SUMMER MATH WORK ALGEBRA 1 - Academy Of The ...

SUMMER MATH WORK

ALGEBRA 1

Name:________________________________________________ Incoming Algebra I Summer Practice

For each question in this assignment, show all of your work on loose leaf paper. Remember to check

your final answer with the key. Your work must be clearly labeled and easy to follow.

This assignment will be graded for completion and entered as a quiz grade.

This assignment is due on the first day of school. If you turn in this assignment after the first day of school, 10 percentage points will be deducted for each day it is late.

Students entering Algebra I are expected to know how to: evaluate expressions

o apply the order of operations

simplify expressions

write algebraic expressions, equations and inequalities

represent functions as rules, tables and graphs

identify relations as functions

evaluate square roots and compare numbers

classify numbers as real, rational, irrational, integer, whole or natural

solve linear equations

o one-step equations

o two-step equations

o multi-step equations

o with variables on both sides

write and solve proportions

write and solve linear equations

rewrite equations and formulas

plot points in a coordinate plane

o identify x-intercepts o identify y-intercepts

find the slope between two points

graph linear equations written in slope-intercept form

These skills will be incorporated into the Algebra I course throughout the school year.

As a member of the Sacred Heart Community, I pledge to act in a moral, ethical, honest, and honorable way in all that I do.

_________________________________________________________

Student Signature



Topic 1: Evaluate expressions

Evaluate each expression. Write your final answers as improper fractions if necessary. You are expected to complete this section without a calculator. Remember to show each step for questions 6 – 10.

1. 9 1

5 2 2. 5 8 3. 7 4 4.

35 6

4 5.

3 12

7 3

6. 2

33 15 2 6 2

7. 28 7 3q r r when 2q and 10r

8. 2

2

2 2

m n

m n

when 5m and 3n 9. 21.7 14.314 3.4 5.1 (round your answer to the nearest hundredth)

10. 2 6 7 8 4 11. 3 1

24 5

12.

5 4

8 5

13.

7 112

9 3

Topic 2: Simplify expressions

Simplify each expression.

14. 6 2 2 6x x 15. 2 5 7r r 16. 8 4 10 11 5x y y x 17. 6 1 6a

18. 8 3 4m 19. 5 3 7r 20. 3

12 204

d

Topic 3: Write algebraic expressions, equations and inequalities

For questions 21 – 26, translate the statement into an expression, an equation or an inequality.

21. Seven less than twice a number .n

22. Three times a number, decreased by the sum of another number squared and eight.

23. The quotient of the square of a number a and 14 is more than 80.

24. Five more than the square of a number v is 14.

25. The quotient of a number h and 9 is at most 28.

26. The difference of a number b and 7 is no less than 10 and no more than 21.

27. You are making beaded bracelets for your friends. You plan to use 30 beads for each bracelet and want to use

no more than 145 beads. Write an inequality that models this situation, where b represents the number of bracelets you

can make.

28. Write a variable expression for the volume of the cube whose side length is .x

29. A rectangle is twice as long as it is wide.

a) Write a variable expression to represent the perimeter of the rectangle.

b) Write a variable expression to represent the area of the rectangle.

Topic 4: Represent functions as rules, tables and graphs

30. Make a table for the function 4 2y x with domain: 0, 1, 2, 3, 4. Identify the range of the function.

31. Write a rule for the function. a) b) c)

32. Using graph paper, graph the function 1

12

y x with domain: 2,0,2,4,6. List the range.

Topic 5: Identify relations as functions

33. Determine whether the graph represents a function. Explain why or why not.

a) b)

34. Determine whether the relation is a function. Explain why or why not.

a) b)

Topic 6: Evaluate square roots and compare numbers

For questions 35 – 38, evaluate the expression.

35. 81 36. 121 37. 3 25 38. 2 196

For questions 39 & 40, approximate the square root to the nearest tenth.

39. 150 40. 43

41. Order the numbers, 15

169, 7.25, 6, ,2

from least to greatest.

