Answer Key Pre-algebra Skills Needed For Algebra I

Pre-algebra skills needed for Algebra I o o o o o o o o o o o Use the order of operations to simplify expression. Fluently work with all four operations and fractions (math 7 skill) Convert units Solve multiple step equations using inverse operations Evaluate expressions (substitution with positive and negative numbers) Solving Linear equations/inequalities which require the use of distributive property, combining like terms, simplification and completing calculations involving fractions and decimals. Graph and name points on the coordinate plane. Given a two variable function, - Create a table of values and graph the equation - Get the equation in y=mx+b form so you can quickly graph. - Be able to write the equation of a line from a graph Given two points, - Be able to find the slope of a line that connects them, - Be able to write the equation of a line goes through both points. Given an equation of a line, - Write the equation of a line parallel to the given line - Write the equation of a line perpendicular to the given line Multiplying monomials PRACTICE PROBLEMS Using the order of operations to simplify expressions 1. 54 ÷ 3 − 3 × 2 = 18 − 6 = 12 2. 8 ÷ 2(4) − 42 = 8 ÷ 2(4) − 16 = 4(4) − 16 = 16 − 16 = 0 3. 2(4 − 7)2 − 4 ÷ 2 = 2(−3)2 − 2 = 2 ∙ 9 − 2 = 16 4. −32 − 7 ÷ 2 + 5 = −9 − 3.5 + 5 = −7.5 5. (−7) − (−8) ÷ 22 + 5 = −7 + 8 ÷ 4 + 5 = −7 + 2 + 5 = 0 6. (−3)3 − 4 ÷ 2(2) − 10 = −27 − 2 ∙ 2 − 10 = −27 − 4 − 10 = −41 7. 7 − 4(3 − 8) − (−2 + 9) = 7 − 4(−5) − (7) = 7 + 20 − 7 = 20 8. 8 ÷ 4(2) − (6 − 9)2 = 2(2) − (−3)2 = 4 − 9 = −5 Working with all four operations and fractions (math 7 skill) 9. 3 5 10. 11. 3 5 1 3 2 3 3 5 + × 3 2 3 5 1 3 3 2 5 3 10 5 3 3 5 9 = + × = + 1 1 4 4 6 12 + − = 12. × 4 − 1 6 5 5 3 + ÷ 2 = + = =1 5 5 + 3 12 1 6 4 3 − 8 6 2 12 1 6 = = − = − = 1 1 1 3 4 6 13. 2 + 1 − 3 12 1 14. (− ) ÷ 3 3 =2 4 12 +1 3 12 = 27+50 45 = 77 45 5 12 7 6 −3 2 12 1 1 1 3 3 9 3 9 1 9 = ÷ = ∙ = 5 = 12 1 =3 Converting units. 15. 16 ft = __5__ yd __1__ ft 16. 108 in = __9___ ft __-___ in 17. 16 in =__1___ ft __4___ in 18. 86 in = __7___ ft __2___ in 19. 