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COLLEGE ALGEBRA - MIDTERM
1.
Subtracting Integers Find the
difference: 14 â (â15) Rule To subtract in algebra, add the opposite. 15 is the opposite of â15. 14 + 15 = 29 Directions Rewrite each expression as addition. Solve the new expression. EXAMPLE Name Date Period Workbook Activity Chapter 1, Lesson 5 5 1. â4â(â11) 10. â5â(â5) 2. 9 â(+3) 11. 2 â(+9) 3. â1â13 12. 1 â(+4) 4. â6â(+10) 13. 6 â8 5. 7 â(â10) 14. â8â(â3) 6. 4 â(+4) 15. â3â(+7) 7. 2 â(+8) 16. 8 â(â7) 8. â11â(â1) 17. 10 â(+5) 9. 6 â(+2) 18. 5 â6 Directions Solve these problems. Write an expression and the answer. 19. Daraâskite is flying 67 feet high. Jillâsisflying 40 feet high. What is the difference between the heights of these two kites? 20. A helicopter hovers 60 m above the oceanâs surface. A submarine is resting 30 m underwater, directly below the helicopter. What is the difference between the positions of these twoobjects? Algebra©AGS Publishing. Permission is granted to reproduce for classroom use only
2.
Multiplying Integers Notice the
possible combinations for multiplying positive and negative integers. positive (positive) = positive positive (negative) = negative negative (positive) = negative negative (negative) = positive 4(4) = 16 4(â4) = â16 â4(4) = â16 â4(â4) = 16 Multiplying any integer, positive or negative, by 0 gives 0 as the product. Directions Tell whether the product is positive, negative, or zero. Directions Find each product. Write the answer. EXAMPLE Name Date Period Workbook Activity Chapter 1, Lesson 6 6 Algebra©AGS Publishing. Permission is granted to reproduce for classroom use only 1. (4)(â7) 6. (5)(â3) 11. (â3)(â9) 2. (â6)(3) 7. (â15)(â1) 12. (4)(6) 3. (â7)(0) 8. (0)(14) 13. (11)(â2) 4. (â9)(â9) 9. (â5)(7) 14. (2)(9) 5. (2)(â11) 10. (â8)(â2) 15. (â6)(4) 16. (2)(9) 25. (â11)(â2) 17. (â5)(9) 26. (â4)(8) 18. (3)(â9) 27. (â10)(â8) 19. (â10)(2) 28. (5)(â5) 20. (â9)(â7) 29. (â1)(â1) 21. (â5)(10) 30. (7)(10) 22. (12)(2) 23. (â32)(0) 24. (6)(â4)
3.
Name Date Period
Workbook Activity Chapter 1, Lesson 6 7 Integers Algebra©AGS Publishing. Permission is granted to reproduce for classroom use only Data from a climbing expedition is shown in this table. During the climb, some climbers began at base camp and climbed to the summit. Other climbers also began at base camp but did not reach the summitâthese climbers moved back and forth between camps carrying supplies and other necessities. Directions The movements of various climbers in the expedition are shown below. Find the number of feet climbed by each climber. 1. Climber A: Base Camp to Camp 1 to Base Camp 2. Climber C: Base Camp to Camp 5 to Base Camp 3. Climber F: Base Camp to Camp 3 to Base Camp 4. Climber B: Base Camp to Camp 2 to Base Camp 5. Climber H: Base Camp to Camp 6 to Base Camp 6. Climber E: Base Camp to Summit to Base Camp 7. Climber G: Base Camp to Camp 4 to Base Camp 8. Climber D: Base Camp to Camp 5 to Camp 3 to Camp 4 to Base Camp 9. Climber I: Base Camp to Camp 2 to Camp 1 to Camp 6 to Base Camp 10. How many feet above base camp is the summit? Elevationin Feet (Comparedto SeaLevel) BaseCamp â384 Camp 1 +5,027 Camp 2 +7,511 Camp 3 +8,860 Camp 4 +10,103 Camp 5 +10,856 Camp 6 +11,349 Summit +12,015
4.
