Honors Algebra 2 Algebra 1 Review - hasd.us 1 Review Packet...Algebra 1 Review Name: _____ Honors Algebra 2 Algebra 1 Review

Algebra 1 Review Name: ____________________

Honors Algebra 2

Algebra 1 Review

Due: Thursday, August 22, 2019

This packet contains review material based on Algebra 1 concepts. Concepts such as fractions, solving

equations, inequalities, absolute values, writing equations, graphing linear equations, and linear inequalities are

contained in this packet. The packet allows us to start directly into the Algebra 2 curriculum.

This course requires each student to complete a review packet. The packet must be turned into the office no

later than 2:30 pm on August 22, 2019. After successful completion of the packet, you will take a basic

Algebra 1 test on the first day of school. All students must score 85% or higher on the test to remain in the

class. Failure to complete the packet and achieve the required score will result in schedule changes.

I suggest using your Algebra 1 notebook as a resource to assist in completing the packet. If you do not have

your notebook, refer to Khan Academy (www.khanacademy.org ) for video instruction or google the specific

concept.

The packet should take about 3 hours to complete. I recommend working on the packet throughout the summer,

and start reviewing the information a week before school commences.

I will have a copy of each page and answer key posted on my web page. If you have any questions during the

summer, please contact me via e-mail ([email protected] ). I will check my email twice a week, and will

respond promptly.

Have a great summer. See you in the fall.

Mrs. Amoriello

http://www.khanacademy.org/

mailto:[email protected]



Fractions No Calculator!

Show all your work for each problem.

Add or Subtract: rewrite with a common denominator and add/subtract.

1. 12

5

8

3 2.

12

1

4

7 3.

2

1

4

3 4.

2

1

8

7

5. 3

1

5

2 6.

6

5

9

8 7.

14

2

7

6 8.

4

3

10

3

Multiplication: cancel and multiple numerator and denominator.

Canceling factors:

Ex: 21

8

3

4

7

2

33

4

7

32

9

4

7

6

9. 8

3

5

2 10.

8

7

3

10 11.

9

14

7

8 12.

3

4

6

1

13. 16

3

3

8 14.

6

5

15

2 15.

7

24

8

21 16.

22

3

18

11

Multiply or Divide.

Division: Take the reciprocal of the second fraction, and multiply.

17. 5

4

3

2 18.

15

4

8

5 19.

6

5

4

3 20.

6

58

21. 2

1

12

5 22.

10

3

8

7 23.

12

7

16

21 24.

16

15

24

25

1


Solving Equations

Solve the following linear equations.

1. 3286 x 2. 1112 x 3. 12432 x

4. 22284 xx 5. 1629 xx 6. 2825 xx

7. 143 x 8. 10432 x 9. 1514 x

10. xx 3514 11. xx 8172111 12. xx 56853

13. 4563 xx 14. 33234 xxx 15. 367671 xx

16. xxx 3254625 17. xxxx 84285515

2


Fraction Equations

The following equations contain fraction coefficients and constants. In solving these equations, the fraction

rules for adding, subtracting, multiplying and dividing will be applied.

Ex: Solve Ex: Solve

Solve. Show all fraction work. NO Calculators!

1. 6

1

3

1

6

1y 2.

8

5

2

1

4

1x

3. 2

1

6

1

3

1 xx 4.

2

1

8

3

4

3 aa

5. 11363

1p 6. 3128

4

3x

7. 24

13

5

1 nn 8. 7

4

13

2

1 mm

9. 3

2

3

23

4

1

x 10.

6

5

4

1

2

1

3

2

y 11.

