summer review for students entering geometry remember: your high school mathematics courses require...
TRANSCRIPT
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
041923 Mrs McConaughy Geometry
4
Find each square root
8
9
36
49
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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)
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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)
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
- Evaluate each expression
- Find each square root
- Write all classifications that apply to each real number (natural whole integer rational irrational)
- Simplify each expression
- Solve each equation
- Write and solve each proportion
- Solve each inequality and graph on a number line
- Find the slope of each line
- Find the slope of the line containing the given points
- Graph each equation
- Write the equation of the line in slope-intercept form
- PowerPoint Presentation
- Simplify Recall Basic Rules for Exponents
- Evaluate each function for the given input value
- Evaluate the exponential function
- Add or subtract the polynomials
- 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
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
041923 Mrs McConaughy Geometry
4
Find each square root
8
9
36
49
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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)
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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)
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
- Evaluate each expression
- Find each square root
- Write all classifications that apply to each real number (natural whole integer rational irrational)
- Simplify each expression
- Solve each equation
- Write and solve each proportion
- Solve each inequality and graph on a number line
- Find the slope of each line
- Find the slope of the line containing the given points
- Graph each equation
- Write the equation of the line in slope-intercept form
- PowerPoint Presentation
- Simplify Recall Basic Rules for Exponents
- Evaluate each function for the given input value
- Evaluate the exponential function
- Add or subtract the polynomials
- Multiply
- Factor completely
- Yoursquore finished
-
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
041923 Mrs McConaughy Geometry
4
Find each square root
8
9
36
49
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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)
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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)
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
- Evaluate each expression
- Find each square root
- Write all classifications that apply to each real number (natural whole integer rational irrational)
- Simplify each expression
- Solve each equation
- Write and solve each proportion
- Solve each inequality and graph on a number line
- Find the slope of each line
- Find the slope of the line containing the given points
- Graph each equation
- Write the equation of the line in slope-intercept form
- PowerPoint Presentation
- Simplify Recall Basic Rules for Exponents
- Evaluate each function for the given input value
- Evaluate the exponential function
- Add or subtract the polynomials
- Multiply
- Factor completely
- Yoursquore finished
-
Evaluate each expression
6 (-2)3
-8 49
22
3
041923 Mrs McConaughy Geometry
4
Find each square root
8
9
36
49
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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)
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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)
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
- Evaluate each expression
- Find each square root
- Write all classifications that apply to each real number (natural whole integer rational irrational)
- Simplify each expression
- Solve each equation
- Write and solve each proportion
- Solve each inequality and graph on a number line
- Find the slope of each line
- Find the slope of the line containing the given points
- Graph each equation
- Write the equation of the line in slope-intercept form
- PowerPoint Presentation
- Simplify Recall Basic Rules for Exponents
- Evaluate each function for the given input value
- Evaluate the exponential function
- Add or subtract the polynomials
- Multiply
- Factor completely
- Yoursquore finished
-
Find each square root
8
9
36
49
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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)
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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)
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
- Evaluate each expression
- Find each square root
- Write all classifications that apply to each real number (natural whole integer rational irrational)
- Simplify each expression
- Solve each equation
- Write and solve each proportion
- Solve each inequality and graph on a number line
- Find the slope of each line
- Find the slope of the line containing the given points
- Graph each equation
- Write the equation of the line in slope-intercept form
- PowerPoint Presentation
- Simplify Recall Basic Rules for Exponents
- Evaluate each function for the given input value
- Evaluate the exponential function
- Add or subtract the polynomials
- Multiply
- Factor completely
- Yoursquore finished
-
Write all classifications that apply to each real number (natural whole integer rational irrational)
10 89
11 12
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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)
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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)
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
- Evaluate each expression
- Find each square root
- Write all classifications that apply to each real number (natural whole integer rational irrational)
- Simplify each expression
- Solve each equation
- Write and solve each proportion
- Solve each inequality and graph on a number line
- Find the slope of each line
- Find the slope of the line containing the given points
- Graph each equation
- Write the equation of the line in slope-intercept form
- PowerPoint Presentation
- Simplify Recall Basic Rules for Exponents
- Evaluate each function for the given input value
- Evaluate the exponential function
- Add or subtract the polynomials
- Multiply
- Factor completely
- Yoursquore finished
-
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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)
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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)
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
- Evaluate each expression
- Find each square root
- Write all classifications that apply to each real number (natural whole integer rational irrational)
- Simplify each expression
- Solve each equation
- Write and solve each proportion
