Week 1 BASIC MATH REVIEW

SAT Prep

I BASIC ARITHMETIC

A) Sets means ldquobelongs tordquo or ldquois a member ofrdquo

If C is the set of prime numbers then

= in either one or the other or both

= in both

Given X = 2 3 5 7 Y = 1 3 5 7 9

= 1 2 3 5 7 9

= 3 5 7

17 C

X Y

X Y

B) Signed Numbers and Operations

- + 0 | a | = distance a is from 0 (NEVER NEGATIVE)

| a | = 7 then a =

| a ndash 2 | = 7 then a =

7

2 7 or 2 7 a a

5 or 9

Add + sum totalSub - differenceMult x ( ) productDiv divide quotient

Zero Property if ab = 0 then a = 0 or b = 0

Ex What is the product of the integers -3 -2 -1 hellip3 4 5

0

1( ) 1a

a

ProdQuot of EVEN number of negatives is POSITIVEProdQuot of ODD number of negatives is NEGATIVE

Reciprocals

Sign Changes 2 + (-6) = 2 ndash 6 = -42 ndash (-6) = 2 + 6 = 8

C) INTEGERSNumber ne Integer

Consecutive integers x x+1 x+2 x+3 hellip Consecutive oddeven integers x x+2 x+4 hellip

Ex The sum of three consecutive integers is less than 75 What is the largest possible value of the first of the three consecutive integers 1 2 75 x x x

3 3 75 x3 72x

24x

2 26 x

D) FACTORS

Factors ndash Finite set of values - Know your ldquogoes intosrdquoMultiples ndash Infinite set of values

GCF and LCM ndash use product of primes

GCF = product of common primes(1 time)LCM = product of common primes(1 time) and

uncommon primes

Ex Find the GCF and the LCM of 32 and 44

32

2 16

2 8

2 4

2 2

44

11 4

2 2

32 2 2 2 2 2

44 2 2 11

2 2 4 GCF

2 2 2 2 2 11 352 LCM

E) EXPONENTS and ROOTS

Rules of exponents 3 + 3 + 3 + 3 = 4(3)3(3)(3)(3) = 34

0

1

1

b c b c

cb bc

bb c

c

a

a a

a a a

a a

aa

a

Ex If find the value of x

52 2

5

x

x

2 32x

Ex Which of the following if any are true

10

10

10 10

I -2 0

II - -2 0

III 2 (-2 ) 0

Always Negative ---FALSE

Always Positive ---TRUE

Always Positive ---TRUE

II and III

F) SQUARES and SQUARE ROOTS

Know your squaressquare roots 1-151-225Know exact values always + 2 answers +-

2aa

Ex Find the circumference of a circle whose area is 20π

2A r2

2

20

20

20

2 5

r

r

r

r

2

2 2 5 4 5

C r

C

Rules of radicals

Ex Evaluate the following

A) B)

1

3832

1

1nn

nn

ab a b

a a

b b

aa

a a

3

1 1

2 8 3 8 2

G) PEMDAS

Careful with negatives on calculator

H) INEQUALITIES

or x a - SWITCH SIGN

Ex Solve for a if 5 ndash 3a lt 10

5 3 10a 3 5a

3 5

3 3

a

5

3a

Properties of Inequalities between 0 and 1

1 1 if

if 0 1

1 if 0 1

b c

b ca a

a a a

a aa

A) Fractions and Decimals

ComparingDecimals ndash same of places ndash larger is

larger number

Fractions ndash same denom ndash bigger numer is larger fraction

same numer ndash smaller denom is smaller fraction

II RATIONAL NUMBERS

Powers of 10 - move decimal place ndash + exponent ndash move to right

ndash exponent ndash move to the left

Rounding - know rules- do not need to round grid-ins

Operations with fractionsAddsub like denominatorsMultiply numerators and denominatorsDivide multiply by reciprocals