Topic 7: Classify numbers as real, rational, irrational, integer, whole or natural

Tell whether the number is a real number, a rational number, an irrational number, an integer, a whole number, or a natural number. List all categories the number can be classified as, then circle the most specific category.

42. 5.13 43. 7 44. 35 45. 144 46. 5

4

Topic 8: Solve linear equations

Solve each equation. Show each step. Write your final answers as improper fractions if necessary.

47. 4 18x 48. 21 420m 49. 3

104 4

d 50.

7 26

5

a

51. 5 24 5 5w w 52. 12 2 3 5 2n n n 53. 1 2 1 3

2 3 3 2x x

54. 1

60 16 15 44

w w 55. 3 3 1 1 6 10h h h

Topic 9: Write and solve proportions

Solve each proportion. Show each step. Write your final answers as improper fractions if necessary.

56. 2 30

16 80

w 57.

7 3

112 8

c 58.

15 5

42 14

p p

Topic 9: Write and solve proportions

59. Assign a variable, write a proportion to represent the situation, solve the proportion, then answer the question.

Kelli works in the local mailroom at a college. One of her duties is to sort local mail from all of the other mail. She can sort 8 pieces of mail in 10 seconds. How many pieces should Kelli be able to sort in 45 minutes?

60. Assign a variable, write a proportion to represent the situation, solve the proportion, then answer the question.

At an aquarium the ratio of freshwater fish to saltwater fish is 3 to 5. Determine the number of each kind of fish if the aquarium has 640 fish. How many more saltwater fish are there than freshwater fish?

Topic 10: Write and solve linear equations

61. Assign a variable, write an equation to represent the situation, solve the equation, then answer the question.

The length is 5 inches more than the width. The perimeter is 9 times the width. Find the length and width of the rectangle described.


The membership fee for joining a gardening association is $24 per year. A local botanical garden charges members of the gardening association $3 for admission to the garden. Nonmembers of the association are charged $6. After how many visits to the garden is the total cost for members, including the membership fee, the same as the cost for nonmembers?


You helped Daisy move into a new apartment. Daisy rented a truck for $15 an hour and a dolly for $5. She paid a total of $80 for the rental. For how long did Daisy rent the truck?


A car dealership sold 78 new cars and 67 used cars this year. The number of new cars sold by the dealership has been increasing by 6 cars each year. The number of used cars sold by the dealership has been decreasing by 4 cars each year. If these trends continue, in how many years will the number of new cars sold be twice the number of used cars sold?


You are driving to a vacation spot that is 1500 miles away. Including rest stops, it takes you 42 hours to get to the vacation spot. You estimate that you drove at an average speed of 60 miles per hour. How many hours were you not driving? 66. Assign a variable, write an equation to represent the situation, solve the equation, then answer the question.

Information about students who take Spanish and students who take French at a high school is shown in the table. If the trends continue, in how many years will there be 3 times as many students taking Spanish as French?

Topic 11: Rewrite equations and formulas

Solve for the indicated variable.

67. 2C r for 68. C S

Dn

for C 69. Ax By C for y 70.

1

3D A Bc for c

Topic 12: Plot points in the coordinate plane

Plot the following coordinates points on a coordinate plane then identify the quadrant in which the point is located. If the coordinate is an x-intercept or y-intercept, state it. Use graph paper, label your axes and scale. Remember to label each coordinate point with the assigned letter.

71. 5, 1R 72. 3,4S 73. 4, 1T 74. 5,5U 75. 0, 2V 76. 1,0W

77. Give the coordinates of the points labeled , , , and .A B C D

Topic 13: Find the slope between two points

Find the slope of the line that passes through the points. 78. 79. 80.

81. 4, 5 & 3, 2 82. 7, 1 & 7,5

Topic 14: Graph linear equations in slope-intercept form

Graph the following equations on a coordinate plane. Each equation must be graph on a separate coordinate plane. Use graph paper, label your axes and scale. Use a straightedge to graph the line.

83. 5 2y x 84. 2x 85. 3y 86. 1

33

y x

Answers:

1. 13

10 2. 13 3. 11 4.

1

4 5.

40

21 6. 35 7. 71 8.