1.5 hr = ___90_______ min 20. 72 min = __1___ hr __12__ min 21. 90 min = __1.5__ hr 22. 2.5 hr = ___2___ hr __30__ min Solve multiple step equations using inverse operations 23. 3𝑥 𝑥 + 8𝑥 𝑥 = −11 11𝑥 𝑥 = −11 𝑥 𝑥 = −1 24. −4𝑥𝑥 − 9 = 13 −4𝑥 𝑥 = 22 22 11 𝑥 𝑥 = − 𝑜𝑜𝑜𝑜 − 4 2 25. −7𝑡𝑡 − 6𝑡 𝑡 = 0 −13𝑡 𝑡 = 0 𝑡𝑡=0 26. −𝑦𝑦 + 3 + 8𝑦 𝑦 = 17 3 + 7𝑦 𝑦 = 17 7𝑦 𝑦 = 14 𝑦𝑦=2 27. 𝑏𝑏 − (5 − 3𝑏𝑏) = 19 𝑏𝑏 − 5 + 3𝑏 𝑏 = 19 4𝑏𝑏 − 5 = 19 4𝑏 𝑏 = 24 𝑏𝑏=6 28. 2(𝑡 𝑡 + 3) = 3(7 − 𝑡𝑡) 2𝑡 𝑡 + 6 = 21 − 3𝑡𝑡 5𝑡 𝑡 = 15 𝑡𝑡=3 2 29. 4 − 3 𝑡 𝑡 = 5 2 − 𝑡𝑡=1 3 3 𝑡𝑡=− 2 2 30. ℎ − 3 ℎ = 6 1 ℎ=6 3 ℎ = 18 Evaluate the expressions for x = 2 , y = – 3 31. 3𝑥 𝑥 + 8𝑦 𝑦 = 3(2) + 8(−3) = 6 − 24 = −18 32. 𝑥𝑥 2 − 𝑦𝑦 = 22 − (−3) = 4 + 3 = 7 33. – 𝑥𝑥 2 + 𝑦 𝑦 = −(2)2 + (−3) = −4 − 3 = −7 34. 5 + 𝑥𝑥 − 𝑦𝑦 2 = 5 + 2 − (−3)2 = 5 + 2 − 9 = −2 Solving linear inequalities 35. 6𝑥 𝑥 + 2 > 8 6𝑥 𝑥 > 6 𝑥𝑥>1 36. −4𝑥 𝑥 + 3 ≤ −9 −4𝑥𝑥 ≤ −12 𝑥𝑥 ≥ 3 37. 5(𝑥 𝑥 + 2) < 0 5𝑥 𝑥 + 10 < 0 5𝑥 𝑥 < −10 𝑥 𝑥 < −2 38. 2(𝑥 𝑥 + 1) < 3 1 2𝑥 𝑥 + 2 < 3 5 2𝑥 𝑥 < − 3 5 𝑥𝑥<− 6 2 1 39. (3 − 𝑥𝑥) < 1 3 2(3 − 𝑥𝑥) < 3 6 − 2𝑥 𝑥 < 3 −2𝑥 𝑥 < −3 3 𝑥𝑥> 2 40. 0.2𝑥 𝑥 + 2 < −0.6 0.2𝑥 𝑥 < −2.6 𝑥 𝑥 < −13 Graphing from tables of values 41) Create a table for each and graph the function a) 𝑦 𝑦 = 2𝑥𝑥 − 1 b) 𝑦 𝑦 + 3𝑥 𝑥 = 2 Writing the equation of a line. 42.) a. Find the slope of a line that crosses through G(-4, 5) and H(-2, -1). 5 − (−1) 6 = 𝑚𝑚= = −3 −4 − (−2) −2 b. Write the equation of a line in part (a). 𝑦 𝑦 = 𝑚𝑚𝑥𝑥 + 𝑏𝑏, 𝐺𝐺(−4,5) 5 = −3(−4) + 𝑏𝑏 5 = 12 + 𝑏𝑏 𝑏 𝑏 = −7 𝑦 𝑦 = −3𝑥𝑥 − 7 c. Write an equation of a line parallel to the line in part (a). 𝑦 𝑦 = −3𝑥 𝑥 + 𝑎𝑎𝑎𝑎𝑦𝑦 𝑎𝑎𝑛𝑛𝑚𝑚𝑏𝑏𝑛𝑛𝑜𝑜 𝑜𝑜𝑡𝑡ℎ𝑛𝑛𝑜𝑜 𝑡𝑡ℎ𝑎𝑎𝑎𝑎 − 7 Example: 𝑦 𝑦 = −3𝑥 𝑥 + 2 d. Write an equation of a line perpendicular to the line in part (a). 1 𝑦 𝑦 = 𝑥 𝑥 + 𝑎𝑎𝑎𝑎𝑦𝑦 𝑎𝑎𝑛𝑛𝑚𝑚𝑏𝑏𝑛𝑛𝑜𝑜 3 1 𝑥𝑥+4 Example: 𝑦 𝑦 = 3 43. Write an equation of a line that crosses through F(5, 7) and M(-3, -1). 7 − (−1) 8 = =1 𝑚𝑚= 5 − (−3) 8 𝑦 𝑦 = 𝑚𝑚𝑥𝑥 + 𝑏𝑏 7 = 1(5) + 𝑏𝑏 𝑏𝑏=2 𝑦 𝑦 = 1𝑥 𝑥 + 2 𝑦𝑦 =𝑥𝑥+2 44. Write an equation to the given lines, a) Answer: 𝑦 𝑦 = 2𝑥𝑥 − 3 b) 3 𝑥𝑥 Answer: 𝑦 𝑦 = 5 45) Simplify the expressions. a) (3𝑥𝑥 2 )(−4𝑥𝑥 3 ) = −12𝑥𝑥 5 𝑏𝑏) (3𝑥𝑥 5 )2 = 9𝑥𝑥10 c) 4𝑥𝑥(5𝑥 𝑥 + 4) = 20𝑥𝑥 2 + 16𝑥𝑥