summer review for students entering geometry remember: your high school mathematics courses require...

SUMMER REVIEW for students entering

GEOMETRYREMEMBER Your high school mathematics courses require you to use concepts learned in previous math classes Use this Summer Review to review skills that you will need to be successful in geometry

Surfs up Make waves with math

Give two ways to write each algebraic expression

in wordsNOTE Answers will vary

1 x + 3 2 2m ndash 7 3 5y

041923 Mrs McConaughy Geometry

2

Possible phrases for each of the previous expressions

1 3 more than a number a number increased by 32 7 less than twice a number twice a number decreased by 7

3 5 times a number

Evaluate each expression for

x = 8 y = 5 and z = 44 x + y 8 + 5 135 xz 84 2041923 Mrs McConaughy

Geometry3

Evaluate each expression

6 (-2)3

-8 49

22

3


4

Find each square root

8

9

36

49


5

Time to recall your

perfect squares

8

9

-6

7

Write all classifications that apply to each real number (natural whole integer rational irrational)

10 89

11 12


6

HINT Use the Venn Diagram

Simplify each expression

12 -24 + 22 ndash 4 middot 3 13 10 - 52+ 5 - 24 + 4 ndash 4 3 10 - 25+ 5 - 24 + 4 ndash 12 - 15+ 5

-20 ndash 12 15 + 5

- 32 20

14 12x + 30x 15 8y2 ndash y2

42x 7y2

16 4n + 11n2 17 4 (2x ndash 5) DONE 8x - 518 2(x + 5) ndash 3 (x ndash 2)

Time flies when yoursquore having

fun


7

Recall Order of Operations Combining Like Terms Absolute Value

- x + 16

Solve each equation19 2x + 6 = 10 20

2x = 4 x + 3 = 40

x = 2 x = 37

21 2 (x + 1) = 14 22 2 (3x + 1) ndash 8x = 12

x = 6 x = -5

23 4x + 5 = 7x + 11 24 -7x ndash (x ndash 3)= 2 (5x ndash 3)

x = -2 x = frac12

25

38

5

x

4

25

x

x

Take a break 041923 Mrs McConaughy

Geometry

8x = 10

Write and solve each proportion

26The ratio of band members to non-band members in Seneca Valley Intermediate High School is 25 There are 875 students in grades 9 and 10 How many band members are there

27 Seneca Valley track star I M Fleetfeet ran at a rate of 6 mih What is this speed in milesminute


9

250 band members 625 non- band members

110 mileminute or 1 mileminute

Solve each inequality and graph on a number line

28 18 + 2x le 50 x le 16 16

29 7 ndash 2t le 21 t ge - 7 -7


10

RecallRULE When multiplying or dividing an inequality by a negative number always reverse the symbol of inequality

Find the slope of each line

30 31


11

m = 0 Slope m is undefined

Find the slope of the line containing the given points

32 (12) amp (7 -2)

33 (- 410) amp (03)

Time to cool off with ski

bird


12

m = -2 ndash 2 7 - 1 = -46 = -23

m = 10 ndash 3 -4 - 0 = 7-4

Graph each equation

34 y = -2

35 x = 4

36 y = - frac12 x + 4

37 y = 5x - 3

NOTE Remember to label your lines


13

Write the equation of the line in slope-intercept form

38slope = frac12 y-intercept = -5

39 slope = -3 y-intercept = 0

40 through the points (1-4) and (32)


14

y = mx + b y = 12x - 5

y = mx + b y = -3x

Step 1 Find slope m Step 2 Use point- slope form of a line

y = 3x - 7

41 Find the x and y intercepts of -2x + 4y = 7 x-intercept (-72 0) y-intercept (0 74)42 Is the point (4 14) on the line y = -3x + 2

Explain No because when substituting x and y values into

the equation y = -3x + 2 your final equation is 14 = -10 which is false since 14 ne -10

43 Solve the system of equations by graphing y = x ndash 3 y = -x + 1


15

HINT Step 1 Graph each line on the coordinate plane using slope-intercept method Step 2 Find the coordinates of the point of intersection

SimplifyRecall Basic Rules for Exponents

44 25 middot 26 45 (25)6

2 11 or 2048 230

46 a4 middot b2 middot a5 47 (4x2y6)(-2x3y4)2

a9 b2 16x8y14

48 33 or 27 49 3ab5

5

2

3

3

5 9

4 4

6

2

a b

a b


16

Evaluate each function for the given input value

50 For y = 2x + 10 find y when x = 6

51 For y = frac12 t ndash 3 find y when t = 12


17

Y = 2(6) + 10Y = 12+ 10

Y = 22

Y = frac12 (12) -3Y = 6-3

Y = 3

Evaluate the exponential function

52 The function y = 2(3)x models an insect population after x days What will the population be on the 5th day


18

Substitute 5 for x to determine 486 insects

Add or subtract the polynomials

53 (2x2 ndash x) + x2 + 3x ndash 1) 3x2 +2x -154 (a4 ndash 2a) ndash (3a4 ndash 3a ndash 1) (a4 ndash 2a) ndash 3a4 +3a + 1 -2a4 + a + 1


19

Recall Combine like terms

Like terms have the same variable

and the same exponent

Distribute the negative

Multiply

55 (5x2) (4x3) 56 5 (2x2 + x + 4)

