Unit 1 Notes / Secondary 2 Honors

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1 Unit 1 Notes / Secondary 2 Honors Day 1: Review Linear Equations Graphing and Solving LINEAR EQUATIONS: Slopes of Lines: 1. slope (m) = 2. Horizontal slope = Vertical slope= y y Slope Formula: Point-Slope Form of a Line: Slope-Intercept Form of a line: Write the equation of the line that passes through the given points. Leave answers in Point-Slope form. 3. (4, 2) and (2, -1) 4. (3, -1) and (2, 5) Horizontal and Vertical Lines: Write the equation of the line that passes through the given points. 5. (-2, 3) and (4, 3) 6. (-2, 3) and (-2, 8) -intercept: y-intercept: 7. Find the -intercept and y-intercept for: 4 3y = 6 -int: y-int:

2 Solving Linear Equations: Solve the following equations: 8. 5p 14 = 8p n + 34 = 2(1 7n) 10. 3(4 + 3) + 4(6 + 1) = 43

3 Day 2: Review GCF / Simplifying radicals Greatest Common Factoring: ab c 15a bc 3. 9 y z 15 y z 3 y z Simplify the radicals assume all variables are positive. Pay close attention to the type of root! y y y y 10 3 y Are like terms needed to multiply roots? Are like terms needed to add/subtract roots? Change from root form to fractional eponent form. 14. y p Change from fractional eponent form to root form c

4 Day 3: Review Eponential Functions / Systems of equations Eponentials Definition: An eponential function has the form number other than 1. Are the following functions eponential? 1. 1 y 2 3 y ab where a 0 and the base b is a positive If a > 0 and b > 1 then the function is an eponential growth function If a > 0 and 0 < b < 1 then the function is an eponential decay function 2. y 4 y y y 3.5 Graph the following eponential equations by making a table of values using values of -2, -1, 0, 1 and 2. Plot at least 3 points, draw the asymptote and give the equation of the asymptote, and give the domain and range. Remember arrows where appropriate! 5. y y 3 y y Domain: Range: Domain: Range: Asymptote: Asymptote: 7. Using the graph from #5, investigate the graph of y Asymptote equation: Domain: Range: y Describe how this graph is different from the graph in #5.

5 8. Describe how the graph of y = would be different from the graph of y = Graph y = Quick graphs of eponentials: y Graphs start with: (0, 1) (1, b) -ais asymptote Then shift graph according to etra numbers. SYSTEMS OF EQUATIONS: A system is two or more equations that are solved together. The solution to a system is the point(s) of intersection between the graphs. 10. Solve by substitution. + 3y = 6 2 3y = Solve by elimination: 2 + y = 4 3 2y = Solve using either method: 2y = 9 y = +9 2

6 Day 4: - Midpoint / Distance / Translations Ms. Lopez is planning a treasure hunt for her kindergarten students. She drew a model of the playground on a coordinate plane as shown. She used this model to decide where to place items for the treasure hunt, and to determine how to write the treasure hunt instructions. Each grid square represents one square yard on the playground. 1. Ms. Lopez wants to place some beads in the grass halfway between the merry-go-round and the slide. a. Determine the distance between the merry-go-round and the slide. Eplain your method used. b. How far should the beads be placed from the merry-goround and the slide? c. Write the coordinates for the location eactly half-way between the merry-go-round and the slide. Plot this point. d. How do the - and y-coordinates of the point representing the beads compare to the and y coordinates of the points representing the slide and the merry-go-round? Eplain in a complete sentence. 2. Ms. Lopez wants to place some buttons in the grass halfway between the swings and the merry-go-round. Determine the midpoint between the swings and the merry-go-round. Show your work!

7 The MIDPOINT FORMULA: ( , y 1 + y 2 ) 2 The DISTANCE FORMULA : d ( ) ( y y ) Find the midpoint and the distance for the following points. Show complete work! ( -3, 1) and (9, -7) Midpoint: Distance: TRANSLATION: a rigid motion that slides each point of a figure the same distance and direction. The original figure is called the pre-image and the new figure is called the image. Translate each given line segment or angle on the coordinate plane as described. 4. Translate MN 3 units up 5. Translate DEF 12 units down. 6. Translate NPQ 8 units to the and 10 units to the right. left and 6 units down.

