Module 1 and 2 Study Guide 1.1 Solving Equations Solve the equation. Check your answer. 1. 1 y + 1 = 5 2. 2n + 6 = 2n 11 3. 4 3n = 6 3n 2 3 4 12 4. Julio is paid 1.4 times hos normal hourly rate for each hour he works over 30 hours in a week. Last week he worked 35 hours and earned $436.60. Write and solve an equation to find Julio s normal hourly rate, r. Explain how you know your answer is reasonable. 1.2 Modeling Quantities Use dimensional analysis to convert the measurements. 5. 12 pints to gallons 6. 105 km to miles Use 1 mi = 1.61 km 7. 52 ft/hr to inches per minute
8. Use the table to answer the questions below. Select the best answer. Assume the shadows were measured at the same time of day. A. How tall is the oak tree? Length of Object Shadow (ft.) Height (ft.) Flagpole 8 20 Oak Tree 12 Goal Post 18 Fence 6.5 B. How tall is the goal post? C. What is the length of the fence s shadow? 1.3 Reporting with Precision and Accuracy Determine the number of significant digits of each measurement. 9. 719.080 cm 10. 0.052 kg 11. 10,000 ft. 12. A rectangle has a length of 10 cm and width and 15 cm. Find the area and perimeter. Make sure to round correctly. Choose the more precise measurement in the pair. 13. 1 ft.; 12 in. 14. 5 kg.; 5212 g. 15. 7m.; 7.7 m
16. Every week, a technician in a lab needs to test the scales in the lab to make sure that they are accurate. She uses a standard mass that is exactly 4 g and gets the following results. Scale 1: 4.05 g Scale 2: 3.98 g Scale 3: 4.021 A. Which scale is the most precise? B. Which scale is the most accurate? 2.1 Modeling with Expressions 17. List at least 3 alternate words that can be used for the following: A. Addition B. Subtraction C. Multiplication D. Division E. Equal Identify the terms, coefficient, variables, and constants of each expression. 18. 20 + 5p 7z 19. 8x 20y 10 20. Lorenzo buys 3 pairs of shirts at s dollars apiece and 2 pairs of pants at p dollars apiece. What does the expression 3s + 2p represent? Write the expression for each statement. 21. The price of a winter coat and a 20% discount. 22. The number of students attending school last year and a 20% increase.
2.2 Creating and Solving Equations 23. For the following problem: A. Write an equation to represent the situation using words B. Write an equation to represent the situation using numbers and variables C. Solve the equation and write your answer in a sentence. Aaron and Alice are bowling. Alice s score is twice the difference of Aaron s score and 5. The sum of their scores is 320. Find each student s bowling score. Write an equation to represent each situation. 24. The sum of 14 and a number is equal to 17. 25. The length of a rectangle is twice its width. The perimeter of the rectangle is 126 feet. 2.3 Solving for a Variable. Solve for the indicated variable in each mathematical formula. 26. A = 1 FV OV bh for h 27. A = for OV 2 T 2.4 Creating and Solving Inequalities Write an inequality to represent the description. 28. Six more than five times a number, x, is at least 21. 29. Dave has $15 to spend on an $8 book and two birthday cards, c, for his friends. How much can he spend on each card if he buys the same card for each friend? Solve each inequality. 30. 6x 2(x + 2) > 2 3(x + 3) 31. x + 1 > 5(7 2x)
2.5 Creating and Solving Compound Inequalities Solve each inequality and graph the solutions. 32. x + 7 7 OR 5 + 2x > 7 33. 0 2x 10 20 Write the compound inequality shown by each graph. 34. 35. -1 0 1 2 3 3 4 5 6 7-1 0 1 2 3 3 4 5 6 7 Vocabulary. Write the definition and an example for the following words. Equation Ratio Proportion Scale Dimensional Analysis Rate Conversion Factor Precision Accuracy Coefficient Terms Expression Constant Variable Literal Equation Compound Inequality Intersection Union