1

3

9. 22.59 10. 28 11. 3

10 12.

25

32 13. 28 14. 12 4x 15. 6 9r

16. 9 15 5x y 17. 12 6a 18. 24 32m 19. 15 35r 20. 9 15d

21. 2 7n 22. 23 8x y 23. 2

8014

a 24. 2 5 14v 25. 28

9

h

26. 10 7 21b 27. 30 145b 28. 3x 29. a) 6w b) 22w

30. Range: 2, 2, 6, 10, 14 31. a) 5y x b) 2 3y x c) 1

12

y x 32. Range: 2, 1, 0, 1, 2

33. a) Function; remember to explain why b) Not a function; remember to explain why

34. a) Not a function; remember to explain why b) Function; remember to explain why

35. 9 36. 11 37. 15 38. 28 39. 12.2 40. 6.6

41. 15

169, , 6, 7.252

42. real, rational 43. real, irrational 44. real, rational, integer, whole, natural

45. real, rational, integer 46. real, rational 47. 14x 48. 20m 49. 37d 50. 37

2a

51. No solution 52. 1

2n 53. 13x 54. All real numbers 55. 28h

56. 3w 57. 7

2c 58. 15p

59. Variable: Let # of pieces of mail;m Proportion: 8

;2700 10

m 2160.m Kelli can sort 2,160 pieces of mail in 45 minutes.

60. Sample Answer: Variable: Let # of freshwater fish;x Proportion: 3

;640 8

x 240.x

There are 240 freshwater and 400 saltwater fish in the aquarium. There are 160 more saltwater fish than freshwater fish.

61. Variable: Let width of the rectangle;w Equation: 9 2 5 2 ;w w w 2.w The width of the rectangle is 2 inches,

and the length of the rectangle is 7 inches.

62. Variable: Let # of visits to the garden;n Equation: 3 24 6 ;n n 8.n After 8 visits to the garden, the total cost for

members will be the same as the cost for nonmembers.

63. Variable: Let # of hours Daisy rented the truck;h Equation: 15 5 80;h 5.h Daisy rented the truck for 5 hours.

64. Variable: Let # of years;y Equation: 78 6 2 67 4 ;y y 4.y If these trends continue, in 4 years the number of new

cars sold will be twice the number of used cars sold.

65. Variable: Let # of hours spent driving;h Equation: 60 1500;h 25.h 17 hours of your trip were spent not driving.

66. Variable: Let # of years;y Equation: 555 33 3 230 2 ;y y 3.5.y If these trends continue, in approximately 3 ½

years the there will be three times as many students taking Spanish as French.

67. 2

C

r 68. C Dn S 69.

Ax Cy

B

70.

3 D Ac

B

71. Quadrant III 72. Quadrant II

73. Quadrant IV 74. Quadrant I 75. y-intercept 76. x-intercept

71 – 76, refer to the graph below: 77. 4,1 , 1, 2 , 3,2 , 0,3A B C D

78. 2

3 79. 0 80.

4

5 81. 3

82. undefined

83. 84. 85. 86.

SUMMER MATH WORK

GEOMETRY

Name:________________________________________________ Incoming Geometry Summer Practice



This assignment will be graded for completion and entered as a quiz grade.

This assignment is due on the first day of school.

If you turn in this assignment after the first day of school, 10 percentage points will be deducted for each day it is late.

Students entering Geometry are expected to know how to:

Solve multi-step linear equations

Solve and graph multi-step linear inequalities

Write equations of lines in slope-intercept or standard form given

o two points

o the x and y intercepts

o slope and one point o a point and the equation of a line parallel o a point and the equation of a line perpendicular o a graph

Write equations of vertical and horizontal lines

Recognize positive, negative, zero and undefined slope

Set up and solve proportions

o apply proportions to similar figures

Solve systems of linear equations in two variables using any algebraic method (elimination and substitution)

Simplify radicals (Ex. 8 2 2 )

o Add, subtract, multiply and divide radicals

o Rationalize the denominator (Ex. 1 3

33 )

Simplify polynomial expressions (add, subtract and multiply)

Factor polynomial expressions

Solve quadratic equations o using square roots

o by factoring

o using the quadratic formula

These skills will be incorporated into the Geometry course throughout the school year.