ldquoofrdquo means multiply

B) Percents

Ex Find the following

1) 45 of 200

is

of 100

45

200 100

x

100 45(200)x

90x

90

2) 90 is 45 of what number

3) 90 is what percent of 200

90

200 100

x

90 45

100

x 45 90 100x

200x

200

200 90 100x

45x

45

Percent increasedecrease IncreaseDecrease = ldquoisrdquoOriginal = ldquoofrdquo

C) Ratio and Proportion

Part Part compared to Part Whole

73 710 or 310

Two numbers in a ratio of a to b ndash Apply an x to each

Ex Two acute angles of a right triangle are in a ratio of 513 What is the measure of the larger acute angle

Proportions Cross multiply Ex Tommy types 35 words per minute How long would it take Tommy to type 987 words

5 13 90 x x

18 90x

5x 13 13 5 65 x

35 987

1

x

35 987x

282x28 min 12 secx

Direct Variation vs Inverse Variation orDirectly Proportional vs Inversely Proportional

x uarr y uarr x uarr y darrx darr y darr x darr y uarr

y = kx y = kx or k = xy

Ex If y is directly proportional to x and y = 7 when x = 2 find the value of y when x is 5

35 k

y kx

7 2 k175y

35y x

35 5y

Ex If it takes 4 workers 2 hours to complete a certain job how many minutes would it take 6 workers to complete the same job

480k

k

yx

120(4)k

80y1204

k

480y

x

480

6y

III AVERAGES

A) Average = Mean = Sumcount

Know the average then sum = average x count Ex After 5 tests Tony has an 85 average If Tony had an 83

average after his first three tests what was his average on the last two tests

5 5 85 425T 425 24987

2A

3 3 83 249T

B) Median = Middle

ARRANGE THEM IN ORDER FIRST

Odd of scores - Find middle Even of scores - Find average of middle 2 rsquos

C) Mode = Number that occurs the MOST

The End

• Week 1 BASIC MATH REVIEW
• I BASIC ARITHMETIC
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• II RATIONAL NUMBERS
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• III AVERAGES
• Slide 24
• The End

I BASIC ARITHMETIC

A) Sets means ldquobelongs tordquo or ldquois a member ofrdquo

If C is the set of prime numbers then

= in either one or the other or both

= in both

Given X = 2 3 5 7 Y = 1 3 5 7 9

= 1 2 3 5 7 9

= 3 5 7

17 C

X Y

X Y

B) Signed Numbers and Operations

- + 0 | a | = distance a is from 0 (NEVER NEGATIVE)

| a | = 7 then a =

| a ndash 2 | = 7 then a =

7

2 7 or 2 7 a a

5 or 9

Add + sum totalSub - differenceMult x ( ) productDiv divide quotient

Zero Property if ab = 0 then a = 0 or b = 0

Ex What is the product of the integers -3 -2 -1 hellip3 4 5

0

1( ) 1a

a

ProdQuot of EVEN number of negatives is POSITIVEProdQuot of ODD number of negatives is NEGATIVE

Reciprocals

Sign Changes 2 + (-6) = 2 ndash 6 = -42 ndash (-6) = 2 + 6 = 8

C) INTEGERSNumber ne Integer

Consecutive integers x x+1 x+2 x+3 hellip Consecutive oddeven integers x x+2 x+4 hellip

Ex The sum of three consecutive integers is less than 75 What is the largest possible value of the first of the three consecutive integers 1 2 75 x x x

3 3 75 x3 72x

24x

2 26 x

D) FACTORS

Factors ndash Finite set of values - Know your ldquogoes intosrdquoMultiples ndash Infinite set of values

