Algebra1STAARReview

+1

No comments posted yet

Comments

Slide 1

Algebra 1 STAAR Review Basic Algebra Skills: Exponents, Polynomials, Equations & Inequalities by Interactive Algebra

Slide 2

Part 2: Rewriting polynomials using the distributive property Things to remember: when distributing, multiplying the term on the outside of the parenthesis by each term on the inside of the parenthesis the sign in front of a term goes with it! don’t forget to follow the exponent rules! Part 3: Adding and subtracting polynomials of degree one and degree two Things to remember: distribute first to eliminate parenthesis — if there is a minus sign in front of the parenthesis, then distribute a negative one! combine like terms — terms that have the same variables with the same exponents don’t forget to combine constants too! Name: Date: Period: STAAR Review #1: Basic Algebra Skills Part 1: Simplify expressions using the laws of exponents Things to remember: product rule: add the exponents of like bases aman=am+n power rule: multiply the exponent on the outside of the parentheses with exponents on the inside (am)n=amn any term without an exponent has an exponent of 1!!! 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

Slide 3

Part 5: Solve linear equations using the distributive property and with variables on both sides Things to remember: the goal in solving equations is to isolate the variable (get it by itself!) draw the line through the sign, the distribute and combine if necessary, before you start to eliminate what you do to one side you have to do to the other! CHECK YOUR ANSWER!!! Part 6: Solve linear inequalities using the distributive property and with variables on both sides Things to remember: same rules as solving equations! if you multiply or divide by a negative number, you must flip the inequality symbol! Part 4: Multiplying polynomials of degree one and degree two Things to remember: follow all exponent rules use a box to multiply! check your answer by graphing the problem and the answer — if you get the same graph, then you are right! 12. 13. 11. 14. 15. 16. 17.

Slide 4

Name: Date: Period: STAAR Review #1: Basic Algebra Skills Part 1: Simplify expressions using the laws of exponents (A.11B) 33a6b9 -23x3y21 Part 2: Rewriting polynomials using the distributive property (A.10D) Things to remember: when distributing, multiplying the term on the outside of the parenthesis by each term on the inside of the parenthesis the sign in front of a term goes with it! don’t forget to follow the exponent rules! Part 3: Adding and subtracting polynomials of degree one and degree two (A.10A) Things to remember: distribute first to eliminate parenthesis — if there is a minus sign in front of the parenthesis, then distribute a negative one! combine like terms — terms that have the same variables with the same exponents don’t forget to combine constants too! Things to remember: product rule: add the exponents of like bases aman=am+n power rule: multiply the exponent on the outside of the parentheses with exponents on the inside (am)n=amn any term without an exponent has an exponent of 1!!! 24x12y20 24a13b10 36x4y4 4a3-12a2b -3x-4 4xy+4y2-4x+3y+4x2 2x2-10x

Slide 5

Part 5: Solve linear equations using the distributive property and with variables on both sides (A.5A) Things to remember: the goal in solving equations is to isolate the variable (get it by itself!) draw the line through the sign, the distribute and combine if necessary, before you start to eliminate what you do to one side you have to do to the other! CHECK YOUR ANSWER!!! Part 6: Solve linear inequalities using the distributive property and with variables on both sides (A.5B) Things to remember: same rules as solving equations! if you multiply or divide by a negative number, you must flip the inequality symbol! Part 4: Multiplying polynomials of degree one and degree two (A.10B) Things to remember: follow all exponent rules use a box to multiply! check your answer by graphing the problem and the answer — if you get the same graph, then you are right! 5x2-6x-8 -2n2-5n-3 9x2-24x+16 x=32 x=-0.8 x < 1.5 x < 24

Slide 6

Interactive Algebra Thanks for your purchase! I love teaching algebra, and I hope my interactive activities will get your students up and out of their seats, and having fun with math! If you have any comments, questions or concerns, please contact me at in te rac t i ve alge bra16@gmail .com. Please note, this product is for personal classroom use by a single teacher. If you would like to copy this product for more than one teacher, please download additional licenses. You may: • • • • • use this item for your own personal use use this item for your own classroom and/or students copy this item for use in your classroom by your students purchase additional licenses for others to use this item review this item on social media, provided you include a link for it to be purchased directly from Interactive Algebra You may not: • • • give this item to others copy this item for use by others post this item on a website, including a personal website, classroom website, or district website copy or modify any part of this document to offer others for free or for sale • © Copyright 2016. Interactive Algebra. All rights reser ved. Permission is granted to copy pages specifically designed for student or teacher use by the original purchaser or licensee. The reproduction of any other part of this product is strictly prohibited. Copying any part of this product and placing it on the Internet in any form (even a personal/classroom website) is strictly forbidden. Doing so is a violation of the Digital Millennium Copyright Act (DMCA). Credits: Frame: http://the3amteacher.blogspot.com Polka Dot Paper: https://www.teacherspayteachers.com/Store/The-Hazel-Owl Terms of Use: https://www.teacherspayteachers.com/Store/Selling-Strategies

Slide 7

Algebra 1 STAAR Review Describing & Graphing Linear Functions, Equations, and Inequalities by Interactive Algebra

Slide 8

Name: Date: Period: STAAR Review #2: Linear Equations Part 1: Determine Slope from various representations Things to remember: rise over run on a graph change in y divided by change in x in a table 3. (-4.5, 6) & (-8.5, 14) 6. y - 1 = 2(x - 4) 4. (1, 5) & (-10,5) 7. 3x + 8y = 16 5. y = x + 4 when given an equation, you might have to solve for y be careful of the sign! when all else fails, use the slope formula! Part 2: Calculate the rate of change Things to remember: rate of change is the same thing as slope! the label on the slope is “Y per X” For #10-12, calculate the rate of change. 12. Regina had $450 saved up. After 3 months, she had $540. For #1-9, find the slope from each representation. 1. 2. 8. 9. 10. 11.

