 3x3 - 2x - 14
12) Write these roots as factors with integer coefficients.
4 , -7 , 2/3
x =
-3 , -3/4 , 8/3
x =
( ) ( ) ( )
( ) ( ) ( )

11. 13) Synthetic Substitution on these polynomials. Show work.
Write the answer in (x , y) form.
f(-2) = 4x3 + 6x2 - 3x + 9
f(2) = 3x3 - 5x2 - 4x - 5
( , )
( , )
14) Use Synthetic Division to divide these polynomials.
Write answer in (x - h) (ax2 + bx + c) form.
x3 - 12x2 + 35x ÷ (x - 3)
2x3 + 2x2 - 8x - 8 ÷ (x + 1)
( ) ( )
( ) ( )

12. 15) Factor fully. Use the Quadratic Formula to find the fractional roots.
Show work. Fill in (ax + b) properly.
4x3 - 12x2 - x + 15
( ) ( )
( ) ( ) ( )

13. 16) Use the Graphing Calculator to find the x-intercepts.
Write the zeroes on the blanks, and then use them to get the factors. Use the rational zeroes list to find the fractional values for decimal answers. Write the zeroes as factors with integer coefficients.
3x3 + 19x2 + 4x - 12
2x3 - 3x2 - 14x + 15
x = ______ , ______ , ______
x = ______ , ______ , ______
( ) ( ) ( )
( ) ( ) ( )

14. 17)
18)

18. 26) State the x-intercepts
26) State the x-intercepts. Circle all the x-intercept values where the graph will “bounce”. Sketch the graph

19. Review Test: Using Trig
Use the Pythagorean thm (a2 + b2 = c2) or a trig function (sin, cos, tan) to find the value of the variable. Show work.

21. Use the Law of Cosines to find the indicated value
Use the Law of Cosines to find the indicated value. Round answers off to 1 decimal place.
Law of Cosines: a2 = b2 + c2 - 2bc cos A or cos A =

22. Review Test: Shift Rules & Transformations