57 (x + 2) (x ndash 5) 58 (x -5)2

59 (2x + 7) (2x ndash 7) 60 (x ndash 3) (x2 + 2x + 3)


20

20x5

x2 -3x-10

4x2 - 49

10x2 + 5x + 20

x2 - 10x + 25

x3 + 2x2 + 3x

- 3x2 - 6x - 9 +x3 - x2 - 3x - 9

Factor completely

61 4x2 ndash 3x 62 x2 + 6x + 8

63 x2 ndash 10 x + 16 64 x2 + 7x -18

65 x2 + 12x + 36 66 25x2 - 81

67 5x2 ndash 14x + 8 68 4x2 + 19x - 5


21

x (4x ndash 3)

(x ndash 8) (x-2)

(x + 6)2

(5x - 4) (x ndash 2)

(x + 4) (x + 2)

(x + 9) (x - 2)

(5x - 9) (5x + 9)

(4x - 1) (x + 5)

Yoursquore finished


22

SUMMER REVIEW for students entering GEOMETRY

Give two ways to write each algebraic expression in words

Evaluate each expression for x = 8 y = 5 and z = 4





Solve each equation





Graph each equation


PowerPoint Presentation

Simplify Recall Basic Rules for Exponents




Multiply

Factor completely

Yoursquore finished

Give two ways to write each algebraic expression

in wordsNOTE Answers will vary

1 x + 3 2 2m ndash 7 3 5y


2

Possible phrases for each of the previous expressions

1 3 more than a number a number increased by 32 7 less than twice a number twice a number decreased by 7

3 5 times a number



Geometry3


6 (-2)3

-8 49

22

3


4


8

9

36

49


5

Time to recall your

perfect squares

8

9

-6

7


10 89

11 12


6




-20 ndash 12 15 + 5

- 32 20

14 12x + 30x 15 8y2 ndash y2

42x 7y2



fun


7


- x + 16


2x = 4 x + 3 = 40

x = 2 x = 37

21 2 (x + 1) = 14 22 2 (3x + 1) ndash 8x = 12

x = 6 x = -5


x = -2 x = frac12

25

38

5

x

4

25

x

x


Geometry

8x = 10





9




28 18 + 2x le 50 x le 16 16

29 7 ndash 2t le 21 t ge - 7 -7


10



30 31


11



32 (12) amp (7 -2)

33 (- 410) amp (03)


bird


12

m = -2 ndash 2 7 - 1 = -46 = -23

m = 10 ndash 3 -4 - 0 = 7-4

Graph each equation

34 y = -2

35 x = 4

36 y = - frac12 x + 4

37 y = 5x - 3



13






14

y = mx + b y = 12x - 5

y = mx + b y = -3x


y = 3x - 7






15



44 25 middot 26 45 (25)6

2 11 or 2048 230


a9 b2 16x8y14

48 33 or 27 49 3ab5

5

2

3

3

5 9

4 4

6

2

a b

a b


16





17

Y = 2(6) + 10Y = 12+ 10

Y = 22

Y = frac12 (12) -3Y = 6-3

Y = 3




18





19





Multiply

55 (5x2) (4x3) 56 5 (2x2 + x + 4)

57 (x + 2) (x ndash 5) 58 (x -5)2



20

20x5

x2 -3x-10

4x2 - 49

10x2 + 5x + 20

x2 - 10x + 25

x3 + 2x2 + 3x

- 3x2 - 6x - 9 +x3 - x2 - 3x - 9

Factor completely

61 4x2 ndash 3x 62 x2 + 6x + 8

63 x2 ndash 10 x + 16 64 x2 + 7x -18

65 x2 + 12x + 36 66 25x2 - 81

67 5x2 ndash 14x + 8 68 4x2 + 19x - 5


21

x (4x ndash 3)

(x ndash 8) (x-2)

(x + 6)2

(5x - 4) (x ndash 2)

(x + 4) (x + 2)

(x + 9) (x - 2)

(5x - 9) (5x + 9)

(4x - 1) (x + 5)

Yoursquore finished


22








Solve each equation





Graph each equation







Multiply

Factor completely

Yoursquore finished



Geometry3


6 (-2)3

-8 49

22

3


4


8

9

36

49


5

Time to recall your

perfect squares

8

9

-6

7


10 89

11 12


6




-20 ndash 12 15 + 5

- 32 20

14 12x + 30x 15 8y2 ndash y2

42x 7y2



fun


7


- x + 16


2x = 4 x + 3 = 40

x = 2 x = 37

21 2 (x + 1) = 14 22 2 (3x + 1) ndash 8x = 12

x = 6 x = -5


x = -2 x = frac12

25

38

5

x

4

25

x

x


Geometry

8x = 10





9




28 18 + 2x le 50 x le 16 16

29 7 ndash 2t le 21 t ge - 7 -7


10



30 31


11



32 (12) amp (7 -2)

33 (- 410) amp (03)


bird


12

m = -2 ndash 2 7 - 1 = -46 = -23

m = 10 ndash 3 -4 - 0 = 7-4

Graph each equation

34 y = -2

35 x = 4

36 y = - frac12 x + 4

37 y = 5x - 3



13






14

y = mx + b y = 12x - 5

y = mx + b y = -3x


y = 3x - 7






15



44 25 middot 26 45 (25)6

2 11 or 2048 230


a9 b2 16x8y14

48 33 or 27 49 3ab5

5

2

3

3

5 9

4 4

6

2

a b

a b


16





17

Y = 2(6) + 10Y = 12+ 10

Y = 22

Y = frac12 (12) -3Y = 6-3

Y = 3




18





19





Multiply

55 (5x2) (4x3) 56 5 (2x2 + x + 4)