- Solve each inequality and graph on a number line
- Find the slope of each line
- Find the slope of the line containing the given points
- Graph each equation
- Write the equation of the line in slope-intercept form
- PowerPoint Presentation
- Simplify Recall Basic Rules for Exponents
- Evaluate each function for the given input value
- Evaluate the exponential function
- Add or subtract the polynomials
- Multiply
- Factor completely
- Yoursquore finished
-
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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)
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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)
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
- Evaluate each expression
- Find each square root
- Write all classifications that apply to each real number (natural whole integer rational irrational)
- Simplify each expression
- Solve each equation
- Write and solve each proportion
- Solve each inequality and graph on a number line
- Find the slope of each line
- Find the slope of the line containing the given points
- Graph each equation
- Write the equation of the line in slope-intercept form
- PowerPoint Presentation
- Simplify Recall Basic Rules for Exponents
- Evaluate each function for the given input value
- Evaluate the exponential function
- Add or subtract the polynomials
- Multiply
- Factor completely
- Yoursquore finished
-
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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)
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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)
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
- Evaluate each expression
- Find each square root
- Write all classifications that apply to each real number (natural whole integer rational irrational)
- Simplify each expression
- Solve each equation
- Write and solve each proportion
- Solve each inequality and graph on a number line
- Find the slope of each line
- Find the slope of the line containing the given points
- Graph each equation
- Write the equation of the line in slope-intercept form
- PowerPoint Presentation
- Simplify Recall Basic Rules for Exponents
- Evaluate each function for the given input value
- Evaluate the exponential function
- Add or subtract the polynomials
- Multiply
- Factor completely
- Yoursquore finished
-
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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)
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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)
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
- Evaluate each expression
- Find each square root
- Write all classifications that apply to each real number (natural whole integer rational irrational)
- Simplify each expression
- Solve each equation
- Write and solve each proportion
- Solve each inequality and graph on a number line
- Find the slope of each line
- Find the slope of the line containing the given points
- Graph each equation
- Write the equation of the line in slope-intercept form
- PowerPoint Presentation
- Simplify Recall Basic Rules for Exponents
- Evaluate each function for the given input value
- Evaluate the exponential function
- Add or subtract the polynomials
- Multiply
- Factor completely
- Yoursquore finished
-
Find the slope of each line
30 31
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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)
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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)
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
- Evaluate each expression
- Find each square root
- Write all classifications that apply to each real number (natural whole integer rational irrational)
- Simplify each expression
- Solve each equation
- Write and solve each proportion
- Solve each inequality and graph on a number line
- Find the slope of each line
- Find the slope of the line containing the given points
- Graph each equation
- Write the equation of the line in slope-intercept form
- PowerPoint Presentation
- Simplify Recall Basic Rules for Exponents
- Evaluate each function for the given input value
- Evaluate the exponential function
- Add or subtract the polynomials
- Multiply
- Factor completely
- Yoursquore finished
-
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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)
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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)
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
- Evaluate each expression
- Find each square root
- Write all classifications that apply to each real number (natural whole integer rational irrational)
- Simplify each expression
- Solve each equation
- Write and solve each proportion
- Solve each inequality and graph on a number line
- Find the slope of each line
- Find the slope of the line containing the given points
- Graph each equation
- Write the equation of the line in slope-intercept form
- PowerPoint Presentation
- Simplify Recall Basic Rules for Exponents
- Evaluate each function for the given input value
- Evaluate the exponential function
- Add or subtract the polynomials
- Multiply
- Factor completely
- Yoursquore finished
-
Graph each equation
34 y = -2
35 x = 4
36 y = - frac12 x + 4
37 y = 5x - 3
NOTE Remember to label your lines
041923 Mrs McConaughy Geometry
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)
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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)
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
- Evaluate each expression
- Find each square root
- Write all classifications that apply to each real number (natural whole integer rational irrational)
- Simplify each expression
- Solve each equation
- Write and solve each proportion
- Solve each inequality and graph on a number line
- Find the slope of each line
- Find the slope of the line containing the given points
- Graph each equation
- Write the equation of the line in slope-intercept form
- PowerPoint Presentation
- Simplify Recall Basic Rules for Exponents
- Evaluate each function for the given input value
- Evaluate the exponential function
- Add or subtract the polynomials
- Multiply
- Factor completely
- Yoursquore finished
-
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)
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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)
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
- Evaluate each expression
- Find each square root
- Write all classifications that apply to each real number (natural whole integer rational irrational)
- Simplify each expression
- Solve each equation
- Write and solve each proportion
- Solve each inequality and graph on a number line
- Find the slope of each line
- Find the slope of the line containing the given points
- Graph each equation
- Write the equation of the line in slope-intercept form