6

5

2

5

4

3

3

2

2

3

8

3pp

3

2

3

4

2

3

3

4

6

9

4

3

3

4

6

4

6

5

4

3

3

2

6

5

4

3

6

5

3

2

4

3

x

xx

xx

x

15

49

4

15

15

49

15

4

4

15

15

49

15

4

15

40

15

9

15

4

3

8

5

3

15

4

5

3

3

8

15

4

5

34

5

2

3

2

xxx

xxx

x


Solving for y

Solve the following equations for y. Ex: 1052 yx

1. 32 yx 2. 74 yx 3. 22 yx 4. 69 yx

5. 1684 yx 6. 935 yx 7. 1028 yx 8. 7412 yx

9. 3093 yx 10. 1275 yx 11. 112 yx 12. 1036 yx

Rewriting Formulas

Solve the formula for the indicated variable.

13. Solve for w: wlA 14. Solve for t: trd

15. Solve for r: rC 2 16. Solve for P: PI rt

17. Solve for b: hbA2

1 18. Solve for h: hrV 2

3

1

4

1025 xy

5

10

5

2

xy

25

2

xy


Solving Simple Inequalities

-Switch the inequality symbol when you or by a negative number.

1. 135 x 2. 1956 x 3. 1714 x

4. 1265 x 5. 2517 x 6. 7415 x

7. 149 x 8. 1637 x 9. 6212 x

Solving Complex Inequalities 1) Distribute

2) Combine Like Terms

3) Move Variables to one side

4) Move Numbers to the other side

10. 342 x 11. 282

1x 12. 642 x

13. 42

315 x 14. 234 xx 15. 146 xx

16. 2539 xx 17. xx 4733 18. 6326 xx

5


Compound Inequalities:

-two simple inequalities joined by “and” or “or”.

Ex: “AND” Solve 10832 x Ex: “OR” Solve 974532 xORx

1836 x 16422 xx

62 x 1x 4x

Solve the inequality and graph its solution.

1. 71211 x 2. 6118 x

3. 065 x 4. 742

310 x

5. 151231 xorx 6. 6366715 xorx

7. 4421024 xorx 8. 21451312 xorx

6


Absolute Value Equations Ex: 952 x 952952 xx

14242 xx

72 xx

Solve the equation.

1. 45 x 2. 952 x 3. 5132 x

4. 1374 x 5. 2043 x 6. 12315 x

Absolute Value Inequalities

Ex: Less Than 1172 x AND Ex: Greater Than 823 x OR

117211 x 823823 xORx

4218 x 10363 xORx

29 x 3

102 xORx

Solve the inequality.

7. 352 x 8. 243 x 9. 1172 x

10. 823 x 11. 1354 x 12. 26610 x

7


Point-Slope Form: )( 11 xxmyy

Ex: 2,5;3m

1. Substitute m and the point. )( 11 xxmyy 532 xy

1532 xy

2. Change to slope-intercept form. bmxy 173 xy

Write the equation of the line that passes through the given point with the given slope.

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

4. 5,8,4

3m 5. 7,2,0m 6. 3,5,

5

2m

7. 1,4,6m 8. 2,7,2 m 9. 8,1,9 m

Parallel Lines Ex: 9,3,155 xy

-Parallel Lines have the same slope. 5m

359 xy solve for y.

Write the equation of the line that is parallel to the given line and passes through the given point.

10. 3,2,62 xy 11. 6,9,113 xy 12. 7,8,6 xy

13. 1,2,82

1 xy 14. 7,3,14 xy 15. 5,3,

3

2 xy

8


Perpendicular lines – opposite, reciprocal slopes

Ex: 1,1,62

1 xy

2m

121 xy solve for y.

Write the equation of the line that is perpendicular to the given line and passes through the given point

16. 4,2;3 xy 17. 2,5;92

1 xy

18. 1,3;73 xy 19. 3,8;65

4 xy

Two Points:

To write an equation given two points: Ex: 2,18,4 and

1. Find m. 23

6

14

28

m

2. Select a point. 2,1

3. Substitute m and the point. )( 11 xxmyy 122 xy

222 xy

4. Change to slope-intercept form. bmxy xy 2

Write in slope-intercept form the equation of the line that passes through the given points.

20. 3,18,0 and 21. 3,59,7 and 22. 5,32,4 and

23. 15,37,1 and 24. 14,102,6 and 25. 4,85,4 and

9


Standard Form: CByAx

-integer coefficients

- A is positive Ex:

Write the equation in standard form.

