Algebra 2
(ACP1 & Honors)
Summer Assignment
This summer bridge assignment represents topics from the first chapter of the text. These topics will not be taught in class.
Vocabulary:
absolute value / formula / open sentence / solutionalgebraic expressions / integers / order of operations / union
compound inequality / intersection / rational numbers / variable
empty set / irrational numbers / real numbers / whole numbers
equation / natural numbers / set–builder notation
Write whether each sentence is true or false. If false, replace the underlined word or number to make a true sentence.
1. –5x2 = –125 is an example of an equation.
2. An equation like –3|2x – 1| = 8 has a solution set that is the empty set.
3. A number that can be written as a fraction or ratio of two integers is called a(n) irrational number.
4. The absolute value of a number is the number of units between that number and 0 on a number line.
5. The graph of a compound inequality containing the word and is the union of the graphs of the two separate inequalities.
6. The rational numbers are the numbers that can be written as ratios of two integers, with the integer in the denominator not being 0.
7. The set of all rational numbers is in the set of all natural numbers.
8. Each real number corresponds to exactly one point on the number line.
9. A solution is a specific case that shows that a statement is true.
10. An expression that contains at least one variable is called a(n) formula.
Define each term in your own words.
11. irrational number
12. algebraic expressions
Evaluate each expression if a = – 4, b = 6, and c = –9.
1. 3ab – 2bc 2. a3 + c2 – 3b 3. 2ac – 12b 4. b(a – c) – 2b
5. acb + 2ba 6. 3b - 4 c2b - (c - b) 7. 3ab c+ 2cb 8. b2ac – c
Using the diagram above, name the sets of numbers to which each number belongs.
9. 34 10. –525 11. 0.875 12. 123 13. – 9 14. 30
Solve each equation. Check your solution.
15. 4m + 2 = 18 16. x + 4 = 5x + 2 17. 3t = 2t + 5
18. –3b + 7 = –15 + 2b 19. –5x = 3x – 24 20. 4v + 20 – 6 = 34
21. a – 2a5 = 3 22. 2.2n + 0.8n + 5 = 4n
Solve each equation or formula for the specified variable.
23. I = prt, for p 24. y = 14x – 12, for x 25. A = x + y2, for y 26. A = 2πr2 + 2πrh, for h
Solve each equation. Check your solutions.
27. |x – 5| = 45 28. |m + 3| = 12 – 2m 29. |5b + 9| + 16 = 2
30. |15 – 2k| = 45 31. 5n + 24 = |8 – 3n| 32.40 – 4x = 2|3x – 10|
33. 13|4p – 11| = p + 4 34. |3x – 1| = 2x + 11 35. 13x+3 = –1
Solve each inequality. Then graph the solution set on a number line.
36. 7(7a – 9) ≤ 84
37. 3(9z + 4) > 35z – 4
38. 5(12 – 3n) < 165
39. 18 – 4k < 2(k + 21) 40. 4(b – 7) + 6 < 22 41. 2 + 3(m + 5) ≥ 4(m+ 3)
42. Jim makes $5.75 an hour. Each week, 26% of his total pay is deducted for taxes. How many hours does Jim have to work if he wants his take–home pay to be at least $110 per week? Write and solve an inequality for this situation.
Solve each inequality. Graph the solution set on a number line.
43. –10 < 3x + 2 ≤ 14
44. 3a + 8 < 23 or 14a – 6 > 7
45. 18 < 4x – 10 < 50
46. 5k + 2 < –13 or 8k – 1 > 19
Solve each inequality. Graph the solution set on a number line.
5. |2f – 11| > 9 48. |5w + 2| < 28
49. |10 – 2k| < 2 50. x2-5 + 2 > 10