57 (x + 2) (x ndash 5) 58 (x -5)2



20

20x5

x2 -3x-10

4x2 - 49

10x2 + 5x + 20

x2 - 10x + 25

x3 + 2x2 + 3x

- 3x2 - 6x - 9 +x3 - x2 - 3x - 9

Factor completely

61 4x2 ndash 3x 62 x2 + 6x + 8

63 x2 ndash 10 x + 16 64 x2 + 7x -18

65 x2 + 12x + 36 66 25x2 - 81

67 5x2 ndash 14x + 8 68 4x2 + 19x - 5


21

x (4x ndash 3)

(x ndash 8) (x-2)

(x + 6)2

(5x - 4) (x ndash 2)

(x + 4) (x + 2)

(x + 9) (x - 2)

(5x - 9) (5x + 9)

(4x - 1) (x + 5)

Yoursquore finished


22








Solve each equation





Graph each equation







Multiply

Factor completely

Yoursquore finished


6 (-2)3

-8 49

22

3


4


8

9

36

49


5

Time to recall your

perfect squares

8

9

-6

7


10 89

11 12


6




-20 ndash 12 15 + 5

- 32 20

14 12x + 30x 15 8y2 ndash y2

42x 7y2



fun


7


- x + 16


2x = 4 x + 3 = 40

x = 2 x = 37

21 2 (x + 1) = 14 22 2 (3x + 1) ndash 8x = 12

x = 6 x = -5


x = -2 x = frac12

25

38

5

x

4

25

x

x


Geometry

8x = 10





9




28 18 + 2x le 50 x le 16 16

29 7 ndash 2t le 21 t ge - 7 -7


10



30 31


11



32 (12) amp (7 -2)

33 (- 410) amp (03)


bird


12

m = -2 ndash 2 7 - 1 = -46 = -23

m = 10 ndash 3 -4 - 0 = 7-4

Graph each equation

34 y = -2

35 x = 4

36 y = - frac12 x + 4

37 y = 5x - 3



13






14

y = mx + b y = 12x - 5

y = mx + b y = -3x


y = 3x - 7






15



44 25 middot 26 45 (25)6

2 11 or 2048 230


a9 b2 16x8y14

48 33 or 27 49 3ab5

5

2

3

3

5 9

4 4

6

2

a b

a b


16





17

Y = 2(6) + 10Y = 12+ 10

Y = 22

Y = frac12 (12) -3Y = 6-3

Y = 3




18





19





Multiply

55 (5x2) (4x3) 56 5 (2x2 + x + 4)

57 (x + 2) (x ndash 5) 58 (x -5)2



20

20x5

x2 -3x-10

4x2 - 49

10x2 + 5x + 20

x2 - 10x + 25

x3 + 2x2 + 3x

- 3x2 - 6x - 9 +x3 - x2 - 3x - 9

Factor completely

61 4x2 ndash 3x 62 x2 + 6x + 8

63 x2 ndash 10 x + 16 64 x2 + 7x -18

65 x2 + 12x + 36 66 25x2 - 81

67 5x2 ndash 14x + 8 68 4x2 + 19x - 5


21

x (4x ndash 3)

(x ndash 8) (x-2)

(x + 6)2

(5x - 4) (x ndash 2)

(x + 4) (x + 2)

(x + 9) (x - 2)

(5x - 9) (5x + 9)

(4x - 1) (x + 5)

Yoursquore finished


22








Solve each equation





Graph each equation







Multiply

Factor completely

Yoursquore finished


8

9

36

49


5

Time to recall your

perfect squares

8

9

-6

7


10 89

11 12


6




-20 ndash 12 15 + 5

- 32 20

14 12x + 30x 15 8y2 ndash y2

42x 7y2



fun


7


- x + 16


2x = 4 x + 3 = 40

x = 2 x = 37

21 2 (x + 1) = 14 22 2 (3x + 1) ndash 8x = 12

x = 6 x = -5


x = -2 x = frac12

25

38

5

x

4

25

x

x


Geometry

8x = 10





9




28 18 + 2x le 50 x le 16 16

29 7 ndash 2t le 21 t ge - 7 -7


10



30 31


11



32 (12) amp (7 -2)

33 (- 410) amp (03)


bird


12

m = -2 ndash 2 7 - 1 = -46 = -23

m = 10 ndash 3 -4 - 0 = 7-4

Graph each equation

34 y = -2

35 x = 4

36 y = - frac12 x + 4

37 y = 5x - 3



13






14

y = mx + b y = 12x - 5

y = mx + b y = -3x


y = 3x - 7






15



44 25 middot 26 45 (25)6

2 11 or 2048 230


a9 b2 16x8y14

48 33 or 27 49 3ab5

5

2

3

3

5 9

4 4

6

2

a b

a b


16





17

Y = 2(6) + 10Y = 12+ 10

Y = 22

Y = frac12 (12) -3Y = 6-3

Y = 3




18





19





Multiply

55 (5x2) (4x3) 56 5 (2x2 + x + 4)