As a member of the Sacred Heart Community, I pledge to act in a moral, ethical, honest, and honorable way in all that I do.

_________________________________________________________

Student Signature

For each question in this assignment, show all of your work on loose leaf paper. Remember to check your final answer

with the key. Your work must be clearly labeled and easy to follow.

Topic 1: Solving multi-step linear equations

Solve each equation. Write your final answers as improper fractions if necessary.

1. 5 3

112

x

2.

18 9

2x 3. 10 4 5 3 7 6x x x 4. 6 7 2 3 5 1y y

5. 2 9 3 4 5 2 3x x x 6. 3 11 12 3y y 7. 1

4 3 9 123

y y

Topic 2: Solving and graph multi-step linear inequalities

Solve each inequality and graph the solution(s) on a number line. Write your final answers as improper fractions if necessary.

8. 4 7 1x 9. 8 2 26n 10. 7 11 3 3 4p p p 11. 2 3 1 2 5n n

12. 9 3 12 33x 13. 14 5 or 6 42x x

14. Write an inequality or compound inequality to represent 8, 7, and 4x x x .

15. Write an inequality or compound inequality to represent 2, and 6x x .

Topic 3: Write equations of lines in slope-intercept and standard form

Use the given information to write the equation of the line in slope-intercept form. If it is not possible to write the equation in slope-intercept form, write the equation in standard form. Use improper fractions in your final answers if necessary.

16. 10,7 & 5, 3 17. 5,12 & 5, 4 18. 11, 3 & 6, 3

19. passes through the point 3,5 and has a slope of 2 20. x-intercept is 4 and y-intercept is 2

21. passes through the point 2,3 and is parallel to the line 2 4 10x y

22. passes through the point 3,2 and is perpendicular to the line 2 4 10x y 23.

24. passes through the point 7, 5 and is perpendicular to the line 4y

25. passes through the point 3, 11 and is parallel to the line 8y

Topic 4: Write equations of vertical and horizontal lines

26. Write the equation of the horizontal line that passes through the point 9, 6 .

27. Write the equation of the vertical line that passes through the point 9, 6 .

Topic 5: Recognize positive, negative, undefined and zero slope

Find the slope of the line that passes through the given points. Write your final answers as improper fractions if necessary.

28. 1,4 & 7, 2 29. 11, 14 & 11, 21

30. 5, 14 & 1, 14 31. 4, 5 & 11, 8

32. Find the slope of each line. a) b) c)

Topic 6: Set up and solve proportions

Solve each proportion. Write your final answers as improper fractions if necessary.

33. 7

5 3

x 34.

7 8

10c 35.

6 9

1 7m

36.

3 9

10

x

x

37.

5 8

9 5r r

38. Mary reduced the size of a painting to a width of 3.3 inches . What is the new height if it was originally 32.5 inches tall and

42.9 inches wide? Round your answer to the nearest tenth.

Each pair of figures is similar. Find the value of .x Write your final answers as improper fractions if necessary.

39. 40. 41.

Topic 7: Solve systems of linear equations in two variables using any algebraic method (elimination and substitution)

Solve the linear system by using substitution or elimination. Write your final answers as improper fractions if necessary.

42. 3 2 24

2 8

x y

y x

43.

3 2 4

6 8 4

x y

x y

44. 4 3

3 2 1

y x

x y

45. 2 6

6 3 21

y x

x y

Topic 8: Radicals – simplify (add, subtract, multiply and rationalize the denominator)


46. 45 47. 3 48 48. 200 49. 7 5 5 5 50. 3 8 2 8

51. 6 6 9 6 52. 3 10 53. 3 5 2 12 54. 3 3 3 55. 2

19

56. 25 57.

6

2 58.

12

3 59.

10

10 60.