Slide 9

Part 3: Graph and identify key features Things to remember: begin on B, move with M identify the x and y variables (independent and dependent quantity) to help determine the meaning of different parts of the graph For #13-15, graph the equation and identify the key attributes. 13. y = -1/3x - 5 14. A scuba diver is 40 feet below the surface and is ascending at a rate of 2 feet per minute. 15. 12x - 4y = 16

Slide 10

Part 4: Linear Inequalities Things to remember: solve for y begin on B, move with M if you multiply or divide by a negative, flip the inequality symbol shade! Part 5: Transformations of the Linear Parent Function Things to remember: the linear parent function is f(x)=x outside of f(x) are vertical changes, inside the parenthesis are horizontal changes vocabulary: horizontal compression/stretch/translation left or right, vertical compression/stretch/translation up or down, reflect across x or y axis Describe the changes: 19. 2f(x) 20. f(2x) 21. -f(x) 22. f(-x) 23. f(x-2) 24. f(x+2) 25. f(x)-2 26. f(x)+2 For 16-17, graph the inequality on the given coordinate plane. 16. y < -x + 4 17. 4x - 3y > 12 18. Which ordered pair is not a solution? (0,0) (0,4) (4,-2) (-4,1)

Slide 11

27. y = 1/2x + 4 y = -3/2x - 8 28. y = 2/3x + 1 y = 2/3x - 2 29. 3y = 3x + 6 y = x + 2 32. y < 3 x > 4 Part 6: Graphing Systems Things to remember: solve for y if needed begin on B, move with M the solution is the ordered pair where the two lines meet there are 3 types of solutions: one solution, no solution, and infinitely many solutions For #27-29, graph the system and identify the solution. 33. y > 2/3x - 4 y > -1/2x - 2 34. 3x - 4y > 8 4y > x 30. 31. For #30-31, identify the solution. For #32-34, graph the system.

Slide 12

Name: Date: Period: STAAR Review #2: Linear Equations Part 1: Determine Slope from various representations Things to remember: rise over run on a graph change in y divided by change in x in a table 3. (-4.5, 6) & (-8.5, 14) 4. (1, 5) & (-10,5) 5. y = x + 4 m = 1 6. y - 1 = 2(x - 4) m = 2 7. 3x + 8y = 16 when given an equation, you might have to solve for y be careful of the sign! when all else fails, use the slope formula! Part 2: Calculate the rate of change Things to remember: rate of change is the same thing as slope! the label on the slope is “Y per X” For #10-12, calculate the rate of change. 12. Regina had $450 saved up. After 3 months, she had $540. m = -3/2 8. m = undefined m = -2 m = 0 m = -3/8 m = -4/5 m = 1/4 m = $.50 per topping m = -$2.50 per lunch m = $30 per month For #1-9, find the slope from each representation. 1. 2. 9. 10. 11.

Slide 13

Part 3: Graph and identify key features Things to remember: begin on B, move with M identify the x and y variables (independent and dependent quantity) to help determine the meaning of different parts of the graph # of minutes # of feet 13. y = -1/3x - 5 14. A scuba diver is 40 feet below the surface and is ascending at a rate of 2 feet per minute. 15. 12x - 4y = 16 For #13-15, graph the equation and identify the key attributes.

Slide 14

Part 4: Linear Inequalities Things to remember: solve for y begin on B, move with M if you multiply or divide by a negative, flip the inequality symbol shade! Part 5: Transformations of the Linear Parent Function Things to remember: the linear parent function is f(x)=x outside of f(x) are vertical changes, inside the parenthesis are horizontal changes vocabulary: horizontal compression/stretch/translation left or right, vertical compression/stretch/translation up or down, reflect across x or y axis Which ordered pair is not a solution? (0,0) (0,4) (4,-2) (-4,1) 19. 2f(x) vertical stretch by a factor of 2 20. f(2x) horizontal compression by a factor of 2 reflect across x-axis reflect across y-axis horizontal translation right 2 horizontal translation left 2 vertical translation down 2 vertical translation up 2 16. y < -x + 4 17. 4x - 3y > 12 Describe the changes: 21. -f(x) 22. f(-x) 23. f(x-2) 24. f(x+2) 25. f(x)-2 26. f(x)+2

Slide 15

(-6,1) no solution infinitely many solutions (2.5, 125) (-2.1, -5.4) Part 6: Graphing Systems Things to remember: solve for y if needed begin on B, move with M the solution is the ordered pair where the two lines meet there are 3 types of solutions: one solution, no solution, and infinitely many solutions For #27-29, graph the system and identify the solution. 27. y = 1/2x + 4 y = -3/2x - 8 28. y = 2/3x + 1 y = 2/3x - 2 29. 3y = 3x + 6 y = x + 2 32. y < 3 x > 4 33. y > 2/3x - 4 y > -1/2x - 2 34. 3x - 4y > 8 4y > x 30. 31. For #30-31, identify the solution. For #32-34, graph the system.

