Algebra Practice Set Expressions *Evaluate number and algebraic expressions using rational numbers and Order of Operations *Translate algebraic expressions into words using appropriate language *Write algebraic expressions to represent real world situations and solve problems 1. What is the value of: 5 + 2 4 6 7 2 24 3 + 26 (1/2) 5 2. Write the following algebraic expressions in words: r + 21 n 6 s 6 3. Write algebraic expressions for the following: 7 less than 3 times a number 3 times the sum of a number and 5 The quotient of the sum of x plus 4 and 2 4. Evaluate the expression 4x + 2y when x is equal to 5 and y is equal to 3.4. 1 5. Evaluate 5(n + 3) 7n, when n =. 2
6. Evaluate the following expression when x = 4 and y = 2: x 2 y 3 3 7. It costs $150 to rent the skating rink plus $5 per person. Write an expression to find the cost for any number (n) of people. What is the cost for 30 people? 8. The expression c + 0.07c can be used to find the total cost of an item with 7% sales tax, where c is the cost of the item before tax. Use the expression to find the total cost of an item that cost $40. Properties and Expressions *Use number properties to simplify expressions into an equivalent expression *Model the Distributive Property using an area model *Use the Distributive Property to factor expressions and write equivalent expressions 9. Use the distributive property to write an algebraic expression for the finding the area of the flower bed below. x 4 5.5 Tulips Roses 10. Use the distributive property to find the dimensions of the rectangle with the given area below. 20x 15 11. What is the length and width of the rectangle below? 2a 6b
12. Write an equivalent expression for 7(x + 5) 9. 13. An equilateral triangle has a perimeter of 9x + 15. What is the length of each side of the triangle? 14. Write an equivalent expression for 5(x + 4) + 2(x + 3) Equations *Write and solve simple equations to represent real world situations *Solve equations with rational and integer values *Write and solve linear equations to represent relationships between two variables *Use models to explain and justify equations and linear equations in context 15. Joey had 34 papers in his desk. His teacher gave him some more and now he has 80. How many papers did his teacher give him? Write an equation and solve. 16. A country fair charges $18 to enter and $0.50 per ticket. Write a linear equation to represent the total amount cost (C) for any number of tickets. 17. Anthony has a summer job doing yard work. He is paid $20 per hour and a $25 bonus when he completes the yard. He was paid $85 for completing one yard. Write and solve an equation to represent the amount of money he earned and find the number of hours he worked. 18. Describe a problem situation that can be solved using the equation 2c + 3 = 15; where c represents the cost of an item 19. Meghan spent $56.58 on three pairs of jeans, as is shown in the model below. If each pair of jeans costs the same amount, write an algebraic equation that represents this situation and solve to determine how much one pair of jeans cost. $56.58 J J J 20. Jahra got paid $30 for babysitting. She spends $2.99 on a birthday card and $8.50 on lunch. Write and solve an equation to show how much money Jahra has left. Make a model to represent this situation.
21. Write a linear equation that illustrates the relationship between the two variables in the table below. x 1 2 3 4 y 2.5 5 7.5 10 22. Given a square patio as shown in the picture, write at least two different linear equations to find the total number of tiles in the border. Let T represent the total number of tiles and L represent the length of the patio. Explain how each of the equation relates to the diagram. 23. The glee club is going to competition for regionals. The trip costs $52, including $11 for registration and the cost of two passes, one for meals in the cafeteria and one for admissions to the gym. Each of the passes cost the same price. Write an equation representing the cost of the trip and find the price of one pass. 2 24. Solve: x 4 = -16 3 25. Mindy had $26 dollars to spend on school supplies. After buying 10 pens, she had $14.30 left. How much did each pen cost including tax? 26. The sum of three consecutive even numbers is 54. What is the smallest of these numbers? Inequalities *Find rational values to satisfy the conditions of an inequality *Write simple inequalities to represent situations and solve problems *Write and solve linear inequalities for real world problems *Represent the solutions to an inequality on a number line 27. Fifteen is less than 3 times another number can be shown by the inequality 15 < 3n. What numbers could possibly make this a true statement?