GCF and LCM ndash use product of primes

GCF = product of common primes(1 time)LCM = product of common primes(1 time) and

uncommon primes

Ex Find the GCF and the LCM of 32 and 44

32

2 16

2 8

2 4

2 2

44

11 4

2 2

32 2 2 2 2 2

44 2 2 11

2 2 4 GCF

2 2 2 2 2 11 352 LCM

E) EXPONENTS and ROOTS

Rules of exponents 3 + 3 + 3 + 3 = 4(3)3(3)(3)(3) = 34

0

1

1

b c b c

cb bc

bb c

c

a

a a

a a a

a a

aa

a

Ex If find the value of x

52 2

5

x

x

2 32x

Ex Which of the following if any are true

10

10

10 10

I -2 0

II - -2 0

III 2 (-2 ) 0

Always Negative ---FALSE

Always Positive ---TRUE

Always Positive ---TRUE

II and III

F) SQUARES and SQUARE ROOTS

Know your squaressquare roots 1-151-225Know exact values always + 2 answers +-

2aa

Ex Find the circumference of a circle whose area is 20π

2A r2

2

20

20

20

2 5

r

r

r

r

2

2 2 5 4 5

C r

C

Rules of radicals

Ex Evaluate the following

A) B)

1

3832

1

1nn

nn

ab a b

a a

b b

aa

a a

3

1 1

2 8 3 8 2

G) PEMDAS

Careful with negatives on calculator

H) INEQUALITIES

or x a - SWITCH SIGN

Ex Solve for a if 5 ndash 3a lt 10

5 3 10a 3 5a

3 5

3 3

a

5

3a

Properties of Inequalities between 0 and 1

1 1 if

if 0 1

1 if 0 1

b c

b ca a

a a a

a aa

A) Fractions and Decimals

ComparingDecimals ndash same of places ndash larger is

larger number

Fractions ndash same denom ndash bigger numer is larger fraction

same numer ndash smaller denom is smaller fraction

II RATIONAL NUMBERS

Powers of 10 - move decimal place ndash + exponent ndash move to right

ndash exponent ndash move to the left

Rounding - know rules- do not need to round grid-ins

Operations with fractionsAddsub like denominatorsMultiply numerators and denominatorsDivide multiply by reciprocals

ldquoofrdquo means multiply

B) Percents

Ex Find the following

1) 45 of 200

is

of 100

45

200 100

x

100 45(200)x

90x

90

2) 90 is 45 of what number

3) 90 is what percent of 200

90

200 100

x

90 45

100

x 45 90 100x

200x

200

200 90 100x

45x

45

Percent increasedecrease IncreaseDecrease = ldquoisrdquoOriginal = ldquoofrdquo

C) Ratio and Proportion

Part Part compared to Part Whole

73 710 or 310

Two numbers in a ratio of a to b ndash Apply an x to each

Ex Two acute angles of a right triangle are in a ratio of 513 What is the measure of the larger acute angle

Proportions Cross multiply Ex Tommy types 35 words per minute How long would it take Tommy to type 987 words

5 13 90 x x

18 90x

5x 13 13 5 65 x

35 987

1

x

35 987x

282x28 min 12 secx

Direct Variation vs Inverse Variation orDirectly Proportional vs Inversely Proportional

x uarr y uarr x uarr y darrx darr y darr x darr y uarr

y = kx y = kx or k = xy

Ex If y is directly proportional to x and y = 7 when x = 2 find the value of y when x is 5

35 k

y kx

7 2 k175y

35y x

35 5y

Ex If it takes 4 workers 2 hours to complete a certain job how many minutes would it take 6 workers to complete the same job

480k

k

yx

120(4)k

80y1204

k

480y

x

480

6y

III AVERAGES

A) Average = Mean = Sumcount

Know the average then sum = average x count Ex After 5 tests Tony has an 85 average If Tony had an 83

average after his first three tests what was his average on the last two tests

5 5 85 425T 425 24987

2A

3 3 83 249T

B) Median = Middle

ARRANGE THEM IN ORDER FIRST

Odd of scores - Find middle Even of scores - Find average of middle 2 rsquos

C) Mode = Number that occurs the MOST

The End

• Week 1 BASIC MATH REVIEW
• I BASIC ARITHMETIC
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• II RATIONAL NUMBERS
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• III AVERAGES
• Slide 24
• The End

