Factoring Review Types of Factoring: 1. GCF: a. b.

Transcription

1 Factoring Review Types of Factoring: 1. GCF: a. b. Ex. A B DOS: a. b. c. Ex. A. 9 B Plain x Trinomials: Start Signs Factors Ex. A B. 2 3

2 4. Non-Plain x Trinomials: a. b. c. Ex. A B Grouping: a. b. c. Ex. A B PST: a. b. c. Ex. A B

3 Unit One Order of operations has turned into a -step plan 1. Groupings 2. Exponents 3. Multiplication 4. Addition You use these rules to simplify and evaluate expressions. Simplify. Evaluate. A. 4 2[7 5(2 3)] B. when = 2 and = 3 C. 3[2(5 + 4) 3(7 + 3)] D. ( ) 2 when = 6, = 0.4, =, = 3 Practice Problems: Simplify each expression [3(5 )+ 5( )] 2. 4(14 10 ) 5( + 4 ) 3. ( ) (19 8 ) [3( 2) 4 8] ( 3 4 ) ( 15) [3 2(4 + 3)]

4 Evaluate each variable expression for = 3, = 2, = ( ) This is technically an order of operations question: (2 7)(3 + 4) BUT what should you do/think when you see this type? or (any other names?) How do you know that this what you do? What exactly does that mean? What format do you like best? There are a few to choose from, you use what you like the best! Don t be afraid to try something different if you have trouble with the way you were taught. Here are few of my favorite ways to organize the work! Practice with these! 13. (4 + 5)(3 7) 14. (2 3 )(4 5 ) 15. (7 + 10)(7 10) 16. (3 2 )(5 2 1) 17. ( + ) 18. (2 11 )

5 Unit One Solving Equations To Solve: A) Undo by doing the opposite to EACH side of the equation. B) Undo by doing the opposite to EACH side of the equation. C) There are possible solutions: 1. (Contradiction) 2. (Conditional) 3. (Identity) D) Always!!!!!! You can use the calculator for this! Solve each of the following. SHOW ALL WORK! A. 10 = B = 487 C. 5 9 = 3( 7) D. + = E. = F. = Determine the type of solution for each equation. G. + 1 = + 4 H. 5(3 2) 7( 4)=

6 Now try these: = = = ( 3) 5 = 4( 5) (1 2 )= 4 3( + 1) 6. 5 = 3 7. = (hint: cross multiply) 8. = (hint: cross multiply) Classify each equation as a contradiction, a conditional, or an identity. 9. 3( 5)= = 3( 1) 11. = + 8

7 Unit One Lines Slope: Equation for Slope: 4 Types: Slope-Intercept Form: = + where m = and b = Find the slope of each of the following. SHOW ALL WORK! A. (7,2),(1,1) B. ( )= C. (2,3),(2,9) D. ( 3, 5),(6, 5) Writing Equations: Given the slope and a point: Given 2 points: = and it goes through the point ( 2,4) (1,2),( 4,7) A) Find the slope between the two points (m). 1) Start with = + form and 1) Plug what you know into = +. fill in what you can. Pick one of the points and plug it in for and. 2) Solve for. 2) Solve for. Write the equation of the following. SHOW ALL WORK! The line between (8, 4) and (10, 7)

8 Now practice these. 1. Find the slope between (3, 7) and (3,2). 2. Find the slope between ( 3,4) and( 4, 2). 3. Find the equation of the line with = 0, and =. 4. Find the equation of the line through ( 3,2) and = Find the equation of the line through (3,1) and ( 1,4).

9 Unit One Parallel and Perpendicular Lines Parallel Lines: Lines that will never and will have the same. = 2 = = 2 5 Perpendicular Lines: lines that intersect at a and will have. = 2 = Tell whether the lines are parallel, perpendicular or neither. SHOW ALL WORK! A. a) = + 3 B. a) = 2 C. a) 8 4 = 10 b) = 2 b) = b) = 2 ma mb ma mb ma mb parallel perpendicular neither parallel perpendicular neither parallel perpendicular neither Find the equation of the specified line. SHOW ALL WORK! A. The line parallel to = through the B. The line perpendicular to = through point (1, 2). the point (1, 2). 1) Determine your slope 1) Determine your slope 2) Plug in slope and point 2) Plug in slope and point 3) Simplify 3) Simplify

10 Recall Graphing Lines: 1. Make a t-chart with at least 3-5 values. 2. Graph the points. 3. Connect the points. Examples: Graph each of the following equations. A. + = 4 B. 2 + = 2 x y x y 1. Find the equation of the line parallel to = + 3 and passes through the point ( 4,2). 2. Find the equation of the line perpendicular to 4 = 6 and passes through the point (5,2). 3. Graph the function by first finding several points: = Graph the function by first finding several points: 3 = 9 x y x y

11 Unit One Interval and Set Builder notation Old notation: Graph the following. A. 5 B. 3 < 4 C. < 1 New way to graph: A. 5 B. 3 < 4 C. < 1 2 new ways to write: 1. Notation: A. B. C. 2. Notation: A. B. C. Practice Problems: Graph each using the interval method (new way). Rewrite the inequality in both interval and set builder notation. A. < 3 B. 2 C. 5 3 D. 3 < 7

12 Intersection ( ) VS. Union ( ) It s best to graph first so you know what you are actually looking at. Graph the following and rewrite in the opposite form: D. { 2 < 4 5 7} E. ( 2,3) [0, ) You try it one more time! 1. > < < < 5 5. { 4 < 2 3 < 0} 6. [0,6] (,3)