28. The class must raise at least $100 to go to the museum. They have collected $20. Write an inequality to represent the amount of money, m, the class still needs to raise and represent this inequality on a number line. 29. The Torres family spent less than $200.00 last month on groceries. Write an inequality to represent this amount and graph this inequality on a number line 30. Florencia has at most $60 to spend on clothes. She wants to buy a pair of jeans for $28 dollars and spend the rest on t-shirts. Each t-shirt costs $8. Write an inequality for the number of t-shirts she can purchase. 31. Salvador has $25 dollars to spend. He spent $10.81, including tax, to buy a new CD. He needs to save $10.00 but he wants to buy a snack. If sunflower seeds cost $0.38 per package including tax, what is the maximum number of packages that Salvador can buy? 32. Solve 7 x > 5.4 33. Solve -0.5x 5 < -1.5 and graph the solution on a number line. Exponents and Roots *Know and apply rules for integer exponents *Use exponents and square and cube roots to solve equations and problems 34. Simplify: 3 2 2 4 35. Simplify: (3 2 )(3 4 ) 36. Simplify: (4 3 ) 2 (3 2 ) 4 37. Simplify: (3 2 )(3 3 ) 4 38. Solve: x 2 = 9 39. Solve: x 3 = 27 40. In the equation 4 x = 64, what does x equal?
41. What is the side length of a square with an area of 49 ft 2? Scientific Notation *Write numbers in both scientific and standard notation *Compare numbers in scientific notation with different exponents 42. Write 35,000,000,000 in scientific notation. 43. Write 0.0000789 in scientific notation. 44. Express 2.37 x 10 5 in standard form. 45. Which is the larger value: 3 x 10 6 or 8 x 10 5? 46. In July 2010 there were approximately 500 million Facebook users. In July 2011 there were approximately 750 million Facebook users. How many more users were there in 2011? Write your answer in scientific notation. 47. (6.45 x 10 11 )(3.2 x 10 4 ) = 48. (0.0025)(5.2 x 10 4 ) = Systems of Equations *Solve equations with variables on both sides *Write and solve systems of equations in two variables 49. Solve 10x 23 = 29 3x 50. Two more than a certain number is 15 less than twice the number. Find the number. 51. Two plants are on two different growing cycles represented by the equations below. At which week will the plants have the same height? Explain your reasoning. Plant A H = 2W + 4 Plant B H = 4W + 2 52. Vince is half as old as Molly. The sum of their ages is 54. How old is Vince? Functions
*Compare and identify properties of functions *Construct functions to represent linear equations using various pieces of information *Describe and identify functions as linear or not linear 53. Compare the following functions to determine which has the greater rate of change. Function 1: y = 2x +4 Function 2: x y -1-6 0-3 2 3 54. Which linear function listed below has a negative slope? Function 1: Samantha starts with $20 on a gift card for the bookstore. She spends $3.50 per week to buy a magazine. Let y be the amount remaining as a function of the number of weeks, x. x y 0 20 1 16.50 2 13.00 3 9.50 Function 2: The school bookstore rents graphing calculators for $5 per month. It also collects a non-refundable fee of $10.00 for the school year. The rule for the total cost (c) of renting a calculator as a function of the number of months (m) is c = 10 + 5m. 55. Determine if the functions listed below are linear or non-linear. Explain your reasoning. 1. y = -2x 2 + 3 2. y = 0.25 + 0.5(x 2) 3. A = r 2 4. X Y 1 12 2 7 3 2 4-3
5. 56. Write an equation that models the linear relationship in the table below. x y -2 8 0 2 1-1 57. A line has a zero slope and passes through the point (-8, 4). What is the equation of the line? 58. Write an equation for the line that has a slope of ½ and passes though the point (-2, 5) 59. A rental company charges $45 a day for a van as well as charging a one-time $25 gas and maintenance fee. Write an expression for the cost in dollars, c, as a function of the number of days, d, the van was rented.