Module 3 Study Guide

Vocabulary Match! Match the term on the left with the definition on the left!

1. Congruent

2. Factoring

3. Like terms

4. Coefficient

5. Constant

6. Least Common Denominator

7. Algebraic Equation

8. Order of Operations

______

9. Peter is trying to buy fencing for the perimeter of his garden. His garden is in the shape of a rectangle with a length of 2(x+6)feet and a width of 3.5x feet. How many feet of fencing will he need to buy? Write and simplify an expression to represent this situation? What properties did you use?

10. Write an expression equivalent to the following:

a. 4x + 20 b. 15x + 10

A. The smallest whole number that is divisible by both denominators.

B. Terms that have the same variable with equal powers such as 3y and 4y.

C. The rules for the order of calculations in an expression; parentheses, exponents, multiplication and division, addition and subtraction.

D. Same measure; the sides of a square are congruent because they are all the same length.

E. Term in an algebraic expression that contains only numbers (ex. In the expression 5y + 6, 6 is a constant).

F. Taking a number or expression apart and writing it as a product of two or more factors.

G. The number part of a term with variables (ex. 3y has a coefficient of 3).

H. An equation that includes one or more variables (ex. −3x − 4 = −28).

11. All services at the salon are 25% off today. Maria decided to get a haircut that originally costs $22.

a. What would her total bill be with the discount?

b. Now she needs to leave a 20% tip. How much should she leave?

12. How do we estimate numbers?

13. Estimate how much money Jonah will make in an 8hr work day if he makes $7.59 per hour but 10% must go to taxes. Please show your work.

14. Why is estimation an important tool?

15. Sarah went to the farmers market because she needed 5 more apples for her Granny’s jam recipe. The recipe calls for 32 apples. How many apples did Sarah have before her trip to the farmers market? Please define a variable, then write and solve an equation for this scenario. Show all of your work step by step.

16. Circle the equations and put an X through the non-equations.

a. 3 +4 = x

b. 2x – 5 = 20

c. 3 + 2 = x + 7

d. 3x -4

Equation Practice! Please solve the following.

17. 2x = 22

18. x4 = 5

19. -2n + 6 = 12

20. -7 + 4n = 9

21. What operations would you use in order to solve 3x – 4 = 26. Please write the operations in the order you would use them.

22. Last year Chelsea and Sonya took 236 pictures during Thanksgiving. This year Chelsea and Sonya each took the same amount of pictures. All together they took 500 pictures in both years. How many pictures did each girl take at Thanksgiving this year? Please write an solve an equation, make sure you show your work.

23. What are the 4 inequality signs?

Symbol Description in words

24. What is the most important rule to remember when solving inequalities with negative numbers?

Please solve and graph each inequality 25-28

25. x -7 < -12

26. n3 ≤ 3

27. -9x ≥ 90

28. 3 + v > -9

29. Zach has $9.50 and plans to purchase songs from Itunes. Each song he wants to purchase is $1.25. He needs to make sure he has $5.75 left over for the app he wants to buy. Write and solve an inequality to see how many songs Zach can buy.

30. The sum of 2 numbers is 61. The greater number is 9 more than the smaller number. Write and solve an equation to find the 2 numbers.

31. Tabitha earns $8.50 per hour at her summer job. She want to save money to buy a tablet that costs $289 plus 6% sales tax. Tabitha has already saved $75. Write and solve an inequality that shows how many hours Tabitha will need to work to have enough money to buy the tablet.

Module 3 Study Guide