57 (x + 2) (x ndash 5) 58 (x -5)2



20

20x5

x2 -3x-10

4x2 - 49

10x2 + 5x + 20

x2 - 10x + 25

x3 + 2x2 + 3x

- 3x2 - 6x - 9 +x3 - x2 - 3x - 9

Factor completely

61 4x2 ndash 3x 62 x2 + 6x + 8

63 x2 ndash 10 x + 16 64 x2 + 7x -18

65 x2 + 12x + 36 66 25x2 - 81

67 5x2 ndash 14x + 8 68 4x2 + 19x - 5


21

x (4x ndash 3)

(x ndash 8) (x-2)

(x + 6)2

(5x - 4) (x ndash 2)

(x + 4) (x + 2)

(x + 9) (x - 2)

(5x - 9) (5x + 9)

(4x - 1) (x + 5)

Yoursquore finished


22








Solve each equation





Graph each equation







Multiply

Factor completely

Yoursquore finished


10 89

11 12


6




-20 ndash 12 15 + 5

- 32 20

14 12x + 30x 15 8y2 ndash y2

42x 7y2



fun


7


- x + 16


2x = 4 x + 3 = 40

x = 2 x = 37

21 2 (x + 1) = 14 22 2 (3x + 1) ndash 8x = 12

x = 6 x = -5


x = -2 x = frac12

25

38

5

x

4

25

x

x


Geometry

8x = 10





9




28 18 + 2x le 50 x le 16 16

29 7 ndash 2t le 21 t ge - 7 -7


10



30 31


11



32 (12) amp (7 -2)

33 (- 410) amp (03)


bird


12

m = -2 ndash 2 7 - 1 = -46 = -23

m = 10 ndash 3 -4 - 0 = 7-4

Graph each equation

34 y = -2

35 x = 4

36 y = - frac12 x + 4

37 y = 5x - 3



13






14

y = mx + b y = 12x - 5

y = mx + b y = -3x


y = 3x - 7






15



44 25 middot 26 45 (25)6

2 11 or 2048 230


a9 b2 16x8y14

48 33 or 27 49 3ab5

5

2

3

3

5 9

4 4

6

2

a b

a b


16





17

Y = 2(6) + 10Y = 12+ 10

Y = 22

Y = frac12 (12) -3Y = 6-3

Y = 3




18





19





Multiply

55 (5x2) (4x3) 56 5 (2x2 + x + 4)

57 (x + 2) (x ndash 5) 58 (x -5)2



20

20x5

x2 -3x-10

4x2 - 49

10x2 + 5x + 20

x2 - 10x + 25

x3 + 2x2 + 3x

- 3x2 - 6x - 9 +x3 - x2 - 3x - 9

Factor completely

61 4x2 ndash 3x 62 x2 + 6x + 8

63 x2 ndash 10 x + 16 64 x2 + 7x -18

65 x2 + 12x + 36 66 25x2 - 81

67 5x2 ndash 14x + 8 68 4x2 + 19x - 5


21

x (4x ndash 3)

(x ndash 8) (x-2)

(x + 6)2

(5x - 4) (x ndash 2)

(x + 4) (x + 2)

(x + 9) (x - 2)

(5x - 9) (5x + 9)

(4x - 1) (x + 5)

Yoursquore finished


22








Solve each equation





Graph each equation







Multiply

Factor completely

Yoursquore finished



-20 ndash 12 15 + 5

- 32 20

14 12x + 30x 15 8y2 ndash y2

42x 7y2



fun


7


- x + 16


2x = 4 x + 3 = 40

x = 2 x = 37

21 2 (x + 1) = 14 22 2 (3x + 1) ndash 8x = 12

x = 6 x = -5


x = -2 x = frac12

25

38

5

x

4

25

x

x


Geometry

8x = 10





9




28 18 + 2x le 50 x le 16 16

29 7 ndash 2t le 21 t ge - 7 -7


10



30 31


11



32 (12) amp (7 -2)

33 (- 410) amp (03)


bird


12

m = -2 ndash 2 7 - 1 = -46 = -23

m = 10 ndash 3 -4 - 0 = 7-4

Graph each equation

34 y = -2

35 x = 4

36 y = - frac12 x + 4

37 y = 5x - 3



13






14

y = mx + b y = 12x - 5

y = mx + b y = -3x


y = 3x - 7






15



44 25 middot 26 45 (25)6

2 11 or 2048 230


a9 b2 16x8y14

48 33 or 27 49 3ab5

5

2

3

3

5 9

4 4

6

2

a b

a b


16





17

Y = 2(6) + 10Y = 12+ 10

Y = 22

Y = frac12 (12) -3Y = 6-3

Y = 3




18





19





Multiply

55 (5x2) (4x3) 56 5 (2x2 + x + 4)

57 (x + 2) (x ndash 5) 58 (x -5)2



20

20x5

x2 -3x-10

4x2 - 49

10x2 + 5x + 20

x2 - 10x + 25

x3 + 2x2 + 3x

- 3x2 - 6x - 9 +x3 - x2 - 3x - 9

Factor completely

61 4x2 ndash 3x 62 x2 + 6x + 8

63 x2 ndash 10 x + 16 64 x2 + 7x -18

65 x2 + 12x + 36 66 25x2 - 81

67 5x2 ndash 14x + 8 68 4x2 + 19x - 5


21

x (4x ndash 3)