B) Signed Numbers and Operations

- + 0 | a | = distance a is from 0 (NEVER NEGATIVE)

| a | = 7 then a =

| a ndash 2 | = 7 then a =

7

2 7 or 2 7 a a

5 or 9

Add + sum totalSub - differenceMult x ( ) productDiv divide quotient

Zero Property if ab = 0 then a = 0 or b = 0

Ex What is the product of the integers -3 -2 -1 hellip3 4 5

0

1( ) 1a

a

ProdQuot of EVEN number of negatives is POSITIVEProdQuot of ODD number of negatives is NEGATIVE

Reciprocals

Sign Changes 2 + (-6) = 2 ndash 6 = -42 ndash (-6) = 2 + 6 = 8

C) INTEGERSNumber ne Integer

Consecutive integers x x+1 x+2 x+3 hellip Consecutive oddeven integers x x+2 x+4 hellip

Ex The sum of three consecutive integers is less than 75 What is the largest possible value of the first of the three consecutive integers 1 2 75 x x x

3 3 75 x3 72x

24x

2 26 x

D) FACTORS

Factors ndash Finite set of values - Know your ldquogoes intosrdquoMultiples ndash Infinite set of values

GCF and LCM ndash use product of primes

GCF = product of common primes(1 time)LCM = product of common primes(1 time) and

uncommon primes

Ex Find the GCF and the LCM of 32 and 44

32

2 16

2 8

2 4

2 2

44

11 4

2 2

32 2 2 2 2 2

44 2 2 11

2 2 4 GCF

2 2 2 2 2 11 352 LCM

E) EXPONENTS and ROOTS

Rules of exponents 3 + 3 + 3 + 3 = 4(3)3(3)(3)(3) = 34

0

1

1

b c b c

cb bc

bb c

c

a

a a

a a a

a a

aa

a

Ex If find the value of x

52 2

5

x

x

2 32x

Ex Which of the following if any are true

10

10

10 10

I -2 0

II - -2 0

III 2 (-2 ) 0

Always Negative ---FALSE

Always Positive ---TRUE

Always Positive ---TRUE

II and III

F) SQUARES and SQUARE ROOTS

Know your squaressquare roots 1-151-225Know exact values always + 2 answers +-

2aa

Ex Find the circumference of a circle whose area is 20π

2A r2

2

20

20

20

2 5

r

r

r

r

2

2 2 5 4 5

C r

C

Rules of radicals

Ex Evaluate the following

A) B)

1

3832

1

1nn

nn

ab a b

a a

b b

aa

a a

3

1 1

2 8 3 8 2

G) PEMDAS

Careful with negatives on calculator

H) INEQUALITIES

or x a - SWITCH SIGN

Ex Solve for a if 5 ndash 3a lt 10

5 3 10a 3 5a

3 5

3 3

a

5

3a

Properties of Inequalities between 0 and 1

1 1 if

if 0 1

1 if 0 1

b c

b ca a

a a a

a aa

A) Fractions and Decimals

ComparingDecimals ndash same of places ndash larger is

larger number

Fractions ndash same denom ndash bigger numer is larger fraction

same numer ndash smaller denom is smaller fraction

II RATIONAL NUMBERS

Powers of 10 - move decimal place ndash + exponent ndash move to right

ndash exponent ndash move to the left

Rounding - know rules- do not need to round grid-ins

Operations with fractionsAddsub like denominatorsMultiply numerators and denominatorsDivide multiply by reciprocals

ldquoofrdquo means multiply

B) Percents

Ex Find the following

1) 45 of 200

is

of 100

45

200 100

x

100 45(200)x

90x

90

2) 90 is 45 of what number

3) 90 is what percent of 200

90

200 100

x

90 45

100

x 45 90 100x

200x

200

200 90 100x

45x

45

Percent increasedecrease IncreaseDecrease = ldquoisrdquoOriginal = ldquoofrdquo

C) Ratio and Proportion

Part Part compared to Part Whole

73 710 or 310

Two numbers in a ratio of a to b ndash Apply an x to each

Ex Two acute angles of a right triangle are in a ratio of 513 What is the measure of the larger acute angle