Slide 16

Interactive Algebra Thanks for your purchase! I love teaching algebra, and I hope my interactive activities will get your students up and out of their seats, and having fun with math! If you have any comments, questions or concerns, please contact me at in te rac t i ve alge bra16@gmail .com. Please note, this product is for personal classroom use by a single teacher. If you would like to copy this product for more than one teacher, please download additional licenses. You may: • • • • • use this item for your own personal use use this item for your own classroom and/or students copy this item for use in your classroom by your students purchase additional licenses for others to use this item review this item on social media, provided you include a link for it to be purchased directly from Interactive Algebra You may not: • • • give this item to others copy this item for use by others post this item on a website, including a personal website, classroom website, or district website copy or modify any part of this document to offer others for free or for sale • © Copyright 2016. Interactive Algebra. All rights reser ved. Permission is granted to copy pages specifically designed for student or teacher use by the original purchaser or licensee. The reproduction of any other part of this product is strictly prohibited. Copying any part of this product and placing it on the Internet in any form (even a personal/classroom website) is strictly forbidden. Doing so is a violation of the Digital Millennium Copyright Act (DMCA). Credits: Frame: http://the3amteacher.blogspot.com Polka Dot Paper: https://www.teacherspayteachers.com/Store/The-Hazel-Owl Terms of Use: https://www.teacherspayteachers.com/Store/Selling-Strategies

Slide 17

Algebra 1 STAAR Review Write and Solve Linear Functions, Equations, and Inequalities inc. Systems by Interactive Algebra

Slide 18

Name: Date: Period: STAAR Review #3: Write and Solve Linear Functions, Equations and Inequalities Part 1: Determine domain and range from various representations Things to remember: domain: the x values in a representation range: the y values in a representation discrete: data that can be counted, write domain and range as a list continuous: data that can be measured, write domain and range using inequalities 1. 2. 3. 4.

Slide 19

5. Margie sells her homemade cookies by the dozen. She uses the formula y = 2.5x + 7 to determine the cost y, of x dozen cookies. She can make at most 6 dozen cookies at a time. Determine the domain and range of this scenario. Discrete or continuous? (circle one) X represents: Y Represents: Domain: Range: 6. Jorge’s motorcycle has a five gallon gas tank and gets about 50 miles per gallon. Determine a reasonable domain and range for this scenario. Discrete or continuous? (circle one) X represents: Y Represents: Domain: Range: 7. A photographer charges a $75 fee plus $40 per half hour to take pictures at a wedding. If a couple takes pictures for 3 and a half hours, what is the largest value in the range of this situation? Discrete or continuous? (circle one) X represents: Y Represents: Domain: Range: Answer the question being asked: 8. A landscaping company charges a flat fee of $150 plus $15 per plant to plant a flowerbed. If Rory wants between 10 and 15 plants planted in her flowerbed, what is the domain of this situation? Discrete or continuous? (circle one) X represents: Y Represents: Domain: Range: Answer the question being asked: Part 1: Determine domain and range from various representations Things to remember: domain: the x values in a representation range: the y values in a representation discrete: data that can be counted, write domain and range as a list continuous: data that can be measured, write domain and range using inequalities

Slide 20

Part 2: Write linear equations in various forms given a point and slope, or two points Things to remember: always start with the slope first! if slope is not given, use the slope formula if the point is a y-intercept, use slope-intercept form if the point given is not the y-intercept, use point-slope form Write the equation of the line in various forms given the following information:

Slide 21

Part 3: Write linear equations given a table, graph, or verbal description Things to remember: always start with the slope first! if slope is not given, use the slope formula if the point is a y-intercept, use slope-intercept form if the point given is not the y-intercept, use point-slope form look for key words to determine the slope from a word problem: Per, every, each look for the starting point to determine the y-intercept from a word problem to find the constant of variation, divide! A membership to a local gym costs $15 plus $5 every 2 weeks. A farmer charges $20 plus $5 per pound for customers to pick their own vegetables. You start with a $40 gift card and spend $4 per coffee. The number of miles varies directly with the number of gallons in a gas tank. A car can go 60 miles on 2 gallons. Write the direct variation equation. How many miles can the car go on 5 gallons? Write an equation in slope-intercept form for each representation. 12. 13. 14. 15. 16. 17.

Slide 22

Part 4: Parallel and Perpendicular Things to remember: HOY VUX: horizontal, zero slope, y=y-intercept; vertical, undefined slope, x=x-intercept parallel lines have the same slope perpendicular lines have opposite reciprocal slopes 22. Write the equation of the line in slope- intercept form that goes through the point (0,8) and is parallel to y=2/3x + 4. 23. Write the equation of the line in slope-intercept form that goes through the point (0,8) and is perpendicular to y=2/3x + 4. 24. Write the equation of the line in slope- intercept form that goes through the point (-2,1) and is parallel to 3x - 4y = 8. 25. Write the equation of the line in slope- intercept form that goes through the point (-2,1) and is perpendicular to 3x - 4y = 8. Write the equation of a line that goes through the point (-5, 7) and is parallel to the y-axis. Write the equation of a line that goes through the point (-4, 3) and is parallel to the x-axis. Write the equation of a line that goes through the point (4, -2) and is perpendicular to the x-axis. Write the equation of a line that goes through the point (-3, 1) and is perpendicular to the y-axis. Part 5: Writing Inequalities Things to remember: <, < shade below >, > shade above <, > solid line <, > dashed line 30. A rental car costs $25 per day plus $0.15 per mile. You can spend no more than $250. Write an inequality representing this situation where x represents the number of days and y represents the number of miles. 31. 32.