8 Day 5: Inductive & Deductive Reasoning / Logic Statements Vocabulary: Deductive Reasoning: Inductive Reasoning: Eample: 1. Emma considered the following statements. 4 2 = 4 4 Nine cubed is equal to nine times nine times nine. 10 to the fourth power is equal to four factors of 10 multiplied together. She concluded that raising a number to a power is the same as multiplying the number as many times as indicated by the eponent. Rickey read that raising a number to a power is the same as multiplying that number many times as indicated by the eponent. He had to determine seven to the fourth power using a calculator. So, he entered Compare Emma s reasoning to Rickey s reasoning. Decide whether inductive or deductive reasoning is used to reach the conclusion. Eplain your reasoning. 2. Liz knows that Jason is older than Seth. She also knows that Seth is older than Makaela. Liz reasons that Jason is older than Makaela. 3. Jose is told that all garter snakes are not venomous. He sees a garter snake in his backyard and concludes that it is not venomous. 4. The rule at your school is that you must attend all of your classes in order to participate in sports after school. You played in a soccer game after school on Monday. Therefore, you went to all of your classes on Monday. 5. For the past 5 years, you have fed your neighbor s dog on July 4 th while your neighbors were out of town. You conclude that you will be asked to feed their dog on July 4 th net year. 6. Caitlyn has been told that every tai in New York City is yellow. When she sees a red car in New York City, she concludes that it cannot be a tai.

9 Vocabulary: Countereample: a specific eample that shows that a general statement is not true. **To show a statement is false you can provide a countereample. Show the conjecture is FALSE by providing a countereample. 7. The sum of two numbers is always 8. All prime numbers are odd. 9. The value of is always greater greater than the larger number. than the value of. 2 Vocabulary: Conditional If Hypothesis (p), then conclusion(q) p q Inverse Converse switch the hypothesis and the conclusion Contrapositive ~q ~p Eamples: Write the converse, inverse, and contrapositive of each statement. Then determine if the statement is true or false. 10. If a Dog is a Great Dane, then it is large. Converse T F Inverse T F Contrapositive T F 11. If an integer is even, then the integer is divisible by two. Converse T F Inverse T F Contrapositive T F 12. If an angle measure is 122 o, then the angle is an obtuse angle. Converse T F Inverse T F Contrapositive T F

Day 6: Angle Pairs and Relationships Vocabulary: Angles: two angles whose sum is 90 Angles: two angles whose sum is 180 Angles: two angles that share a common side and verte.

10 Day 6: Angle Pairs and Relationships Vocabulary: Angles: two angles whose sum is 90 Angles: two angles whose sum is 180 Angles: two angles that share a common side and verte. Angles: congruent, nonadjacent angles formed by two intersecting lines. : adjacent (net to; share a common side), supplementary angles *Be careful, because there is a difference between supplementary angles and a linear pair. Using the diagram, identify the following: 1. Complementary angles: 2. Vertical Angles: 3. Linear Pair: 4. Supplementary angles: Identify the type of angles given and then find the value of Use the diagram at the right to answer the following questions. 8. If ma 114, find mb, m C, and m D. 9. If md 57, find mc, ma, m B.

11 Solve for and y Parallel Lines and Transversals Vocabulary: Transversal: a line that crosses at least two other lines. Parallel lines: two lines that are in the same plane and never intersect. When parallel lines are intersected by a transversal, several angle pairs are created. Corresponding Angles: Two angles are corresponding angles if they have corresponding positions. These angles are CONGRUENT. Alternate interior angles: Two angles are alternate interior angles if they lie between the two lines and on opposite sides of the transversal. Same-side interior angles: Two angles are same-side interior angles if they lie between the two lines and on the same side of the transversal. These angles are Alternate eterior angles: Two angles are alternate eterior angles if they lie outside the two lines and on opposite sides of the transversal. These angles are Same-side eterior angles: Two angles are same-side eterior angles if they lie outside the two lines and on the same side of the transversal. These angles are These angles are

12 Eample: Classify all possible numbered angles. 12. Corresponding: 13. Alternate interior: 14. Alternate eterior: 15. Same-side interior: 16. Same-side eterior: Eample: Solve for given m is parallel to n or a is parallel to b. Write which angle property you use to justify your math Given mdoc 43 find the measure of: COB DOE BOA EOA 20. Find the missing angles given that m n. m1 m2 m3 m4 m5

Prerequisite Skills Appendix

Prerequisite Skills Appendix Prerequisite Skills Appendi Adding Polnomials To add, add the like terms. 9 1. Add. a) b) 7 6 7 c) 6 d) a a 8 a a 1 e) f) 6a b a b 7 Angle Properties To find the measure of, recall that the sum of the