Introduction to College Algebra Assignment

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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