Slide 23

Part 6: Writing and Solving Systems of Equations Things to remember: make sure you write 2 equations! always start with the slope first! if slope is not given, use the slope formula or count rise over run on a graph if the point is a y-intercept, use slope-intercept form if the point given is not the y-intercept, use point-slope form look for key words to determine the slope from a word problem: Per, every, each look for the starting point to determine the y-intercept from a word problem the solution to a system of equations is the point of intersection on a graph, or the ordered pair contained on both lines 38. A combination of 90 quarters and dimes totals $15. Write a system of equations where x represents the number of quarters and y represents the number of dimes. 39. A combination of 15 tickets costs $35. Adult tickets cost $5 and student tickets only cost $1. Write a system of equations where x represents the number of adult tickets and y represents the number of student tickets. Write and solve each system. 33. 34. 36. 35. 37.

Slide 24

Part 7: Solving Equations, Inequalities, and Systems Things to remember: distribute to eliminate parentheses if needed move all variables to one side solve using the opposite operation when solving inequalities, if you multiply or divide by a negative number remember to flip the inequality symbol! methods for solving systems: graphing, elimination, substitution 40. 3(x - 4) + 1.5 = 6(x + 1) 42. 1/2(6x - 4) > 4x + 1 41. -11x + 4.5 < 5(x - 7.5) 43. 2/3(6x - 12) = 4x + 6 44. 1/8(4x - 16) = 0.5x - 2 45. 2(2.3x - 5.4) = 5.5x + 1.8

Slide 25

Part 7: Solving Equations, Inequalities, and Systems Things to remember: distribute to eliminate parentheses if needed move all variables to one side solve using the opposite operation when solving inequalities, if you multiply or divide by a negative number remember to flip the inequality symbol! methods for solving systems: graphing, elimination, substitution 46. Solve by graphing: y=1/3x-4 y=-2/3x+2 47. Solve by graphing: y + 1 = 4/3(x - 5) y - 2 = 4/3(x - 1) 48. Solve by elimination method: 3x + 4y = 16 -3x + 4y = 24 49. Solve by elimination method: x - 7y = 10 -x + 7y = 10 50. Solve by substitution method: y = 2x + 4 4x - 2y = -8

Slide 26

Name: Date: Period: STAAR Review #3: Write and Solve Linear Functions, Equations and Inequalities Part 1: Determine domain and range from various representations Things to remember: domain: the x values in a representation range: the y values in a representation discrete: data that can be counted, write domain and range as a list continuous: data that can be measured, write domain and range using inequalities 1. 2. 3. 4.

Slide 27

5. Margie sells her homemade cookies by the dozen. She uses the formula y = 2.5x + 7 to determine the cost y, of x dozen cookies. She can make at most 6 dozen cookies at a time. Determine the domain and range of this scenario. Discrete or continuous? (circle one) X represents: # of dozens of cookies Y Represents: cost of cookies Domain: 0, 1, 2, 3, 4, 5, 6 Range: 7, 9.5, 12, 14.5, 17, 19.5, 22 6. Jorge’s motorcycle has a five gallon gas tank and gets about 50 miles per gallon. Determine a reasonable domain and range for this scenario. Discrete or continuous? (circle one) X represents: # of gallons Y Represents: # of miles Domain: 0 < x < 5 Range: 0 < y < 250 7. A photographer charges a $75 fee plus $40 per half hour to take pictures at a wedding. If a couple takes pictures for 3 and a half hours, what is the largest value in the range of this situation? Discrete or continuous? (circle one) X represents: # of half hours Y Represents: cost Domain: 0, 1, 2, 3, 4, 5, 6, 7 Range: 75, 115, 155, 195, 235, 275, 315, 355 Answer the question being asked: The largest value in the range is $375. 8. A landscaping company charges a flat fee of $150 plus $15 per plant to plant a flowerbed. If Rory wants between 10 and 15 plants planted in her flowerbed, what is the domain of this situation? Discrete or continuous? (circle one) X represents: # of plants Y Represents: cost Domain: 10, 11, 12, 13, 14, 15 Range: 300, 315, 330, 345, 360, 375 Answer the question being asked: The domain is 10, 11, 12, 13, 14, 15. Part 1: Determine domain and range from various representations Things to remember: domain: the x values in a representation range: the y values in a representation discrete: data that can be counted, write domain and range as a list continuous: data that can be measured, write domain and range using inequalities

Slide 28

Part 2: Write linear equations in various forms given a point and slope, or two points Things to remember: always start with the slope first! if slope is not given, use the slope formula if the point is a y-intercept, use slope-intercept form if the point given is not the y-intercept, use point-slope form Write the equation of the line in various forms given the following information:

Slide 29

Part 3: Write linear equations given a table, graph, or verbal description Things to remember: always start with the slope first! if slope is not given, use the slope formula if the point is a y-intercept, use slope-intercept form if the point given is not the y-intercept, use point-slope form look for key words to determine the slope from a word problem: Per, every, each look for the starting point to determine the y-intercept from a word problem to find the constant of variation, divide! y=-4/3x-3 y=375-15x A membership to a local gym costs $15 plus $5 every 2 weeks.y = 5/2x + 15 A farmer charges $20 plus $5 per pound for customers to pick their own vegetables.y = 5x + 20 20. You start with a $40 gift card and spend $4 per coffee. 21. The number of miles varies directly with the number of gallons in a gas tank. A car can go 60 miles on 2 gallons. Write the direct variation equation. How many miles can the car go on 5 gallons? y = 30x, 150 miles Write an equation in slope-intercept form for each representation. 12. 13. 14. y=-3/2x-8.5 y=0.5x+5 y = 3 x = -1 y = 40-4x 15. 16. 17.