Dividing Positive and
Negative Integers Notice the possible combinations for dividing positive and negative integers. positive Ă· positive = positive positive Ă· negative = negative negative Ă· positive = negative negative Ă· negative = positive 6 Ă· 2 = 3 6 Ă· â2 = â3 â6 Ă· 2 = â3 â6 Ă· â2 = 3 Dividing 0 by any integer, positive or negative, produces 0 as the quotient. Directions Tell whether the quotient is positive, negative, or zero. Directions Find and write each quotient. EXAMPLE Name Date Period Workbook Activity Chapter 1, Lesson 7 8 Algebra©AGS Publishing. Permission is granted to reproduce for classroom use only 1. 16 Ă· â4 9. â27Ă· 3 2. â63Ă· â9 10. 0 Ă· â4 3. â10Ă· 2 11. â81Ă· â9 4. 33 Ă·11 12. 19 Ă· â1 5. â12Ă· 4 13. 56 Ă· 8 6. 100 Ă·10 14. 500 Ă· 5 7. 36 Ă· â9 15. 32 Ă· â8 8. 15 Ă· â5 16. 36 Ă·12 24. â50Ă· 10 17. 21 Ă· â7 25. 27 Ă·â9 18. 18 Ă· â3 26. â14Ă· 2 19. â35Ă· 7 27. 0 Ă·16 20. â24Ă· 2 28. â72Ă· â9 21. â16Ă· â8 29. â1Ă· â1 22. 45 Ă· â9 30. 9 Ă·3 23. â200Ă·â200
5.
Simplifying ExpressionsâOne Variable Simplify
2n + 2 + 4n. 1. Look for like terms. 2n and 4n are like terms, because they have the same variable, n. 2. Combine the terms: 2n + 4n = 6n 3. Rewrite the whole expression: 6n + 2 Now you are finished, because 6n cannot combine with 2. Directions In each expression, underline the like terms. Directions Simplify each expression. EXAMPLE Name Date Period Workbook Activity Chapter 1, Lesson 8 9 Algebra©AGS Publishing. Permission is granted to reproduce for classroom use only 1. 3k â8 + 2k 2. p+ 12 + p 3. 100 + 4w+ 4w 4. 5m â3 + 2m 5. 7x + 5x â12 6. â2+ 11c + c 4 7. ââ+2m + 3m7 8. 2y â(â3y)+ 7 9. 4x â13 + 5x 10. 8r + (â3r) 11. 3b + b 21. 2y + (â2y)+ 5 12. 11y + 2y + y 22. â5+ 6n â4n 13. 7j + 3j â2j 23. 2x + 11x â13 14. 2k â17 + k 24. âh+ 7h 15. 11x + x â14 25. â11â(â3k)+ k 16. 22 + 2d + 8d 26. 7d âd + 40 17. 9g+ (â2g)+ 4 27. 8 + 3m â(âm) 18. 14h â3 â2h 28. 3w + (â5w) 19. 2m + (â8m) 29. 2 + 5x â2x 20. 3 + 4k â3k 30. 8g+ (â5g)â6
6.
Name Date Period
Workbook Activity Chapter 1, Lesson 9 10 Simplifying ExpressionsâSeveral Variables Simplify 2j + 4 + j â 1 + 3k. 1. Scan for variables. The expression has two: j and k. 2j + j = 3j 3k (no combining required) 2. Combine j terms: 3. Combine k terms: 4. Combine integers: 4 + (â1) = +3 5. Rewrite the whole expression: 3j + 3k + 3 Now you are finished, because you cannot combine unlike terms. Directions Check the column or columns to show which kinds of terms each expressionincludes. Directions Combine like terms. Simplify each expression. 6. 3k â2k + 12 + 5r 7. 2c+ 3b + 8b + c 8. 5k + 3 + 2j â2 âk 9. 7 + 4p â6 + 2m â2p 10. â4n+ 4 â(â2d)+ n â5 11. 18 + (â4x)+ 1 â3x + 8y 12. 2w + (â11)+ 18y + 2w â11 13. 6h â12 â9h + 8k + (â3k) 14. 3 â3m â3m â8p â3p 15. 14x â7 + 3y â7x â7x EXAMPLE Expression xterms yterms Integers 1. 3x + 2x + 3 + 6y 2. 3y â14 3. x + 2y â10 + 3y 4. 72 â68 5. x â8 Algebra©AGS Publishing. Permission is granted to reproduce for classroom use only
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