(x ndash 8) (x-2)

(x + 6)2

(5x - 4) (x ndash 2)

(x + 4) (x + 2)

(x + 9) (x - 2)

(5x - 9) (5x + 9)

(4x - 1) (x + 5)

Yoursquore finished


22








Solve each equation





Graph each equation







Multiply

Factor completely

Yoursquore finished


2x = 4 x + 3 = 40

x = 2 x = 37

21 2 (x + 1) = 14 22 2 (3x + 1) ndash 8x = 12

x = 6 x = -5


x = -2 x = frac12

25

38

5

x

4

25

x

x


Geometry

8x = 10





9




28 18 + 2x le 50 x le 16 16

29 7 ndash 2t le 21 t ge - 7 -7


10



30 31


11



32 (12) amp (7 -2)

33 (- 410) amp (03)


bird


12

m = -2 ndash 2 7 - 1 = -46 = -23

m = 10 ndash 3 -4 - 0 = 7-4

Graph each equation

34 y = -2

35 x = 4

36 y = - frac12 x + 4

37 y = 5x - 3



13






14

y = mx + b y = 12x - 5

y = mx + b y = -3x


y = 3x - 7






15



44 25 middot 26 45 (25)6

2 11 or 2048 230


a9 b2 16x8y14

48 33 or 27 49 3ab5

5

2

3

3

5 9

4 4

6

2

a b

a b


16





17

Y = 2(6) + 10Y = 12+ 10

Y = 22

Y = frac12 (12) -3Y = 6-3

Y = 3




18





19





Multiply

55 (5x2) (4x3) 56 5 (2x2 + x + 4)

57 (x + 2) (x ndash 5) 58 (x -5)2



20

20x5

x2 -3x-10

4x2 - 49

10x2 + 5x + 20

x2 - 10x + 25

x3 + 2x2 + 3x

- 3x2 - 6x - 9 +x3 - x2 - 3x - 9

Factor completely

61 4x2 ndash 3x 62 x2 + 6x + 8

63 x2 ndash 10 x + 16 64 x2 + 7x -18

65 x2 + 12x + 36 66 25x2 - 81

67 5x2 ndash 14x + 8 68 4x2 + 19x - 5


21

x (4x ndash 3)

(x ndash 8) (x-2)

(x + 6)2

(5x - 4) (x ndash 2)

(x + 4) (x + 2)

(x + 9) (x - 2)

(5x - 9) (5x + 9)

(4x - 1) (x + 5)

Yoursquore finished


22








Solve each equation





Graph each equation







Multiply

Factor completely

Yoursquore finished





9




28 18 + 2x le 50 x le 16 16

29 7 ndash 2t le 21 t ge - 7 -7


10



30 31


11



32 (12) amp (7 -2)

33 (- 410) amp (03)


bird


12

m = -2 ndash 2 7 - 1 = -46 = -23

m = 10 ndash 3 -4 - 0 = 7-4

Graph each equation

34 y = -2

35 x = 4

36 y = - frac12 x + 4

37 y = 5x - 3



13






14

y = mx + b y = 12x - 5

y = mx + b y = -3x


y = 3x - 7






15



44 25 middot 26 45 (25)6

2 11 or 2048 230


a9 b2 16x8y14

48 33 or 27 49 3ab5

5

2

3

3

5 9

4 4

6

2

a b

a b


16





17

Y = 2(6) + 10Y = 12+ 10

Y = 22

Y = frac12 (12) -3Y = 6-3

Y = 3




18





19





Multiply

55 (5x2) (4x3) 56 5 (2x2 + x + 4)

57 (x + 2) (x ndash 5) 58 (x -5)2



20

20x5

x2 -3x-10

4x2 - 49

10x2 + 5x + 20

x2 - 10x + 25

x3 + 2x2 + 3x

- 3x2 - 6x - 9 +x3 - x2 - 3x - 9

Factor completely

61 4x2 ndash 3x 62 x2 + 6x + 8

63 x2 ndash 10 x + 16 64 x2 + 7x -18

65 x2 + 12x + 36 66 25x2 - 81

67 5x2 ndash 14x + 8 68 4x2 + 19x - 5


21

x (4x ndash 3)

(x ndash 8) (x-2)

(x + 6)2

(5x - 4) (x ndash 2)

(x + 4) (x + 2)

(x + 9) (x - 2)

(5x - 9) (5x + 9)

(4x - 1) (x + 5)

Yoursquore finished


22








Solve each equation





Graph each equation







Multiply

Factor completely

Yoursquore finished


28 18 + 2x le 50 x le 16 16

29 7 ndash 2t le 21 t ge - 7 -7


10



30 31


11



32 (12) amp (7 -2)

33 (- 410) amp (03)


bird


12

m = -2 ndash 2 7 - 1 = -46 = -23

m = 10 ndash 3 -4 - 0 = 7-4

Graph each equation

34 y = -2

35 x = 4

36 y = - frac12 x + 4

37 y = 5x - 3



13






14

y = mx + b y = 12x - 5

y = mx + b y = -3x


y = 3x - 7






15



44 25 middot 26 45 (25)6

2 11 or 2048 230


a9 b2 16x8y14

48 33 or 27 49 3ab5

5

2

3

3

5 9

4 4

6

2

a b

a b


16





17

Y = 2(6) + 10Y = 12+ 10

Y = 22

Y = frac12 (12) -3Y = 6-3

Y = 3




18





19





Multiply

55 (5x2) (4x3) 56 5 (2x2 + x + 4)