Slide 30

Part 4: Parallel and Perpendicular Things to remember: HOY VUX: horizontal, zero slope, y=y-intercept; vertical, undefined slope, x=x-intercept parallel lines have the same slope perpendicular lines have opposite reciprocal slopes 22. Write the equation of the line in slope- intercept form that goes through the point (0,8) and is parallel to y=2/3x + 4. 23. Write the equation of the line in slope-intercept form that goes through the point (0,8) and is perpendicular to y=2/3x + 4. 24. Write the equation of the line in slope- intercept form that goes through the point (-2,1) and is parallel to 3x - 4y = 8. 25. Write the equation of the line in slope- intercept form that goes through the point (-2,1) and is perpendicular to 3x - 4y = 8. 26. Write the equation of a line that goes through the point (-5, 7) and is parallel to the y-axis. 27. Write the equation of a line that goes through the point (-4, 3) and is parallel to the x-axis. 28. Write the equation of a line that goes through the point (4, -2) and is perpendicular to the x-axis. 29. Write the equation of a line that goes through the point (-3, 1) and is perpendicular to the y-axis. Part 5: Writing Inequalities Things to remember: <, < shade below >, > shade above <, > solid line <, > dashed line 30. A rental car costs $25 per day plus $0.15 per mile. You can spend no more than $250. Write an inequality representing this situation where x represents the number of days and y represents the number of miles. y = 2/3x + 8 y = 3/4x + 2.5 y = -3/2x + 8 y = -4/3x - 5/3 x = -5 y = 3 x = 4 y = 1 25x + .15y < 250 y > 2/5x-5 answers will vary 31. 32.

Slide 31

Part 6: Writing and Solving Systems of Equations Things to remember: make sure you write 2 equations! always start with the slope first! if slope is not given, use the slope formula or count rise over run on a graph if the point is a y-intercept, use slope-intercept form if the point given is not the y-intercept, use point-slope form look for key words to determine the slope from a word problem: Per, every, each look for the starting point to determine the y-intercept from a word problem the solution to a system of equations is the point of intersection on a graph, or the ordered pair contained on both lines y=2x+4 y=-4x-1 y=80x y=400-50x y=-1/3x y=-1/3x-6 f(x)=-4x-8 g(x)=-2x-1 f(x)=500-x g(x)=x 38. A combination of 90 quarters and dimes totals $15. Write a system of equations where x represents the number of quarters and y represents the number of dimes. .25x+.10y=15 x+y=90 39. A combination of 15 tickets costs $35. Adult tickets cost $5 and student tickets only cost $1. Write a system of equations where x represents the number of adult tickets and y represents the number of student tickets. 5x + y = 35 x + y = 15 Write and solve each system. (2.5,9) no solution (3.1, 246.2) (-3.5, 6) (250, 250) (40, 50) (5, 10) 33. 34. 36. 35. 37.

Slide 32

Part 7: Solving Equations, Inequalities, and Systems Things to remember: distribute to eliminate parentheses if needed move all variables to one side solve using the opposite operation when solving inequalities, if you multiply or divide by a negative number remember to flip the inequality symbol! methods for solving systems: graphing, elimination, substitution 40. 3(x - 4) + 1.5 = 6(x + 1) x=-5.5 42. 1/2(6x - 4) > 4x + 1 x < -3 41. -11x + 4.5 < 5(x - 7.5) x > 2.625 43. 2/3(6x - 12) = 4x + 6 no solution 44. 1/8(4x - 16) = 0.5x - 2 infinitely many solutions 45. 2(2.3x - 5.4) = 5.5x + 1.8 x = -14

Slide 33

Part 7: Solving Equations, Inequalities, and Systems Things to remember: distribute to eliminate parentheses if needed move all variables to one side solve using the opposite operation when solving inequalities, if you multiply or divide by a negative number remember to flip the inequality symbol! methods for solving systems: graphing, elimination, substitution 46. Solve by graphing: y=1/3x-4 y=-2/3x+2 47. Solve by graphing: y + 1 = 4/3(x - 5) y - 2 = 4/3(x - 1) no solution 48. Solve by elimination method: 3x + 4y = 16 -3x + 4y = 24 49. Solve by elimination method: x - 7y = 10 -x + 7y = 10 no solution (-4/3,5) 50. Solve by substitution method: y = 2x + 4 4x - 2y = -8 infinitely many solutions (6, -2)

