Name____________________________________

Introduction to College Algebra

Summer Assignment

You have enrolled in Introduction to College Algebra for the next school year. Show ALL of your work on this

paper and write your final answer(s) on the blank provided. Leave simplified, exact answers (improper

fractions, simplified radicals, etc). All work must be shown; just answers will receive a zero. When graphing,

be sure to number both axes, use a ruler, and plot at least 3 points. This assignment is due on the first day of

class next year. There will be a test on the topics during the first week of school. No assignments will be

accepted late!

A TI-83, TI-83+, or TI-84+ graphing calculator is mandatory for success in this class (and all other math

courses until you graduate college). If you do not already have one, and plan to purchase one over the summer;

please save the TI Reward Points. Staple the Reward Points to this sheet so you do not lose it. Thank you!

Perform the indicated operations.

1. 5⎡⎣3+ 4(8)⎤⎦ −53 1. ________________

2. 9 ÷3(5)−8÷ 2 + 3 27 2. ________________

3. ( ) ( )

2

5 5 4 4

2 1

−

−

3. ________________

4. −25 +5 8− 4 +8

4. ________________

Write in Scientific Notation.

5. 1,200,000 5. ______________________

6. 0.0000034 6. ______________________

Write in Standard Notation.

7. 3.9×105 7. ______________________

8. 8.35 10−4 × 8. ______________________

Evaluate each given a = 3, b = 4, c = −1.

9. abc − 4c 9. ________________

10. 2c3 +5b 10. _______________

Solve.

11. 2 5 3

3

x − = x − 11. _______________

12. 5(x + 4) = 7(x + 2) 12. _______________

13. x −1−(x + 2)−(x −3) = x 13. _______________

Solve and graph on a number line.

14. −5(2t +3) < 2t −3 14. _________________________________

15. 3

4

x +1≥ 4 15. _________________________________

16. −3 < 2x −5 < 5 16. _________________________________

Simplify.

17. (3×2 −5x −6)+(4x +5×2 + 4) 17. _____________________

18. (3×0 y5z6 )(−2xy3z6 ) 18. _____________________

19. −2a5b7c9 ( )6

19. _____________________

20. ( )

( )

5 4 3 2

3 7 3 2

2

3

a b c

a b c

− −

−

20. _____________________

21. (2a −5)(3a +8) 21. _____________________

22. ( )2 5a +6 22. _____________________

23. (2r −5)(3r2 −4r +7) 23. _____________________

Factor each completely.

24. x2 − 6x − 27 24. _____________________

25. 49×2 − 25 25. _____________________

26. x2 +12x + 32 26. _____________________

27. 4×2 − 20x + 25 27. _____________________

Simplify. All variables represent positive real numbers.

28. 10 8 28. _______________

29. 4

81

x

29. _______________

30. 24 p3q6 30. _______________

31. 2(3 6 + 6) 31. _______________

32. 2 18 −5 32 32. _______________

33. (7 + 3 2 )(4 −5 6 ) 33. _____________________

34. (3+ 8)(3− 8) 34. _____________________

35. 12

3

35. _______________

Solve.

36. 4×2 + 9x + 2 = 0 36. _______________

37. x2 + 3x = 4 37. _______________

Coordinate Geometry: Using the points A(−3, 6) and B(2,−1) , find each of the following.

*All equations should be stated in Ax + By +C = 0 form.

The A value is a natural number (1, 2,3,…) , and B and C are integers (… -3, -2, -1, 0, 1, 2, 3, …).

38. What is the length of segment AB? 38. _______________

39. What is the midpoint of segment AB? 39. _______________

40. What is the slope of line AB? 40. _______________

41. What is the equation of line AB? 41. _____________________

42. What is the slope of the line perpendicular to line AB? 42. _______________

43. What is the slope of the line parallel to line AB? 43. _______________

Use the Pythagorean Theorem to solve the following problems. Drawing a diagram may be helpful.

44. A 14-meter ladder is leaning against a building. The bottom of the ladder

is 7 meters from the building. How high is the top of the ladder? 44. _______________

45. Find the length of a diagonal of a square tile that has sides 4 cm long. 45. _______________

46. A square has a diagonal length of 10 meters. Find the area of the square. 46. _______________

Graph. Reminder: label both axes with numbers, use a ruler, and use 3 points to graph each line.

47. y = x 48. y = 4

49. 2x + 3y =12 50. x = 3

51. 2 3

7

y = x +

This assignment will be graded for accuracy.

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