Name:____________________________ HPMS Algebra I

FALL EXAM REVIEW

Date

Assigned Assignment # missed

Monday

December 9, 2019

Units 1 and 4

Tuesday

December 10, 2019

Unit 2

Wednesday

December 11, 2019

Unit 3

Thursday

December 12, 2019

Unit 5; begin Unit 6

Friday

December 13, 2019

Finish Unit 6; Unit 7

Monday

December 16, 2019

STUDY!

The day of your exam you will TURN IN your Exam Review Packet.

Tuesday 12/17: 1st period Exam

Wednesday 12/18: 2nd and 3rd period Exam

Thursday 12/19: 4th and 5th period Exam

Friday 12/20: 6th and 8th period Exam

Unit 1: Real Number System

Simplify each expression.

1. 3 4 10 2 1 2. 2 6 8 3 1 3. 8 3 2 35 5

4. 235 3 6 2 5. 2

5 6 3 4 2

6. 6 3 2

5 9

7.

4 5 7

6 2 4

8. 4 4 12 9. 23 4 7

Name the property that justifies each statement.

10. a b c a c b 11. 20 20x x 12. 2 2a x ax

13. 4 16 7 4 16 7 14. 1b b 15. 0y y

16. 2 5 2 5y y 17. If 6 9x and 6 9 15 , 18. 2 3 2 6x x

then 15x

19. 24 16x so 8x 20. 1

4 14

21. 5 5 0

Classify each Real number as natural, whole, integer, rational, or irrational.

22. 2 23. 0 24. 35

25. .275 26. 1

12

27. 0.28475

28. 29. 16 30. 15

Unit 2 Equation Solving Solve each equation.

1. 1

69

x 2. 8 4 13x 3. 2 10 5 17x x

4. 4

6 123

n 5. 8 ( 8) 2 9y y 6. 2 10 5 17x x

7. 1

4 8 8 642

x x 8. 2 1

6 9 10 23 2

x x 9. 1

3 9 6 102

x x

Solve each equation for the indicated variable.

10. P a b c for a 11. y kx for K 12. A lw for w

Solve so that y is a function of x.

13. 2 3 18x y 14. 3 7x y 15. 1 2

102 5

x y

Solve each proportion.

16. 2 2

3 15x 17.

12 1

3 4x

18.

6

2 8

x x

19. 3 3 5 3

7 9

x x 20.

1 3

2 9

x

x

Define your variables, then write an equation and solve.

21. An angle measures 12 degrees more than its complement. Find the number of degrees in each

angle.

22. A flower garden is in the shape of a triangle. The middle length is one foot less than twice the

length of the shortest side. The longest side is four feet less than three times the shortest side. Find

the lengths of the three sides of the garden if the perimeter is 43 feet. To define your variables you

may draw a picture.

23. Nineteen less than three-fourths of a number is thirty-two. Find the number.

24. The width of the rectangle is 8 and the length is 2x – 1. Find the length of the rectangle if the

area is 100.

25. The perimeter of a square is 16x and each side is x + 6. Find x.

26. The perimeter of a rectangle is 140 inches. The length is 28 inches greater than the width. Find

the width of the rectangle.

27. The ratio of two integers is 9:7. Their sum is 1024. Find the two integers.

28. The sum of four consecutive odd integers is 336. Find the largest integer.

29. For three consecutive integers, the sum of the first integer, twice the second integer, and three

times the third integer is –64. Find the three integers.

30. Find three consecutive odd integers if the sum of the first two integers is equal to twenty-four

less than four times the third integer.