57 (x + 2) (x ndash 5) 58 (x -5)2



20

20x5

x2 -3x-10

4x2 - 49

10x2 + 5x + 20

x2 - 10x + 25

x3 + 2x2 + 3x

- 3x2 - 6x - 9 +x3 - x2 - 3x - 9

Factor completely

61 4x2 ndash 3x 62 x2 + 6x + 8

63 x2 ndash 10 x + 16 64 x2 + 7x -18

65 x2 + 12x + 36 66 25x2 - 81

67 5x2 ndash 14x + 8 68 4x2 + 19x - 5


21

x (4x ndash 3)

(x ndash 8) (x-2)

(x + 6)2

(5x - 4) (x ndash 2)

(x + 4) (x + 2)

(x + 9) (x - 2)

(5x - 9) (5x + 9)

(4x - 1) (x + 5)

Yoursquore finished


22








Solve each equation





Graph each equation







Multiply

Factor completely

Yoursquore finished


30 31


11



32 (12) amp (7 -2)

33 (- 410) amp (03)


bird


12

m = -2 ndash 2 7 - 1 = -46 = -23

m = 10 ndash 3 -4 - 0 = 7-4

Graph each equation

34 y = -2

35 x = 4

36 y = - frac12 x + 4

37 y = 5x - 3



13






14

y = mx + b y = 12x - 5

y = mx + b y = -3x


y = 3x - 7






15



44 25 middot 26 45 (25)6

2 11 or 2048 230


a9 b2 16x8y14

48 33 or 27 49 3ab5

5

2

3

3

5 9

4 4

6

2

a b

a b


16





17

Y = 2(6) + 10Y = 12+ 10

Y = 22

Y = frac12 (12) -3Y = 6-3

Y = 3




18





19





Multiply

55 (5x2) (4x3) 56 5 (2x2 + x + 4)

57 (x + 2) (x ndash 5) 58 (x -5)2



20

20x5

x2 -3x-10

4x2 - 49

10x2 + 5x + 20

x2 - 10x + 25

x3 + 2x2 + 3x

- 3x2 - 6x - 9 +x3 - x2 - 3x - 9

Factor completely

61 4x2 ndash 3x 62 x2 + 6x + 8

63 x2 ndash 10 x + 16 64 x2 + 7x -18

65 x2 + 12x + 36 66 25x2 - 81

67 5x2 ndash 14x + 8 68 4x2 + 19x - 5


21

x (4x ndash 3)

(x ndash 8) (x-2)

(x + 6)2

(5x - 4) (x ndash 2)

(x + 4) (x + 2)

(x + 9) (x - 2)

(5x - 9) (5x + 9)

(4x - 1) (x + 5)

Yoursquore finished


22








Solve each equation





Graph each equation







Multiply

Factor completely

Yoursquore finished


32 (12) amp (7 -2)

33 (- 410) amp (03)


bird


12

m = -2 ndash 2 7 - 1 = -46 = -23

m = 10 ndash 3 -4 - 0 = 7-4

Graph each equation

34 y = -2

35 x = 4

36 y = - frac12 x + 4

37 y = 5x - 3



13






14

y = mx + b y = 12x - 5

y = mx + b y = -3x


y = 3x - 7






15



44 25 middot 26 45 (25)6

2 11 or 2048 230


a9 b2 16x8y14

48 33 or 27 49 3ab5

5

2

3

3

5 9

4 4

6

2

a b

a b


16





17

Y = 2(6) + 10Y = 12+ 10

Y = 22

Y = frac12 (12) -3Y = 6-3

Y = 3




18





19





Multiply

55 (5x2) (4x3) 56 5 (2x2 + x + 4)

57 (x + 2) (x ndash 5) 58 (x -5)2



20

20x5

x2 -3x-10

4x2 - 49

10x2 + 5x + 20

x2 - 10x + 25

x3 + 2x2 + 3x

- 3x2 - 6x - 9 +x3 - x2 - 3x - 9

Factor completely

61 4x2 ndash 3x 62 x2 + 6x + 8

63 x2 ndash 10 x + 16 64 x2 + 7x -18

65 x2 + 12x + 36 66 25x2 - 81

67 5x2 ndash 14x + 8 68 4x2 + 19x - 5


21

x (4x ndash 3)

(x ndash 8) (x-2)

(x + 6)2

(5x - 4) (x ndash 2)

(x + 4) (x + 2)

(x + 9) (x - 2)

(5x - 9) (5x + 9)

(4x - 1) (x + 5)

Yoursquore finished


22








Solve each equation





Graph each equation







Multiply

Factor completely

Yoursquore finished

Graph each equation

34 y = -2

35 x = 4

36 y = - frac12 x + 4

37 y = 5x - 3



13






14

y = mx + b y = 12x - 5

y = mx + b y = -3x


y = 3x - 7






15



44 25 middot 26 45 (25)6

2 11 or 2048 230


a9 b2 16x8y14

48 33 or 27 49 3ab5

5

2

3

3

5 9

4 4

6

2

a b

a b


16





17

Y = 2(6) + 10Y = 12+ 10

Y = 22

Y = frac12 (12) -3Y = 6-3

Y = 3




18





19





Multiply

55 (5x2) (4x3) 56 5 (2x2 + x + 4)