Slide 34

Interactive Algebra Thanks for your purchase! I love teaching algebra, and I hope my interactive activities will get your students up and out of their seats, and having fun with math! If you have any comments, questions or concerns, please contact me at in te rac t i ve alge bra16@gmail .com. Please note, this product is for personal classroom use by a single teacher. If you would like to copy this product for more than one teacher, please download additional licenses. You may: • • • • • use this item for your own personal use use this item for your own classroom and/or students copy this item for use in your classroom by your students purchase additional licenses for others to use this item review this item on social media, provided you include a link for it to be purchased directly from Interactive Algebra You may not: • • • give this item to others copy this item for use by others post this item on a website, including a personal website, classroom website, or district website copy or modify any part of this document to offer others for free or for sale • © Copyright 2016. Interactive Algebra. All rights reser ved. Permission is granted to copy pages specifically designed for student or teacher use by the original purchaser or licensee. The reproduction of any other part of this product is strictly prohibited. Copying any part of this product and placing it on the Internet in any form (even a personal/classroom website) is strictly forbidden. Doing so is a violation of the Digital Millennium Copyright Act (DMCA). Credits: Frame: http://the3amteacher.blogspot.com Polka Dot Paper: https://www.teacherspayteachers.com/Store/The-Hazel-Owl Terms of Use: https://www.teacherspayteachers.com/Store/Selling-Strategies

Slide 35

Algebra 1 STAAR Review Quadratic Functions and Equations by Interactive Algebra

Slide 36

Name: Date: Period: STAAR Review #4: Quadratic Equations Part 1: Determine domain and range Things to remember: domain: the x values in a situation range: the y values in a situation 1. Domain: Range: When the graph has arrows on both ends: domain: all real numbers range: opens up y > #, down y < # 2. Domain: Range: 3. Domain: Range: y = x2 - 3 4.Domain: Range: Range: Range: The height of an object dropped off a building can be determined by the function h(t) = -16t2 + 45. 5. Domain: 6. Domain: A quadratic function contains the given points in the table below. For problems #4-6, sketch the graph below.

Slide 37

Part 2: Writing Quadratic Equations Things to remember: if given solutions, used factored form if given a graph, or a point on the graph and the vertex, use vertex form 7. Write a quadratic equation containing the point (-2,17) with a vertex at (4,-1) in vertex form. Convert to standard form: 8. Write a quadratic equation with the given solutions x = -4, 8 in standard form. 9. Write a quadratic equation from the given graph in vertex form: Convert to standard form: 10. Write a quadratic equation from the given graph in standard form:

Slide 38

Part 3: Graph and identify key features Things to remember: x-intercepts are also called: roots, solutions, zeros, horizontal intercepts vertex: turning point, located on the axis of symmetry maximum or minimum value is the y value of the vertex and depends on which direction the parabola opens identify the x and y variables (independent and dependent quantity) to help determine the meaning of different parts of the graph 11. 12. 13. time in seconds distance from ground in feet

Slide 39

Part 4: Linear factors and quadratic zeros Things to remember: a quadratic equation is created by multiplying two linear equations together when graphed separately, the linear factors share the same x-intercepts as the quadratic function! 14. Factor: 2x2 + 5x - 12 Graph each linear factor on the given graph Part 5: Transformations of the Quadratic Parent Function Things to remember: the quadratic parent function is f(x)=x2 outside of f(x) are vertical changes, inside the parenthesis are horizontal changes vocabulary: horizontal compression/stretch/translation left or right, vertical compression/stretch/translation up or down, reflect across x or y axis 15. Describe the changes: 3f(x) 1/3f(x) f(3x) f(1/3x) f(x-3) f(x+3) f(x)-3 f(x)+3 -f(x) f(-x) -2f(x)-4 f(x+3)-5 f(-1/2x)-2 1/3f(x-2)

Slide 40

Part 6: Solving Quadratic Equations Things to remember: there are several methods for solving: graphing, quadratic formula, factoring, completing the square, and square root method the easiest method is graphing: set equal equal to zero, graph and find x-intercepts there are 3 types of solutions: 1 solution (1 x-intercept/vertex), 2 solutions (2 x-intercepts), no solution (no x-intercepts) 16. Solve by factoring: x2 + 4x - 12 = 0 17. Solve by quadratic formula: x2 + 5x - 10 = 0 19. Solve by completing the square: x2 + 4x = 10 18 Solve by square root method: 4x2 - 72 = 0

Slide 41

20. Solve by graphing: x2 + 6x = 9 21. Solve by any method: (2x-3)2 = 12 Part 7: Quadratic Regressions Things to remember: use graphing technology to make a table and perform the regression use the new equation to make a prediction: when given specific values for x, substitute them in to find y Equation: Given the equation, what is the value of y when x = 4?

Slide 42

Name: Date: Period: STAAR Review #4: Quadratic Equations Part 1: Determine domain and range Things to remember: domain: the x values in a situation range: the y values in a situation 1. Domain: y = x2 - 3 y < 1 Range: When the graph has arrows on both ends: domain: all real numbers range: opens up y > #, down y < # 2. Domain: 0 < y < 1.55 Range: 3. Domain: -2 < y < 7 Range: 4.Domain: 0 < t < 1.7 0 < h(t) < 45 Range: 5. Domain: all real numbers y < 5 Range: Range: The height of an object dropped off a building can be determined by the function h(t) = -16t2 + 45. A quadratic function contains the given points in the table below. 6. Domain: For problems #4-6, sketch the graph below. KEY all real numbers 0 < x < 1 -6 < x < 0 all real numbers y > -3