Proportions Cross multiply Ex Tommy types 35 words per minute How long would it take Tommy to type 987 words

5 13 90 x x

18 90x

5x 13 13 5 65 x

35 987

1

x

35 987x

282x28 min 12 secx

Direct Variation vs Inverse Variation orDirectly Proportional vs Inversely Proportional

x uarr y uarr x uarr y darrx darr y darr x darr y uarr

y = kx y = kx or k = xy

Ex If y is directly proportional to x and y = 7 when x = 2 find the value of y when x is 5

35 k

y kx

7 2 k175y

35y x

35 5y

Ex If it takes 4 workers 2 hours to complete a certain job how many minutes would it take 6 workers to complete the same job

480k

k

yx

120(4)k

80y1204

k

480y

x

480

6y

III AVERAGES

A) Average = Mean = Sumcount

Know the average then sum = average x count Ex After 5 tests Tony has an 85 average If Tony had an 83

average after his first three tests what was his average on the last two tests

5 5 85 425T 425 24987

2A

3 3 83 249T

B) Median = Middle

ARRANGE THEM IN ORDER FIRST

Odd of scores - Find middle Even of scores - Find average of middle 2 rsquos

C) Mode = Number that occurs the MOST

The End

• Week 1 BASIC MATH REVIEW
• I BASIC ARITHMETIC
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• II RATIONAL NUMBERS
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• III AVERAGES
• Slide 24
• The End

Add + sum totalSub - differenceMult x ( ) productDiv divide quotient

Zero Property if ab = 0 then a = 0 or b = 0

Ex What is the product of the integers -3 -2 -1 hellip3 4 5

0

1( ) 1a

a

ProdQuot of EVEN number of negatives is POSITIVEProdQuot of ODD number of negatives is NEGATIVE

Reciprocals

Sign Changes 2 + (-6) = 2 ndash 6 = -42 ndash (-6) = 2 + 6 = 8

C) INTEGERSNumber ne Integer

Consecutive integers x x+1 x+2 x+3 hellip Consecutive oddeven integers x x+2 x+4 hellip

Ex The sum of three consecutive integers is less than 75 What is the largest possible value of the first of the three consecutive integers 1 2 75 x x x

3 3 75 x3 72x

24x

2 26 x

D) FACTORS

Factors ndash Finite set of values - Know your ldquogoes intosrdquoMultiples ndash Infinite set of values

GCF and LCM ndash use product of primes

GCF = product of common primes(1 time)LCM = product of common primes(1 time) and

uncommon primes

Ex Find the GCF and the LCM of 32 and 44

32

2 16

2 8

2 4

2 2

44

11 4

2 2

32 2 2 2 2 2

44 2 2 11

2 2 4 GCF

2 2 2 2 2 11 352 LCM

E) EXPONENTS and ROOTS

Rules of exponents 3 + 3 + 3 + 3 = 4(3)3(3)(3)(3) = 34

0

1

1

b c b c

cb bc

bb c

c

a

a a

a a a

a a

aa

a

Ex If find the value of x

52 2

5

x

x

2 32x

Ex Which of the following if any are true

10

10

10 10

I -2 0

II - -2 0

III 2 (-2 ) 0

Always Negative ---FALSE

Always Positive ---TRUE

Always Positive ---TRUE

II and III

F) SQUARES and SQUARE ROOTS

Know your squaressquare roots 1-151-225Know exact values always + 2 answers +-

2aa

Ex Find the circumference of a circle whose area is 20π

2A r2

2

20

20

20

2 5

r

r

r

r

2

2 2 5 4 5

C r

C

Rules of radicals

Ex Evaluate the following

A) B)

