Download Algebra 2

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
solution
algebraic 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. –5𝑥 2 = –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
5.
𝑎𝑐
𝑏
+
2𝑏
𝑎
2. 𝑎3 + 𝑐 2 – 3b
3𝑏 − 4 𝑐
6. 2𝑏 − (𝑐 − 𝑏)
3. 2ac – 12b
7.
3𝑎𝑏
𝑐
+
4. b(a – c) – 2b
𝑏2
2𝑐
8. 𝑎𝑐 – c
𝑏
Using the diagram above, name the sets of numbers to which each number belongs.
9. 34
10. –525
11. 0.875
12.
12
3
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 –
2𝑎
5
=3
22. 2.2n + 0.8n + 5 = 4n
Solve each equation or formula for the specified variable.
23. I = prt, for p
1
24. y = 4x – 12, for x
25. A =
𝑥+𝑦
2
, for y
26. A = 2𝜋𝑟 2 + 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|
34. |3x – 1| = 2x + 11
35. |3 𝑥 + 3| = –1
1
33. 3|4p – 11| = p + 4
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 4a – 6 > 7
45. 18 < 4x – 10 < 50
46. 5k + 2 < –13 or 8k – 1 > 19
1
Solve each inequality. Graph the solution set on a number line.
5. |2f – 11| > 9
48. |5w + 2| < 28
49. |10 – 2k| < 2
𝑥
50. |2 − 5| + 2 > 10