Slide 43

Part 2: Writing Quadratic Equations Things to remember: if given solutions, used factored form if given a graph, or a point on the graph and the vertex, use vertex form 8. Write a quadratic equation with the given solutions x = -4, 8 in standard form. 10. Write a quadratic equation from the given graph in standard form: 7. Write a quadratic equation containing the point (-2,17) with a vertex at (4,-1) in vertex form. y=1/2(x-4)2-1 Convert to standard form: y=1/2x2 -4x + 7 y=x2 - 4x - 32 9. Write a quadratic equation from the given graph in vertex form: y = -3(x+1)2 - 2 Convert to standard form: y = -3x2 - 6x - 5 y = 2/3x2 + 2x - 12

Slide 44

Part 3: Graph and identify key features Things to remember: x-intercepts are also called: roots, solutions, zeros, horizontal intercepts vertex: turning point, located on the axis of symmetry maximum or minimum value is the y value of the vertex and depends on which direction the parabola opens identify the x and y variables (independent and dependent quantity) to help determine the meaning of different parts of the graph 11. 12. 13. time in seconds distance from ground in feet

Slide 45

Part 4: Linear factors and quadratic zeros Things to remember: a quadratic equation is created by multiplying two linear equations together when graphed separately, the linear factors share the same x-intercepts as the quadratic function! f(1/3x) f(x-3) 14. Factor: 2x2 + 5x - 12 Graph each linear factor on the given graph Factors: (2x-3)(x+4) Part 5: Transformations of the Quadratic Parent Function Things to remember: the quadratic parent function is f(x)=x2 outside of f(x) are vertical changes, inside the parenthesis are horizontal changes vocabulary: horizontal compression/stretch/translation left or right, vertical compression/stretch/translation up or down, reflect across x or y axis 15. Describe the changes: 3f(x) vertical stretch by a factor of 3 1/3f(x) vertical compression by a factor of 1/3 f(3x) f(x+3) horizontal translation left 3 f(x)-3 f(x)+3 -f(x) vertical reflection (across x-axis) f(-x) -2f(x)-4 vertical reflection vertical stretch by a factor of 2 vertical translation down 4 f(x+3)-5 horizontal translation left 3 vertical translation down 5 f(-1/2x)-2 horizontal reflection horizontal stretch by a factor of 1/2 vertical translation down 2 1/3f(x-2) vertical compression by a factor of 1/3 horizontal translation right 2 horizontal compression by a factor of 3 horizontal stretch by a factor of 1/3 horizontal translation right 3 vertical translation down 3 vertical translation up 3 horizontal reflection (across y-axis)

Slide 46

Part 6: Solving Quadratic Equations Things to remember: there are several methods for solving: graphing, quadratic formula, factoring, completing the square, and square root method the easiest method is graphing: set equal equal to zero, graph and find x-intercepts there are 3 types of solutions: 1 solution (1 x-intercept/vertex), 2 solutions (2 x-intercepts), no solution (no x-intercepts) 16. Solve by factoring: x2 + 4x - 12 = 0 17. Solve by quadratic formula: x2 + 5x - 10 = 0 x = -6, 2 19. Solve by completing the square: x2 + 4x = 10 18 Solve by square root method: 4x2 - 72 = 0

Slide 47

20. Solve by graphing: x2 + 6x = 9 21. Solve by any method: (2x-3)2 = 12 Part 7: Quadratic Regressions Things to remember: use graphing technology to make a table and perform the regression use the new equation to make a prediction: when given specific values for x, substitute them in to find y Equation: y = -4x2-7x+12 Given the equation, what is the value of y when x = 4? y = -80 x = -7.2, 1.2

Slide 48

Interactive Algebra Thanks for your purchase! I love teaching algebra, and I hope my interactive activities will get your students up and out of their seats, and having fun with math! If you have any comments, questions or concerns, please contact me at in te rac t i ve alge bra16@gmail .com. Please note, this product is for personal classroom use by a single teacher. If you would like to copy this product for more than one teacher, please download additional licenses. You may: • • • • • use this item for your own personal use use this item for your own classroom and/or students copy this item for use in your classroom by your students purchase additional licenses for others to use this item review this item on social media, provided you include a link for it to be purchased directly from Interactive Algebra You may not: • • • give this item to others copy this item for use by others post this item on a website, including a personal website, classroom website, or district website copy or modify any part of this document to offer others for free or for sale • © Copyright 2016. Interactive Algebra. All rights reser ved. Permission is granted to copy pages specifically designed for student or teacher use by the original purchaser or licensee. The reproduction of any other part of this product is strictly prohibited. Copying any part of this product and placing it on the Internet in any form (even a personal/classroom website) is strictly forbidden. Doing so is a violation of the Digital Millennium Copyright Act (DMCA). Credits: Frame: http://the3amteacher.blogspot.com Polka Dot Paper: https://www.teacherspayteachers.com/Store/The-Hazel-Owl Terms of Use: https://www.teacherspayteachers.com/Store/Selling-Strategies

Slide 49

Algebra 1 STAAR Review Writing and Graphing Exponential Functions by Interactive Algebra

Slide 50

Name: Date: Period: STAAR Review #5: Exponential Functions Part 1: Determine domain and range from various representations Things to remember: domain: the x values in a representation range: the y values in a representation discrete: data that can be counted, write domain and range as a list continuous: data that can be measured, write domain and range using inequalities 4. An exponential function containing the following points: 5. An exponential function given the equation below: y=2/3(4)x 1. 2. 3.