Unit 3 Linear Equations

1. Graph:

a. 3y x

b. 3 2y x

c. 10 8 40x y

Use intercepts

d. 5 3 10y x

e. 4 2 1x y f. 1

3 12

y x

y

x 8 -6 -2 4 8

8

-6

-2

4

8

-8 2

-8

-4

6

-4

-8

-8

2

6

y

x 8 -6 -2 4 8

8

-6

-2

4

8

-8 2

-8

-4

6

-4

-8

-8

2

6

y

x 8 -6 -2 4 8

8

-6

-2

4

8

-8 2

-8

-4

6

-4

-8

-8

2

6

y

x 8 -6 -2 4 8

8

-6

-2

4

8

-8 2

-8

-4

6

-4

-8

-8

2

6

y

x 8 -6 -2 4 8

8

-6

-2

4

8

-8 2

-8

-4

6

-4

-8

-8

2

6

y

x 8 -6 -2 4 8

8

-6

-2

4

8

-8 2

-8

-4

6

-4

-8

-8

2

6

2. Write the equation of the vertical line through (7, -1).

3. Write the equation of the horizontal line through (4, 6).

4. What is the slope of all lines parallel to 4 3y x ?

5. What is the slope of all line perpendicular to y x 3?

6. What is the slope of the y-axis?

7. What is the slope of all horizontal lines?

8. Find the slope between 5, 4 and 7, 1 .

9. Find the slope between 0,8 and 8, 2 .

10. Find the slope of the line 8x y .

11. Find the slope of the line 5 1x y .

12. What is the slope of the line 2x ?

13. What are the x- and y-intercepts of the line: 9 12 36x y .

x-intercept ______________ y-intercept____________

14. What are the x- and y-intercepts of the line: 12 8 60x y .

x-intercept ______________ y-intercept____________

For #15-19, write the equation of the line in point-slope, slope-intercept, and standard form.

(For standard form A, B, C are integers and A is positive).

15. Slope = 1

4 and contains the point 4, 2 .

16. Slope = 2 and contains the point 5, 1 .

For #15-19, write the equation of the line in point-slope, slope-intercept, and standard form.

(For standard form A, B, C are integers and A is positive).

17.

18. Slope = 2

5 and contains the point 7, 2 .

19. Contains the points 1,6 and 4,21 .

20. Write a linear equation in slope-intercept form of a line that is parallel to 3y x and

contains 2,9 .

21. Write a linear equation in slope-intercept form of a line that is perpendicular to 2 4y x and

contains 2,4 .

x y

-5 3

0 0

5 -3

10 -6

22. Write a linear equation in standard form that is perpendicular to 2

55

y x and has the

following points.

23. Write the equation of each line in slope-intercept form.

line k _________________________________

line m _______________________________

line n ________________________________

line p ________________________________

Unit 4 Functions

For each relation state the domain and range. Determine whether each relation is a function.

1. 4,1,2,5,3,1,4,2 2. 3.

4. What is the range of the function 2 3f x x when the domain is 1,1,3 ?

5. What is the domain of the function 23 xxf when the range is 4, 1,2 ?

x y

-2 -6

0 -1

2 4

4 9

6. Write the domain and range using inequality notation.

7. For the function 2 5f x x find each value.

a) 3f b) 5f c) 0f

8. A company pays its salespeople $2000 a month and a commission of 18% of their total sales.

a) Write an equation expressing total monthly income as a function of sales.

b) Name the independent and dependent variables.

___________________________________ ________________________________

c) What would be the monthly income if a sales person had $5000 in sales.

d) How many dollars of sales must the person sell in order to make $3,600 for their total income?

9. Look at the graph.

a. Does this graph represent a function?

b. f (−1) = _____

c. f (______) = −4

d. f (0) = ______

Unit 5: Linear Applications

Find the zero of the following functions. Write your answer as an ordered pair.

1.

13

4y x 2. 2 4y x 3. 3 5 27x y

Direct Variation

4. If y varies directly as x, write an equation using y kx when y = 35 and x = 5.

5. If y varies directly as x, write an equation using y kx when y = 21 and x = 5.

6. If y varies directly as x, write an equation using y kx when y = 6 and x = 24.

7. Using the equation from #4, find y when x = 11.

8. Using the equation from #5, find x when y = 42.

9. Jim’s wages vary directly as the number of hours he works. For seven hours of work he earns

$57.75.

a) Write a direct variation equation to represent this situation.

b) How many hours did he work if he earned $198?

Arithmetic Sequences 1 1na a d n

10. Write an equation to represent the following sequence. Simplify the equation.

8.5, 8, 7.5, 7, 6.5

11. Write an equation to represent the following sequence. Simplify the equation.

– 2, 1, 4, 7, 10

12. Find the 50th term of the sequence from #11.

Linear Transformations

13. Describe the transformation of the function ( )f x x to ( ) 3 2g x x .

14. Describe the transformation of the function 1

( )2

f x x to 1

( )5

g x x .

15. Describe the transformation of the function ( ) 5f x x to ( ) 5g x x .

Linear Applications

16. Jay collects baseball cards. His father gave him some cards to start his collection. Each year

his uncle gives him new cards, the same number each year. A function for the total number of cards,

c, he has after, x, years is given by 15 40c x .

a) What is the meaning of the number 15 (the slope) in this function?

b) What is the meaning of the number 40 (the y-intercept) in this function?

17. The table shows the cost of visiting a working ranch for one day and night for different numbers

of people.

a) Write an equation in slope-intercept form that gives the cost as a function of the number of people in the group.

b) Graph the function using a discrete graph for the x values {1, 2, 3, 4, 5}.

