Name Date Lesson 1: Generating Equivalent Expressions

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1 Mid-Module Assessment Study Guide Name Date Lesson 1: Generating Equivalent Expressions 1. Write an equivalent expression to by combining like terms. 2. Find the sum of and. 3. Write the expression in standard form: ( ) Lesson 2: Generating Equivalent Expressions 4. Write the expression in standard form: ( ) Subtraction as adding the opposite Opposite of a sum is the sum of its opposites Any order, any grouping Combined like terms 5. Find the result when is subtracted from. Original expression Subtraction as adding the opposite ( ) Subtraction as adding the opposite Opposite of a sum is the sum of its opposites Combined like terms Subtraction as adding the opposite

2 Mid-Module Assessment Study Guide 6. Rewrite the expression in standard form: Multiplying by the reciprocal Multiplication Any order, any grouping 9 Lesson 3: Writing Products as Sums and Sums as Products A square fountain area with side length is bordered by two rows of square tiles along its perimeter as shown. Express the total number of grey tiles (only in the second rows) needed in terms of three different ways. or

3 Mid-Module Assessment Study Guide Lesson 4: Writing Products as Sums and Sums as Products 7. Write the expression below in standard form. ( ) Subtraction as adding the inverse Distributive property Apply integer rules Collect like terms 8. Write the expression below as a product of two factors. The GCF for the terms is Therefore, the factors are Lesson 5: Using the Identity and Inverse to Write Equivalent Expressions 9. Find the sum of and the opposite of. Write an equivalent expression using the fewest number of terms. Justify each step. ( ) Associative property of addition Additive inverse Additive identity property of zero 10. For and the multiplicative inverse of, write the product and then write the expression in standard form, if possible. Justify each step. Distributive property Lesson 6: Collecting Rational Number Like Terms Multiplicative inverses, multiplication Multiplicative identity property of one 11. For the problem, Tyson created an equivalent expression to the problem using the following steps: Is his final expression equivalent to the initial expression? Show how you know. If the two expressions are not equivalent, find Tyson s mistake and correct it.

4 Mid-Module Assessment Study Guide No, he added the first two terms correctly, but he forgot the third term and added to the other like terms. If, The expressions are not equal. He should factor out the and place parentheses around the values using the distributive property, in order to make it obvious which rational numbers need to be combined.

5 Mid-Module Assessment Study Guide Lesson 7: Understanding Equations 12. Check whether the given value of is a solution to the equation. Justify your answer. a. False, is NOT a solution to b. True, is a solution to 13. The total cost of four pens and seven mechanical pencils is. The cost of each pencil is cents. a. Find the cost of a pen. ( ) ) b. Let the cost of a pen be dollars. Write an expression for the total cost of four pens and seven mechanical pencils in terms of or c. Write an equation that could be used to find the cost of a pen. or d. Determine a value for for which the equation you wrote in part (b) is true. True, when, the equation is true. e. Determine a value for for which the equation you wrote in part (b) is false. Any value other than will make the equation false.

6 Mid-Module Assessment Study Guide Lesson 8: Using If-Then Moves in Solving Equations 14. Mrs. Canale s class is selling frozen pizzas to earn money for a field trip. For every pizza sold, the class makes $. They have already earned $ toward their $ goal. How many pizzas must they sell to earn $? Arithmetic Approach: Amount of money needed:. Number of pizzas needed: If the class wants to earn then they must sell more pizzas. Algebraic Approach: Let represent the number of pizzas they need to sell. OR If the class wants to earn then they must sell more pizzas. Both approaches subtract from to get. Dividing by is the same as multiplying by. Both result in more pizzas that the class needs to sell.

7 Mid-Module Assessment Study Guide Lesson 9: Using If-Then Moves in Solving Equations 15. Brand A scooter has a top speed that goes 2 miles per hour faster than Brand B. If after 3 hours, Brand A scooter traveled 24 miles, at what rate did Brand B scooter travel at its top speed? Write an equation to determine the solution. Identify the if-then moves used in your solution. Brand : Brand Scooter Scooter possible solution #1: possible solution #2: If-then Moves: Divide both sides by If-then Moves: Subtract from both sides Subtract from both sides Multiply both sides by

8 Mid-Module Assessment Study Guide 16. At each scooter s top speed, Brand A scooter goes 2 miles per hour faster than Brand B. If after 3 hours, Brand A scooter traveled 40.2 miles, at what rate did Brand B scooter travel? Write an equation to determine the solution and then write an equivalent equation using only integers. Brand : Brand Scooter Scooter possible solution #1: possible solution #2: Brand B's scooter travels at miles per hour. Lesson 10: Angle Problems and Solving Equations 17. In a complete sentence, describe the relevant angle relationships in the following diagram. That is, describe the angle relationships you could use to determine the value of. J K E 30 A 3x 5x F H G and are adjacent angles whose measurements are equal to ; and are vertical angles and are of equal measurement.

9 Mid-Module Assessment Study Guide 18. Use the angle relationships described above to write an equation to solve for. Lesson 11: Angle Problems and Solving Equations 19. Write an equation for the angle relationship shown in the figure and solve for. Find the measures of and. R S 3x 221 Q 4x U T Lesson 12: Properties of Inequalities 20. Given the initial inequality, state possible values for that would satisfy the following inequalities: a. b. c. 21. Given the initial inequality, identify which operation preserves the inequality symbol and which operation reverses the inequality symbol. Write the new inequality after the operation is performed. a. Multiply both sides by. Inequality symbol is reversed.

10 Mid-Module Assessment Study Guide b. Add to both sides. Inequality symbol is preserved. c. Divide both sides by. Inequality symbol is preserved. d. Multiply both sides by. Inequality symbol is reversed. e. Subtract from both sides. Inequality symbol is preserved.

11 Mid-Module Assessment Study Guide Lesson 13: Inequalities 22. Shaggy earned per hour plus an additional in tips waiting tables on Saturday. He earned at least in all. Write an inequality and find the minimum number of hours, to the nearest hour, Shaggy worked on Saturday. number of hours worked If Shaggy earned at least, he would have worked at least hours. Lesson 14: Solving Inequalities 23. Games at the carnival cost each. The prizes awarded to winners cost the owner How many games must be played for the owner of the game to make at least? number of games played There must be at least games played to make at least.

12 Lesson 15: Graphing Solutions to Inequalities Mid-Module Assessment Study Guide 24. The junior-high art club sells candles for a fundraiser. The first week of the fundraiser the club sells cases of candles. Each case contains candles. The goal is to sell at least cases. During the second week of the fundraiser, the club meets its goal. Write, solve, and graph an inequality that can be used to find the possible number of candles sold the second week. : the number candles sold the second week The minimum number of candles sold the second week was candles the number of cases of candles sold the second week The minimum number of cases sold the second week was. Since there are candles in each case, the minimum number of candles sold the second week would be