57 (x + 2) (x ndash 5) 58 (x -5)2



20

20x5

x2 -3x-10

4x2 - 49

10x2 + 5x + 20

x2 - 10x + 25

x3 + 2x2 + 3x

- 3x2 - 6x - 9 +x3 - x2 - 3x - 9

Factor completely

61 4x2 ndash 3x 62 x2 + 6x + 8

63 x2 ndash 10 x + 16 64 x2 + 7x -18

65 x2 + 12x + 36 66 25x2 - 81

67 5x2 ndash 14x + 8 68 4x2 + 19x - 5


21

x (4x ndash 3)

(x ndash 8) (x-2)

(x + 6)2

(5x - 4) (x ndash 2)

(x + 4) (x + 2)

(x + 9) (x - 2)

(5x - 9) (5x + 9)

(4x - 1) (x + 5)

Yoursquore finished


22








Solve each equation





Graph each equation







Multiply

Factor completely

Yoursquore finished






14

y = mx + b y = 12x - 5

y = mx + b y = -3x


y = 3x - 7






15



44 25 middot 26 45 (25)6

2 11 or 2048 230


a9 b2 16x8y14

48 33 or 27 49 3ab5

5

2

3

3

5 9

4 4

6

2

a b

a b


16





17

Y = 2(6) + 10Y = 12+ 10

Y = 22

Y = frac12 (12) -3Y = 6-3

Y = 3




18





19





Multiply

55 (5x2) (4x3) 56 5 (2x2 + x + 4)

57 (x + 2) (x ndash 5) 58 (x -5)2



20

20x5

x2 -3x-10

4x2 - 49

10x2 + 5x + 20

x2 - 10x + 25

x3 + 2x2 + 3x

- 3x2 - 6x - 9 +x3 - x2 - 3x - 9

Factor completely

61 4x2 ndash 3x 62 x2 + 6x + 8

63 x2 ndash 10 x + 16 64 x2 + 7x -18

65 x2 + 12x + 36 66 25x2 - 81

67 5x2 ndash 14x + 8 68 4x2 + 19x - 5


21

x (4x ndash 3)

(x ndash 8) (x-2)

(x + 6)2

(5x - 4) (x ndash 2)

(x + 4) (x + 2)

(x + 9) (x - 2)

(5x - 9) (5x + 9)

(4x - 1) (x + 5)

Yoursquore finished


22








Solve each equation





Graph each equation







Multiply

Factor completely

Yoursquore finished






15



44 25 middot 26 45 (25)6

2 11 or 2048 230


a9 b2 16x8y14

48 33 or 27 49 3ab5

5

2

3

3

5 9

4 4

6

2

a b

a b


16





17

Y = 2(6) + 10Y = 12+ 10

Y = 22

Y = frac12 (12) -3Y = 6-3

Y = 3




18





19





Multiply

55 (5x2) (4x3) 56 5 (2x2 + x + 4)

57 (x + 2) (x ndash 5) 58 (x -5)2



20

20x5

x2 -3x-10

4x2 - 49

10x2 + 5x + 20

x2 - 10x + 25

x3 + 2x2 + 3x

- 3x2 - 6x - 9 +x3 - x2 - 3x - 9

Factor completely

61 4x2 ndash 3x 62 x2 + 6x + 8

63 x2 ndash 10 x + 16 64 x2 + 7x -18

65 x2 + 12x + 36 66 25x2 - 81

67 5x2 ndash 14x + 8 68 4x2 + 19x - 5


21

x (4x ndash 3)

(x ndash 8) (x-2)

(x + 6)2

(5x - 4) (x ndash 2)

(x + 4) (x + 2)

(x + 9) (x - 2)

(5x - 9) (5x + 9)

(4x - 1) (x + 5)

Yoursquore finished


22








Solve each equation





Graph each equation







Multiply

Factor completely

Yoursquore finished


44 25 middot 26 45 (25)6

2 11 or 2048 230


a9 b2 16x8y14

48 33 or 27 49 3ab5

5

2

3

3

5 9

4 4

6

2

a b

a b


16





17

Y = 2(6) + 10Y = 12+ 10

Y = 22

Y = frac12 (12) -3Y = 6-3

Y = 3




18





19





Multiply

55 (5x2) (4x3) 56 5 (2x2 + x + 4)

57 (x + 2) (x ndash 5) 58 (x -5)2



20

20x5

x2 -3x-10

4x2 - 49

10x2 + 5x + 20

x2 - 10x + 25

x3 + 2x2 + 3x

- 3x2 - 6x - 9 +x3 - x2 - 3x - 9

Factor completely

61 4x2 ndash 3x 62 x2 + 6x + 8

63 x2 ndash 10 x + 16 64 x2 + 7x -18

65 x2 + 12x + 36 66 25x2 - 81

67 5x2 ndash 14x + 8 68 4x2 + 19x - 5


21

x (4x ndash 3)

(x ndash 8) (x-2)

(x + 6)2

(5x - 4) (x ndash 2)

(x + 4) (x + 2)

(x + 9) (x - 2)

(5x - 9) (5x + 9)