1

5

Topic 9: Simplify polynomial expressions (add, subtract, and multiply)


61. 2 24 2 5 2x x 62. 2 212 2 18 14 3 9x x x x 63. 2 8 3 9x x

64. 2

4x 65. 2

3 1x 66. 5 2 5 2x x 67. 5 4 8x x

68. 4 1 4 1x x 69. 2 2 23 7 11 2 5 12x x x x x x

Topic 10: Factor polynomial expressions

Factor each expression completely.

70. 2 8 7x x 71.

2 13 40y y 72. 22 4 48n n 73.

24 4 8m m

74. 23 8 4z z 75.

24 17 4d d 76. 215 27 6p p 77.

25 20x x

78. 37 28x x

Topic 11: Solve quadratic equations

Solve each equation. Write your final answers as improper fractions or simplified radicals if necessary.

79. 2 8 80x 80.

22 2 144y 81. 26 18x x 82.

28 11 5x x x 83. 22 9 4y y

84. 212 2 11v v 85.

2 10 16z z 86. 28 6 5m m 87.

210 2n n 88. 23 10x x

Answers:

1. 9x 2. 17

16x 3. 1x 4.

13

9y 5.

7

9x 6. No solution

7. All real numbers 8. 9.

10. No Solution; 11. All real numbers; 12.

13. 14. 4 8;x

15. 6;x 16. 2 1

3 3y x 17. 5x 18. 3y

19. 2 1y x 20. 1

22

y x 21. 1

42

y x 22. 2 4y x 23. 3 8y x

24. 7x 25. 11y 26. 6y 27. 9x 28. 1m

29. undefined 30. 0m 31. 1

5m 32. a)

3

2m b) 2m c) undefined

33. 21

5x 34.

35

4c 35.

51

9m 36. 30x 37.

97

3r

38. 2.5 inches 39. 36x 40. 7x 41. 10x 42. 8,0

43. Infinitely many solutions 44. 1, 1 45. No solution 46. 3 5

47. 12 3 48. 10 2 49. 12 5 50. 10 2 51. 3 6

52. 30 53. 12 15 54. 9 55. 19 56. 5

57. 3 2 58. 4 3 59. 10 60. 5

5 61.

27 6x

62. 22 9x x 63.

26 6 72x x 64. 2 8 16x x 65.

29 6 1x x

66. 225 4x 67.

25 4 8x x 68. 216 1x 69.

4 3 23 9 16 12x x x x

70. 1 7x x 71. 5 8y y 72. 2 6 4n n 73. 4 1 2m m

74. 3 2 2z z 75. 4 4 1d d 76. 3 5 1 2p p 77. 5 4x x

78. 7 2 2x x x 79. 6 2x 80. 73y 81. 0 or 3x x

82. 0 or 2x x 83. 1

4 or 2

y y 84. 2 1

or 3 4

v v 85. 8 or 2z z

86. 1 5

or 2 4

m m 87. 5

2 or 2

n n 88. 5

2 or 3

x x

SUMMER MATH WORK

ALGEBRA 2 & HONORS ALGEBRA 2

SUMMER MATH WORK

AP CALCULUS

Welcome to AP Calculus!

AP Calculus Summer Assignment

The following summer assignment must be completed and ready to hand in on the first day of class.

Show your work!

Text:

Calculus of a Single Variable, 11th edition, Ron Larson/ Bruce Edwards

Regular edition (ISBN 9781337275361) or AP edition (ISBN 9781337286909)

p. 2 Rework example problems 1-6

p. 8 Problems 1-73 odd





p. 31 Use your unit circle to rework example problems 1, 2, 5

p. 34 Use your unit circle to work problems 1-11 odd, 15-21 odd, 29-41 odd

Having trouble remembering how to solve a problem? All of the problems are worked out, step by step, on calcchat.com. See you in August!

Mrs. L

SUMMER MATH WORK

HONORS CALCULUS

SUMMER MATH WORK

PRE-CALCULUS & HONORS PRE-CALCULUS

SUMMER MATH WORK

ALGEBRA 2

SUMMER MATH WORK ALGEBRA 1 - Academy Of The ...

Documents

Transcript of SUMMER MATH WORK ALGEBRA 1 - Academy Of The ...