1

3832

1

1nn

nn

ab a b

a a

b b

aa

a a

3

1 1

2 8 3 8 2

G) PEMDAS

Careful with negatives on calculator

H) INEQUALITIES

or x a - SWITCH SIGN

Ex Solve for a if 5 ndash 3a lt 10

5 3 10a 3 5a

3 5

3 3

a

5

3a

Properties of Inequalities between 0 and 1

1 1 if

if 0 1

1 if 0 1

b c

b ca a

a a a

a aa

A) Fractions and Decimals

ComparingDecimals ndash same of places ndash larger is

larger number

Fractions ndash same denom ndash bigger numer is larger fraction

same numer ndash smaller denom is smaller fraction

II RATIONAL NUMBERS

Powers of 10 - move decimal place ndash + exponent ndash move to right

ndash exponent ndash move to the left

Rounding - know rules- do not need to round grid-ins

Operations with fractionsAddsub like denominatorsMultiply numerators and denominatorsDivide multiply by reciprocals

ldquoofrdquo means multiply

B) Percents

Ex Find the following

1) 45 of 200

is

of 100

45

200 100

x

100 45(200)x

90x

90

2) 90 is 45 of what number

3) 90 is what percent of 200

90

200 100

x

90 45

100

x 45 90 100x

200x

200

200 90 100x

45x

45

Percent increasedecrease IncreaseDecrease = ldquoisrdquoOriginal = ldquoofrdquo

C) Ratio and Proportion

Part Part compared to Part Whole

73 710 or 310

Two numbers in a ratio of a to b ndash Apply an x to each

Ex Two acute angles of a right triangle are in a ratio of 513 What is the measure of the larger acute angle

Proportions Cross multiply Ex Tommy types 35 words per minute How long would it take Tommy to type 987 words

5 13 90 x x

18 90x

5x 13 13 5 65 x

35 987

1

x

35 987x

282x28 min 12 secx

Direct Variation vs Inverse Variation orDirectly Proportional vs Inversely Proportional

x uarr y uarr x uarr y darrx darr y darr x darr y uarr

y = kx y = kx or k = xy

Ex If y is directly proportional to x and y = 7 when x = 2 find the value of y when x is 5

35 k

y kx

7 2 k175y

35y x

35 5y

Ex If it takes 4 workers 2 hours to complete a certain job how many minutes would it take 6 workers to complete the same job

480k

k

yx

120(4)k

80y1204

k

480y

x

480

6y

III AVERAGES

A) Average = Mean = Sumcount

Know the average then sum = average x count Ex After 5 tests Tony has an 85 average If Tony had an 83

average after his first three tests what was his average on the last two tests

5 5 85 425T 425 24987

2A

3 3 83 249T

B) Median = Middle

ARRANGE THEM IN ORDER FIRST

Odd of scores - Find middle Even of scores - Find average of middle 2 rsquos

C) Mode = Number that occurs the MOST

The End

• Week 1 BASIC MATH REVIEW
• I BASIC ARITHMETIC
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• II RATIONAL NUMBERS
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• III AVERAGES
• Slide 24
• The End

1( ) 1a

a

ProdQuot of EVEN number of negatives is POSITIVEProdQuot of ODD number of negatives is NEGATIVE

Reciprocals

Sign Changes 2 + (-6) = 2 ndash 6 = -42 ndash (-6) = 2 + 6 = 8

C) INTEGERSNumber ne Integer

Consecutive integers x x+1 x+2 x+3 hellip Consecutive oddeven integers x x+2 x+4 hellip

Ex The sum of three consecutive integers is less than 75 What is the largest possible value of the first of the three consecutive integers 1 2 75 x x x