1. 93 xy 2. 56 xy 3. 4794 yx 4. 392 yx

5. xy 25 6. 1674 xy 7. 136 xy 8. 244 xy

9. 42

1 xy 10. 1

5

2 xy 11. 2

7

3 xy

12. 2

7

2

1 xy 13.

8

5

4

3 xy 14.

4

1

6

5 xy

10

43

1 yx

433

13

yx

123 yx

43

1 xy


Ex: 1,57,0 and 5

6

5

6

50

17

m 7

5

6 xy

05

67 xy 7

5

6 yx

xy5

67 75

5

65

yx

75

6 xy 3556 yx

Write the equation in slope-intercept form, then change it to standard form with integer coefficients.

15. 2,8,6 m 16. 2

1,1,4 m 17.

5

4,5,1 m

18. 1,74,6 and 19. 2,53,10 and 20. 6,29,4 and

11


Graphing Linear Equations

Find b and m. Graph the equation using slope-intercept form (y = mx + b).

1. 12 xy 2. 33 xy 3. 2 xy

b = b = b =

m = m = m =

4. 42

1 xy 5. 6

3

2 xy 6. xy

4

3

b= b = b =

m = m = m =

7. 5y 8. 4y 9. 2y

b = b = b =

m = m = m =

12


10. 32 xy 11. 13 xy 12. 4 xy

b = b = b =

m = m = m =

13. 22

3 xy 14. 5

3

1 xy 15. 3

5

2 xy

b= b = b =

m = m = m =

16. xy4

1 17. 3x 18. 1x

b = b = b =

m = m = m =

13


Graphing Linear Equations in Standard Form

Write the equation in slope-intercept form (y = mx + b). Find b and m, and graph the equation.

1. 52 yx 2. 3 yx 3. 65 yx

y = y = y =

b = m = b = m = b = m =

4. 43 yx 5. 3 yx 6. 1472 yx

y = y = y =

b = m = b = m = b = m =

14


7. 332 yx 8. 043 yx 9. 425 yx

y = y = y =

b = m = b = m = b = m =

10. 44 yx 11. 42 y 12. 323 yx

y = y = y =

b = m = b = m = b = m =

15


Graphing Linear Inequalities: 1) Graph the corresponding equations (Dotted for < > Solid for ≤ ≥)

2) Test point Use (0, 0) if possible.

3) Shade Solutions

Ex: Sketch the graph of 2 yx

Corresponding equation: 2 yx

2 xy

2 xy 21

1 bm

Test: (0, 0)

20 true

Graph the side with (0, 0)

Sketch the graph of each linear inequality.

1. 3y 2. 2x

3. xy 3 4. 52 xy

16

200


5. 1 xy 6. 44 xy

7. 42

1 xy 8.. 3

5

3 xy

9. 423 yx 10. 42 yx

17


Answer Key: Page 1 Fractions:

1. 24

19 2.

6

11 3.

4

5 4.

8

3 5.

15

1 6.

18

1 7. 1 8.

20

9 9.

20

3 10.

12

35 11.

9

16 `

12. 9

2 13.

2

1 14.

9

1 15. 9 16.

12

1 17.

15

8 18.

6

1 19.

8

5 20.

3

20 21.

6

5

22. 12

35 23.

4

9 24.

9

10

Page 2 Solving Equations:

1. 4x 2. 6x 3. 5x 4. 2x 5. 1x 6. 4x 7. 313x 8. 3x 9. 4x

10. 4/7x 11. 2x 12. 1x 13. 19x 14. 21x 15. 5x 16. 10x

17. 5x

Page 3 Solving Fraction Equations:

1. 3y 2. 21x 3. 1x 4. 2a 5. 6p 6. 2x 7. 2n 8. 1m 9. 32x

10. 3y 11. 32p

Page 4 Solving for y

1. 32 xy 2. 74 xy 3. 12/1 xy 4. 69 xy 5. 22/1 xy 6. 33/5 xy

7. 54 xy 8. 4/73 xy 9. 3/103/1 xy 10. 7/127/5 xy 11. 112 xy

12. 3/102 xy

Formulas: 13. lAw / 14. rdt / 15. 2/Cr 16. rtIP / 17. hAb /2 18. 2/3 rVh

Page 5 Simple Inequalities

1. 18x 2. 5x 3. 4x 4. 6/7x 5. 3x 6. 2x 7. 5x 8. 3x 9. 9x

10. 2/11x 11. 12x 12. 5x 13. 6x 14. 2/1x 15. 1x 16. 2/1x 17. 16x

18. 6x .

Page 6 Compound Inequalities

1. 63 x 2. 53 x 3. 16 x 4. 24 x 5. 27 xorx 6. 32/1 xorx

7. 03 xorx 8. 65 xorx

Page 7 Absolute Value

Equations: 1. 19 xx 2. 72 xx 3. 49 xx 4. 52/3 xx

5. 3/168 xx 6. 19 xx

Inequality: 7. 41 x 8. 3/22 xorx 9. 29 x 10. 3/102 xorx

11. 22/9 x 12. 63/8 xorx

Page 8 Writing Equations of Lines

Point-Slope: 1. 75 xy 2. 13 xy 3. xy 4. 14/3 xy 5. 7y 6. 55/2 xy

7. 236 xy 8. 162 xy 9. 19 xy

Parallel Lines: 10. 12 xy 11. 213 xy 12. 1 xy 13. 22/1 xy 14. 54 xy

15. 33/2 xy


Page 9 Writing Equations of Lines

Perpendicular Lines: 16. 6 xy 17. 82 xy 18. 23/1 xy 19. 134/5 xy

Two Points: 20. 85 xy 21. 336 xy 22. 143 xy 23. 34 xy 24. 163 xy

25. 24/3 xy

Page 10 Standard Form

1. 93 yx 2. 56 yx 3. 1194 yx 4. 122 yx 5. 052 yx 6. 1647 yx

7. 93 yx 8. 124 yx 9. 82 yx 10. 552 yx 11. 1473 yx 12. 72 yx

13. 586 yx 14. 31210 yx

Page 11 Standard Form

15. 42 yx 16. 62 yx 17. 2154 yx 18. 345 yx 19. 55 yx 20. 225 yx

Page 12-13 Graphing Slope-Intercept Form

1. 2;1 mb 2. 3;3 mb 3. 1;2 mb 4. 2/1;4 mb 5. 3/2;6 mb 6. 4/3;0 mb

7. 0;5 mb 8. 0;4 mb 9. 0;2 mb 10. 2;3 mb 11. 3;1 mb

12. 1;4 mb 13. 2/3;2 mb 14. 3/1;5 b 15. 5/2;3 mb 16. 4/1;0 mb

17. NoSlopemNoneb ; 18. NoSlopemNoneb ;


Page 14-15 Graphing Standard Form

1. 2;5;52 mbxy 2. 1;3;3 mbxy 3. 5;6;65 mbxy 4. 3;4;43 mbxy

5. 1;3;3 mbxy 6. 7/2;2;27/2 mbxy 7. 3/2;1;13/2 mbxy

8. 4/3;0;4/3 mbxy 9. 2/5;2;22/5 mbxy 10. 4/1;1;14/1 mbxy

11. 0;2;2 mby 12. 2/3;2/3;2/32/3 mbxy

Page 16-17 Graphing Linear Inequalities

1. 0;3 mb 2. NoSlopemNoneb ; 3. 3;0 mb 4. 2;5 mb 5. 1;1 mb

6. 4;4 mb 7. 2/1;4 mb 8. 5/3;3 mb 9. 2/3;2 mb 10. 2;4 mb

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Honors Algebra 2 Algebra 1 Review - hasd.us 1 Review Packet...Algebra 1 Review Name: _____ Honors Algebra 2 Algebra 1 Review