Number

of People

4 6 8 10 12

Cost

(dollars)

350 450 550 650 750

100

300

500

200

400

5 2 4

0 1 5 0 3

18. You have a $10 on a copy card. The copy store charges $.10 for each black and white copy,

and $1 for each color copy.

a) Write and equation in standard form to represent this situation. Let x = b&w and y = color

b) Identify the x and y intercepts. Please write them as an ordered pair.

x-intercept _____________ y-intercept _____________

c) Graph the equation.

d) State the domain and range.

e) List three possible combinations other than the intercepts.

19. You use a garden hose to fill a swimming pool at a constant rate. After 5 minutes, there are

115 gallons of water in the pool. After 30 minutes, there are 190 gallons of water in the pool.

a) Write an equation in slope-intercept form that gives the gallons of water as a function of time

(in minutes) since you began filling the pool.

b) How much water was in the pool to begin with?

c) What is the constant rate of change (slope)?

10

2

6

4

8

0 20 0 40 60 80

0 100

Unit 6: Inequalities and Absolute Value

Solve each inequality.

1. 3 10 14x 2. 9 45x 3. 25 3 33x x

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

4 52

x

7. 19 2 5 or 4x-6 6x 8. 7 3 11x 9. 52 4 3 13x

Graph each linear inequality.

10. 3y

11. 6y x

12. 3 2y x

13. 9 3 12x y

14. 10 4 0y x

y

x 8 -6 -2 4 8

8

-6

-2

4

8

-8 2

-8

-4

6

-4

-8

-8

2

6

y

x 8 -6 -2 4 8

8

-6

-2

4

8

-8 2

-8

-4

6

-4

-8

-8

2

6

y

x 8 -6 -2 4 8

8

-6

-2

4

8

-8 2

-8

-4

6

-4

-8

-8

2

6

y

x 8 -6 -2 4 8

8

-6

-2

4

8

-8 2

-8

-4

6

-4

-8

-8

2

6

y

x 8 -6 -2 4 8

8

-6

-2

4

8

-8 2

-8

-4

6

-4

-8

-8

2

6

Solve each Absolute Value Equation or Inequality.

15. 4 8 20x 16.

33 9

4a 17.

15 3

2x

18. 2 6 4 10y 19.

19

2x 20. 4 2 10x

21. 2 2 1 14b 22. 3 5 20x

Graph each absolute value function. Describe the transformation from the parent function.

23. 1 2y x 24.

15

2y x

y

x 8

8

-8

-8

y

x 8

8

-8

-8

Graph each absolute value function. Describe the transformation from the parent function.

25. y x 26. 3 2y x

Unit 7: Systems of Linear Inequalities

Solve each system by graphing.

1. 6

4 2

y

y x

2.

2

3 3 9

x y

x y

Solve each system using substitution or elimination. Show your work.

3. 12

2

x y

y x

4.

2 6

3 4 1

x y

x y

5. 2 3 6

6 9 9

x y

x y

6.

1 4

3 12 3

x y

x y

y

x 8 -6 -2 4 8

8

-6

-2

4

8

-8 2

-8

-4

6

-4

-8

-8

2

6

y

x 8

8

-8

-8

y

x 8

8

-8

-8

y

x 8 -6 -2 4 8

8

-6

-2

4

8

-8 2

-8

-4

6

-4

-8

-8

2

6

Write a system of equations that represents the situation. Then solve.

7. The length of a rectangle is 4 feet more than the width. The perimeter is 40 feet. Find the length

and the width.

8. Yesterday a total of 24 students were present in Alfred’s class. There were 3 fewer girls than

twice the number of boys. Find the number of girls and boys who were present in Alfred’s class

yesterday.

9. A truck is carrying 1500 pounds of cargo that occupies 138 cubic feet of space. A television

weighs 50 pounds and occupies a space of 4 cubic feet. A microwave oven weighs 30 pounds

and occupies a space of 3 cubic feet. What is the total number of televisions, t, and microwaves,

m, that are in the truck?

10. Mark has $4.95 in quarters and dimes. He has 3 times as many dimes as quarters. What is the

total number of quarters and dimes that Mark has?

11. Kelley has 24 dimes and quarters worth $3.60. How many quarters does she have?

12. A person invests $5000 in treasury notes and bonds. The notes pay 8% annual interest and the

bonds pay 10% annual interest. If the annual income is $480, how much is invested in treasury

notes?

13. Biking into the wind on a flat path, a bicyclist takes 5 hours to travel 30 miles. The return bike

takes 3 hours. The wind speed remains constant during the trip. Remember to find the bicyclist’s

average speed for each leg of the trip. What is the bicyclist’s average speed in still air? What is the

speed of the wind?

Graph the system of inequalities:

14. 2 5

2 6

y x

x y

15.

2

3 4

y

x y

y

x 6

6

-6

-6

y

x 6

6

-6

-6