3 3 75 x3 72x

24x

2 26 x

D) FACTORS

Factors ndash Finite set of values - Know your ldquogoes intosrdquoMultiples ndash Infinite set of values

GCF and LCM ndash use product of primes

GCF = product of common primes(1 time)LCM = product of common primes(1 time) and

uncommon primes

Ex Find the GCF and the LCM of 32 and 44

32

2 16

2 8

2 4

2 2

44

11 4

2 2

32 2 2 2 2 2

44 2 2 11

2 2 4 GCF

2 2 2 2 2 11 352 LCM

E) EXPONENTS and ROOTS

Rules of exponents 3 + 3 + 3 + 3 = 4(3)3(3)(3)(3) = 34

0

1

1

b c b c

cb bc

bb c

c

a

a a

a a a

a a

aa

a

Ex If find the value of x

52 2

5

x

x

2 32x

Ex Which of the following if any are true

10

10

10 10

I -2 0

II - -2 0

III 2 (-2 ) 0

Always Negative ---FALSE

Always Positive ---TRUE

Always Positive ---TRUE

II and III

F) SQUARES and SQUARE ROOTS

Know your squaressquare roots 1-151-225Know exact values always + 2 answers +-

2aa

Ex Find the circumference of a circle whose area is 20π

2A r2

2

20

20

20

2 5

r

r

r

r

2

2 2 5 4 5

C r

C

Rules of radicals

Ex Evaluate the following

A) B)

1

3832

1

1nn

nn

ab a b

a a

b b

aa

a a

3

1 1

2 8 3 8 2

G) PEMDAS

Careful with negatives on calculator

H) INEQUALITIES

or x a - SWITCH SIGN

Ex Solve for a if 5 ndash 3a lt 10

5 3 10a 3 5a

3 5

3 3

a

5

3a

Properties of Inequalities between 0 and 1

1 1 if

if 0 1

1 if 0 1

b c

b ca a

a a a

a aa

A) Fractions and Decimals

ComparingDecimals ndash same of places ndash larger is

larger number

Fractions ndash same denom ndash bigger numer is larger fraction

same numer ndash smaller denom is smaller fraction

II RATIONAL NUMBERS

Powers of 10 - move decimal place ndash + exponent ndash move to right

ndash exponent ndash move to the left

Rounding - know rules- do not need to round grid-ins

Operations with fractionsAddsub like denominatorsMultiply numerators and denominatorsDivide multiply by reciprocals

ldquoofrdquo means multiply

B) Percents

Ex Find the following

1) 45 of 200

is

of 100

45

200 100

x

100 45(200)x

90x

90

2) 90 is 45 of what number

3) 90 is what percent of 200

90

200 100

x

90 45

100

x 45 90 100x

200x

200

200 90 100x

45x

45

Percent increasedecrease IncreaseDecrease = ldquoisrdquoOriginal = ldquoofrdquo

C) Ratio and Proportion

Part Part compared to Part Whole

73 710 or 310

Two numbers in a ratio of a to b ndash Apply an x to each

Ex Two acute angles of a right triangle are in a ratio of 513 What is the measure of the larger acute angle

Proportions Cross multiply Ex Tommy types 35 words per minute How long would it take Tommy to type 987 words

5 13 90 x x

18 90x

5x 13 13 5 65 x

35 987

1

x

35 987x

282x28 min 12 secx

Direct Variation vs Inverse Variation orDirectly Proportional vs Inversely Proportional

x uarr y uarr x uarr y darrx darr y darr x darr y uarr

y = kx y = kx or k = xy

Ex If y is directly proportional to x and y = 7 when x = 2 find the value of y when x is 5

35 k

y kx

7 2 k175y

35y x

35 5y

Ex If it takes 4 workers 2 hours to complete a certain job how many minutes would it take 6 workers to complete the same job