Slide 51

Part 2: Write and Interpret Exponential Equations Things to remember: exponential functions are written in the form y=abx, where a is the starting point (y-intercept) and b is the rate of change when b > 1, the function is exponential growth when 0 < b < 1, the function is exponential decay 12. You purchase a used car for $5,000 and discover that it decreases 10% per year. Write the equation that represents this situation. What is the value of a and what does it represent? What is the value of b and what does it represent? Write the equation for each representation. 6. 7. 13. You purchase rare baseball card for $250 and discover that it increases 12% per year. Write the equation that represents this situation. What is the value of a and what does it represent? What is the value of b and what does it represent? 8. 9. 10. 11.

Slide 52

Part 3: Graph and identify key features Things to remember: the y-intercept is where the graph crosses the y-axis an increasing function is exponential growth a decreasing function is exponential decay every exponential function has an asymptote, a horizontal line that the graph approaches but never crosses 14. 15. 16.

Slide 53

Part 3: Graph and identify key features Things to remember: the y-intercept is where the graph crosses the y-axis an increasing function is exponential growth a decreasing function is exponential decay every exponential function has an asymptote, a horizontal line that the graph approaches but never crosses Graph each representation and identify the key features. y=2(1/4)x y=500(1.05)x Part 4: Exponential Regressions Things to remember: use graphing technology to make a table and perform the regression use the new equation to make a prediction: when given specific values for x, substitute them in to find y 20. The table represents the value of an antique table over time. Find the equation. 21. What is the value of the table after 1- years? 22. Find the equation of the table and write the equation in function notation. 23. What is g(-8)? 17. 18. 19.

Slide 54

Name: Date: Period: STAAR Review #5: Exponential Functions Part 1: Determine domain and range from various representations Things to remember: domain: the x values in a representation range: the y values in a representation discrete: data that can be counted, write domain and range as a list continuous: data that can be measured, write domain and range using inequalities 4. An exponential function containing the following points: 5, An exponential function given the equation below: y=2/3(4)x 1. 2. 3.

Slide 55

Part 2: Write and Interpret Exponential Equations Things to remember: exponential functions are written in the form y=abx, where a is the starting point (y-intercept) and b is the rate of change when b > 1, the function is exponential growth when 0 < b < 1, the function is exponential decay 12. You purchase a used car for $5,000 and discover that it decreases 10% per year. Write the equation that represents this situation. y=5000(.9)x What is the value of a and what does it represent? a = 5000, starts at $5000 What is the value of b and what does it represent? b = 90%, the rate is 90% or 10% decrease y=1/3*6x y=2*4x y=1/8x y=2000*.8x Write the equation for each representation. 6. 7. y=2*3x y=2*1/4x 13. You purchase rare baseball card for $250 and discover that it increases 12% per year. Write the equation that represents this situation. y=250(1.12)x What is the value of a and what does it represent? a = 250, starts at $250 What is the value of b and what does it represent? b = 1.12%, the rate is 112% or 12% increase 8. 9. 10. 11.

Slide 56

Part 3: Graph and identify key features Things to remember: the y-intercept is where the graph crosses the y-axis an increasing function is exponential growth a decreasing function is exponential decay every exponential function has an asymptote, a horizontal line that the graph approaches but never crosses 14. 15. 16.

Slide 57

Part 3: Graph and identify key features Things to remember: the y-intercept is where the graph crosses the y-axis an increasing function is exponential growth a decreasing function is exponential decay every exponential function has an asymptote, a horizontal line that the graph approaches but never crosses Graph each representation and identify the key features. y=2(1/4)x 19. y=500(1.05)x Part 4: Exponential Regressions Things to remember: use graphing technology to make a table and perform the regression use the new equation to make a prediction: when given specific values for x, substitute them in to find y y=750*1.15^x $3034 20. The table represents the value of an antique table over time. Find the equation. 21. What is the value of the table after 1- years? 22. Find the equation of the table and write the equation in function notation. 23. What is g(-8)? y=1/2^x 256 17. 18.

Slide 58

Interactive Algebra Thanks for your purchase! I love teaching algebra, and I hope my interactive activities will get your students up and out of their seats, and having fun with math! If you have any comments, questions or concerns, please contact me at in te rac t i ve alge bra16@gmail .com. Please note, this product is for personal classroom use by a single teacher. If you would like to copy this product for more than one teacher, please download additional licenses. You may: • • • • • use this item for your own personal use use this item for your own classroom and/or students copy this item for use in your classroom by your students purchase additional licenses for others to use this item review this item on social media, provided you include a link for it to be purchased directly from Interactive Algebra You may not: • • • give this item to others copy this item for use by others post this item on a website, including a personal website, classroom website, or district website copy or modify any part of this document to offer others for free or for sale • © Copyright 2016. Interactive Algebra. All rights reser ved. Permission is granted to copy pages specifically designed for student or teacher use by the original purchaser or licensee. The reproduction of any other part of this product is strictly prohibited. Copying any part of this product and placing it on the Internet in any form (even a personal/classroom website) is strictly forbidden. Doing so is a violation of the Digital Millennium Copyright Act (DMCA). Credits: Frame: http://the3amteacher.blogspot.com Polka Dot Paper: https://www.teacherspayteachers.com/Store/The-Hazel-Owl Terms of Use: https://www.teacherspayteachers.com/Store/Selling-Strategies

URL:
More by this User
Most Viewed