(4x - 1) (x + 5)

Yoursquore finished


22








Solve each equation





Graph each equation







Multiply

Factor completely

Yoursquore finished





17

Y = 2(6) + 10Y = 12+ 10

Y = 22

Y = frac12 (12) -3Y = 6-3

Y = 3




18





19





Multiply

55 (5x2) (4x3) 56 5 (2x2 + x + 4)

57 (x + 2) (x ndash 5) 58 (x -5)2



20

20x5

x2 -3x-10

4x2 - 49

10x2 + 5x + 20

x2 - 10x + 25

x3 + 2x2 + 3x

- 3x2 - 6x - 9 +x3 - x2 - 3x - 9

Factor completely

61 4x2 ndash 3x 62 x2 + 6x + 8

63 x2 ndash 10 x + 16 64 x2 + 7x -18

65 x2 + 12x + 36 66 25x2 - 81

67 5x2 ndash 14x + 8 68 4x2 + 19x - 5


21

x (4x ndash 3)

(x ndash 8) (x-2)

(x + 6)2

(5x - 4) (x ndash 2)

(x + 4) (x + 2)

(x + 9) (x - 2)

(5x - 9) (5x + 9)

(4x - 1) (x + 5)

Yoursquore finished


22








Solve each equation





Graph each equation







Multiply

Factor completely

Yoursquore finished




18





19





Multiply

55 (5x2) (4x3) 56 5 (2x2 + x + 4)

57 (x + 2) (x ndash 5) 58 (x -5)2



20

20x5

x2 -3x-10

4x2 - 49

10x2 + 5x + 20

x2 - 10x + 25

x3 + 2x2 + 3x

- 3x2 - 6x - 9 +x3 - x2 - 3x - 9

Factor completely

61 4x2 ndash 3x 62 x2 + 6x + 8

63 x2 ndash 10 x + 16 64 x2 + 7x -18

65 x2 + 12x + 36 66 25x2 - 81

67 5x2 ndash 14x + 8 68 4x2 + 19x - 5


21

x (4x ndash 3)

(x ndash 8) (x-2)

(x + 6)2

(5x - 4) (x ndash 2)

(x + 4) (x + 2)

(x + 9) (x - 2)

(5x - 9) (5x + 9)

(4x - 1) (x + 5)

Yoursquore finished


22








Solve each equation





Graph each equation







Multiply

Factor completely

Yoursquore finished




19





Multiply

55 (5x2) (4x3) 56 5 (2x2 + x + 4)

57 (x + 2) (x ndash 5) 58 (x -5)2



20

20x5

x2 -3x-10

4x2 - 49

10x2 + 5x + 20

x2 - 10x + 25

x3 + 2x2 + 3x

- 3x2 - 6x - 9 +x3 - x2 - 3x - 9

Factor completely

61 4x2 ndash 3x 62 x2 + 6x + 8

63 x2 ndash 10 x + 16 64 x2 + 7x -18

65 x2 + 12x + 36 66 25x2 - 81

67 5x2 ndash 14x + 8 68 4x2 + 19x - 5


21

x (4x ndash 3)

(x ndash 8) (x-2)

(x + 6)2

(5x - 4) (x ndash 2)

(x + 4) (x + 2)

(x + 9) (x - 2)

(5x - 9) (5x + 9)

(4x - 1) (x + 5)

Yoursquore finished


22








Solve each equation





Graph each equation







Multiply

Factor completely

Yoursquore finished

Multiply

55 (5x2) (4x3) 56 5 (2x2 + x + 4)

57 (x + 2) (x ndash 5) 58 (x -5)2



20

20x5

x2 -3x-10

4x2 - 49

10x2 + 5x + 20

x2 - 10x + 25

x3 + 2x2 + 3x

- 3x2 - 6x - 9 +x3 - x2 - 3x - 9

Factor completely

61 4x2 ndash 3x 62 x2 + 6x + 8

63 x2 ndash 10 x + 16 64 x2 + 7x -18

65 x2 + 12x + 36 66 25x2 - 81

67 5x2 ndash 14x + 8 68 4x2 + 19x - 5


21

x (4x ndash 3)

(x ndash 8) (x-2)

(x + 6)2

(5x - 4) (x ndash 2)

(x + 4) (x + 2)

(x + 9) (x - 2)

(5x - 9) (5x + 9)

(4x - 1) (x + 5)

Yoursquore finished


22








Solve each equation





Graph each equation







Multiply

Factor completely

Yoursquore finished

Factor completely

61 4x2 ndash 3x 62 x2 + 6x + 8

63 x2 ndash 10 x + 16 64 x2 + 7x -18

65 x2 + 12x + 36 66 25x2 - 81

67 5x2 ndash 14x + 8 68 4x2 + 19x - 5


21

x (4x ndash 3)

(x ndash 8) (x-2)

(x + 6)2

(5x - 4) (x ndash 2)

(x + 4) (x + 2)

(x + 9) (x - 2)

(5x - 9) (5x + 9)

(4x - 1) (x + 5)

Yoursquore finished


22








Solve each equation





Graph each equation







Multiply

Factor completely

Yoursquore finished

Yoursquore finished


22








Solve each equation





Graph each equation







Multiply

Factor completely

Yoursquore finished

summer review for students entering geometry remember: your high school mathematics courses require...

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