
Algebra 1 STAAR Review Basic Algebra Skills: Exponents, Polynomials, Equations & Inequalities by Interactive Algebra
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.
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.
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 4a312a2b 3x4 4xy+4y24x+3y+4x2 2x210x
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! 5x26x8 2n25n3 9x224x+16 x=32 x=0.8 x < 1.5 x < 24
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/TheHazelOwl Terms of Use: https://www.teacherspayteachers.com/Store/SellingStrategies
Algebra 1 STAAR Review Describing & Graphing Linear Functions, Equations, and Inequalities by Interactive Algebra
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 #1012, calculate the rate of change. 12. Regina had $450 saved up. After 3 months, she had $540. For #19, ﬁnd the slope from each representation. 1. 2. 8. 9. 10. 11.
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 #1315, 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
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(x2) 24. f(x+2) 25. f(x)2 26. f(x)+2 For 1617, 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)
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 #2729, 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 #3031, identify the solution. For #3234, graph the system.
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 #1012, 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 #19, ﬁnd the slope from each representation. 1. 2. 9. 10. 11.
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 #1315, graph the equation and identify the key attributes.
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 xaxis reﬂect across yaxis 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(x2) 24. f(x+2) 25. f(x)2 26. f(x)+2
(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 #2729, 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 #3031, identify the solution. For #3234, graph the system.
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/TheHazelOwl Terms of Use: https://www.teacherspayteachers.com/Store/SellingStrategies
Algebra 1 STAAR Review Write and Solve Linear Functions, Equations, and Inequalities inc. Systems by Interactive Algebra
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.
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
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 yintercept, use slopeintercept form if the point given is not the yintercept, use pointslope form Write the equation of the line in various forms given the following information:
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 yintercept, use slopeintercept form if the point given is not the yintercept, use pointslope form look for key words to determine the slope from a word problem: Per, every, each look for the starting point to determine the yintercept 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 slopeintercept form for each representation. 12. 13. 14. 15. 16. 17.
Part 4: Parallel and Perpendicular Things to remember: HOY VUX: horizontal, zero slope, y=yintercept; vertical, undeﬁned slope, x=xintercept 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 slopeintercept 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 yaxis. Write the equation of a line that goes through the point (4, 3) and is parallel to the xaxis. Write the equation of a line that goes through the point (4, 2) and is perpendicular to the xaxis. Write the equation of a line that goes through the point (3, 1) and is perpendicular to the yaxis. 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.
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 yintercept, use slopeintercept form if the point given is not the yintercept, use pointslope form look for key words to determine the slope from a word problem: Per, every, each look for the starting point to determine the yintercept 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.
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
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=1/3x4 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
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.
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
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 yintercept, use slopeintercept form if the point given is not the yintercept, use pointslope form Write the equation of the line in various forms given the following information:
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 yintercept, use slopeintercept form if the point given is not the yintercept, use pointslope form look for key words to determine the slope from a word problem: Per, every, each look for the starting point to determine the yintercept from a word problem to ﬁnd the constant of variation, divide! y=4/3x3 y=37515x 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 slopeintercept form for each representation. 12. 13. 14. y=3/2x8.5 y=0.5x+5 y = 3 x = 1 y = 404x 15. 16. 17.
Part 4: Parallel and Perpendicular Things to remember: HOY VUX: horizontal, zero slope, y=yintercept; vertical, undeﬁned slope, x=xintercept 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 slopeintercept 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 yaxis. 27. Write the equation of a line that goes through the point (4, 3) and is parallel to the xaxis. 28. Write the equation of a line that goes through the point (4, 2) and is perpendicular to the xaxis. 29. Write the equation of a line that goes through the point (3, 1) and is perpendicular to the yaxis. 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 > 2/5x5 answers will vary 31. 32.
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 yintercept, use slopeintercept form if the point given is not the yintercept, use pointslope form look for key words to determine the slope from a word problem: Per, every, each look for the starting point to determine the yintercept 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=4x1 y=80x y=40050x y=1/3x y=1/3x6 f(x)=4x8 g(x)=2x1 f(x)=500x 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.
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
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=1/3x4 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)
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/TheHazelOwl Terms of Use: https://www.teacherspayteachers.com/Store/SellingStrategies
Algebra 1 STAAR Review Quadratic Functions and Equations by Interactive Algebra
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 #46, sketch the graph below.
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:
Part 3: Graph and identify key features Things to remember: xintercepts 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
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 xintercepts 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(x3) 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(x2)
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 xintercepts there are 3 types of solutions: 1 solution (1 xintercept/vertex), 2 solutions (2 xintercepts), no solution (no xintercepts) 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
20. Solve by graphing: x2 + 6x = 9 21. Solve by any method: (2x3)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?
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 #46, sketch the graph below. KEY all real numbers 0 < x < 1 6 < x < 0 all real numbers y > 3
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(x4)21 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
Part 3: Graph and identify key features Things to remember: xintercepts 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
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 xintercepts as the quadratic function! f(1/3x) f(x3) 14. Factor: 2x2 + 5x  12 Graph each linear factor on the given graph Factors: (2x3)(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 xaxis) 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(x2) 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 yaxis)
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 xintercepts there are 3 types of solutions: 1 solution (1 xintercept/vertex), 2 solutions (2 xintercepts), no solution (no xintercepts) 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
20. Solve by graphing: x2 + 6x = 9 21. Solve by any method: (2x3)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 = 4x27x+12 Given the equation, what is the value of y when x = 4? y = 80 x = 7.2, 1.2
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/TheHazelOwl Terms of Use: https://www.teacherspayteachers.com/Store/SellingStrategies
Algebra 1 STAAR Review Writing and Graphing Exponential Functions by Interactive Algebra
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.
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 (yintercept) 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.
Part 3: Graph and identify key features Things to remember: the yintercept is where the graph crosses the yaxis 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.
Part 3: Graph and identify key features Things to remember: the yintercept is where the graph crosses the yaxis 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.
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.
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 (yintercept) 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.
Part 3: Graph and identify key features Things to remember: the yintercept is where the graph crosses the yaxis 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.
Part 3: Graph and identify key features Things to remember: the yintercept is where the graph crosses the yaxis 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.
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/TheHazelOwl Terms of Use: https://www.teacherspayteachers.com/Store/SellingStrategies
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