- PowerPoint Presentation
- Simplify Recall Basic Rules for Exponents
- Evaluate each function for the given input value
- Evaluate the exponential function
- Add or subtract the polynomials
- Multiply
- Factor completely
- Yoursquore finished
-
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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)
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
- Evaluate each expression
- Find each square root
- Write all classifications that apply to each real number (natural whole integer rational irrational)
- Simplify each expression
- Solve each equation
- Write and solve each proportion
- Solve each inequality and graph on a number line
- Find the slope of each line
- Find the slope of the line containing the given points
- Graph each equation
- Write the equation of the line in slope-intercept form
- PowerPoint Presentation
- Simplify Recall Basic Rules for Exponents
- Evaluate each function for the given input value
- Evaluate the exponential function
- Add or subtract the polynomials
- Multiply
- Factor completely
- Yoursquore finished
-
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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)
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
- Evaluate each expression
- Find each square root
- Write all classifications that apply to each real number (natural whole integer rational irrational)
- Simplify each expression
- Solve each equation
- Write and solve each proportion
- Solve each inequality and graph on a number line
- Find the slope of each line
- Find the slope of the line containing the given points
- Graph each equation
- Write the equation of the line in slope-intercept form
- PowerPoint Presentation
- Simplify Recall Basic Rules for Exponents
- Evaluate each function for the given input value
- Evaluate the exponential function
- Add or subtract the polynomials
- Multiply
- Factor completely
- Yoursquore finished
-
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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)
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
- Evaluate each expression
- Find each square root
- Write all classifications that apply to each real number (natural whole integer rational irrational)
- Simplify each expression
- Solve each equation
- Write and solve each proportion
- Solve each inequality and graph on a number line
- Find the slope of each line
- Find the slope of the line containing the given points
- Graph each equation
- Write the equation of the line in slope-intercept form
- PowerPoint Presentation
- Simplify Recall Basic Rules for Exponents
- Evaluate each function for the given input value
- Evaluate the exponential function
- Add or subtract the polynomials
- Multiply
- Factor completely
- Yoursquore finished
-
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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)
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
- Evaluate each expression
- Find each square root
- Write all classifications that apply to each real number (natural whole integer rational irrational)
- Simplify each expression
- Solve each equation
- Write and solve each proportion
- Solve each inequality and graph on a number line
- Find the slope of each line
- Find the slope of the line containing the given points
- Graph each equation
- Write the equation of the line in slope-intercept form
- PowerPoint Presentation
- Simplify Recall Basic Rules for Exponents
- Evaluate each function for the given input value
- Evaluate the exponential function
- Add or subtract the polynomials
- Multiply
- Factor completely
- Yoursquore finished
-
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
041923 Mrs McConaughy Geometry
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)
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
- Evaluate each expression
- Find each square root
- Write all classifications that apply to each real number (natural whole integer rational irrational)
- Simplify each expression
- Solve each equation
- Write and solve each proportion
- Solve each inequality and graph on a number line
- Find the slope of each line
- Find the slope of the line containing the given points
- Graph each equation
- Write the equation of the line in slope-intercept form
- PowerPoint Presentation
- Simplify Recall Basic Rules for Exponents
- Evaluate each function for the given input value
- Evaluate the exponential function
- Add or subtract the polynomials
- Multiply
- Factor completely
- Yoursquore finished
-
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)
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
- Evaluate each expression
- Find each square root
- Write all classifications that apply to each real number (natural whole integer rational irrational)
- Simplify each expression
- Solve each equation
- Write and solve each proportion
- Solve each inequality and graph on a number line
- Find the slope of each line
- Find the slope of the line containing the given points
- Graph each equation
- Write the equation of the line in slope-intercept form
- PowerPoint Presentation
- Simplify Recall Basic Rules for Exponents
- Evaluate each function for the given input value
- Evaluate the exponential function
- Add or subtract the polynomials
- 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
041923 Mrs McConaughy Geometry
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
041923 Mrs McConaughy Geometry
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
- Evaluate each expression
- Find each square root
- Write all classifications that apply to each real number (natural whole integer rational irrational)
- Simplify each expression
- Solve each equation
- Write and solve each proportion
- Solve each inequality and graph on a number line
- Find the slope of each line
- Find the slope of the line containing the given points
- Graph each equation
- Write the equation of the line in slope-intercept form
- PowerPoint Presentation
- Simplify Recall Basic Rules for Exponents
- Evaluate each function for the given input value
- Evaluate the exponential function
- Add or subtract the polynomials
- Multiply
- Factor completely
- Yoursquore finished
-
Yoursquore finished
041923 Mrs McConaughy Geometry
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
- Evaluate each expression
- Find each square root
- Write all classifications that apply to each real number (natural whole integer rational irrational)
- Simplify each expression
- Solve each equation
- Write and solve each proportion
- Solve each inequality and graph on a number line
- Find the slope of each line
- Find the slope of the line containing the given points
- Graph each equation
- Write the equation of the line in slope-intercept form
- PowerPoint Presentation
- Simplify Recall Basic Rules for Exponents
- Evaluate each function for the given input value
- Evaluate the exponential function
- Add or subtract the polynomials
- Multiply
- Factor completely
- Yoursquore finished
-