480k

k

yx

120(4)k

80y1204

k

480y

x

480

6y

III AVERAGES

A) Average = Mean = Sumcount

Know the average then sum = average x count Ex After 5 tests Tony has an 85 average If Tony had an 83

average after his first three tests what was his average on the last two tests

5 5 85 425T 425 24987

2A

3 3 83 249T

B) Median = Middle

ARRANGE THEM IN ORDER FIRST

Odd of scores - Find middle Even of scores - Find average of middle 2 rsquos

C) Mode = Number that occurs the MOST

The End

• Week 1 BASIC MATH REVIEW
• I BASIC ARITHMETIC
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• II RATIONAL NUMBERS
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• III AVERAGES
• Slide 24
• The End

C) INTEGERSNumber ne Integer

Consecutive integers x x+1 x+2 x+3 hellip Consecutive oddeven integers x x+2 x+4 hellip

Ex The sum of three consecutive integers is less than 75 What is the largest possible value of the first of the three consecutive integers 1 2 75 x x x

3 3 75 x3 72x

24x

2 26 x

D) FACTORS

Factors ndash Finite set of values - Know your ldquogoes intosrdquoMultiples ndash Infinite set of values

GCF and LCM ndash use product of primes

GCF = product of common primes(1 time)LCM = product of common primes(1 time) and

uncommon primes

Ex Find the GCF and the LCM of 32 and 44

32

2 16

2 8

2 4

2 2

44

11 4

2 2

32 2 2 2 2 2

44 2 2 11

2 2 4 GCF

2 2 2 2 2 11 352 LCM

E) EXPONENTS and ROOTS

Rules of exponents 3 + 3 + 3 + 3 = 4(3)3(3)(3)(3) = 34

0

1

1

b c b c

cb bc

bb c

c

a

a a

a a a

a a

aa

a

Ex If find the value of x

52 2

5

x

x

2 32x

Ex Which of the following if any are true

10

10

10 10

I -2 0

II - -2 0

III 2 (-2 ) 0

Always Negative ---FALSE

Always Positive ---TRUE

Always Positive ---TRUE

II and III

F) SQUARES and SQUARE ROOTS

Know your squaressquare roots 1-151-225Know exact values always + 2 answers +-

2aa

Ex Find the circumference of a circle whose area is 20π

2A r2

2

20

20

20

2 5

r

r

r

r

2

2 2 5 4 5

C r

C

Rules of radicals

Ex Evaluate the following

A) B)

1

3832

1

1nn

nn

ab a b

a a

b b

aa

a a

3

1 1

2 8 3 8 2

G) PEMDAS

Careful with negatives on calculator

H) INEQUALITIES

or x a - SWITCH SIGN

Ex Solve for a if 5 ndash 3a lt 10

5 3 10a 3 5a

3 5

3 3

a

5

3a

Properties of Inequalities between 0 and 1

1 1 if

if 0 1

1 if 0 1

b c

b ca a

a a a

a aa

A) Fractions and Decimals

ComparingDecimals ndash same of places ndash larger is

larger number

Fractions ndash same denom ndash bigger numer is larger fraction

same numer ndash smaller denom is smaller fraction

II RATIONAL NUMBERS

Powers of 10 - move decimal place ndash + exponent ndash move to right

ndash exponent ndash move to the left

Rounding - know rules- do not need to round grid-ins

Operations with fractionsAddsub like denominatorsMultiply numerators and denominatorsDivide multiply by reciprocals

ldquoofrdquo means multiply

B) Percents

Ex Find the following

1) 45 of 200

is

of 100

45

200 100

x

100 45(200)x

90x

90

2) 90 is 45 of what number

3) 90 is what percent of 200

90

200 100

x

90 45

100

x 45 90 100x

200x

200

200 90 100x

45x

45

Percent increasedecrease IncreaseDecrease = ldquoisrdquoOriginal = ldquoofrdquo

C) Ratio and Proportion

Part Part compared to Part Whole

73 710 or 310

Two numbers in a ratio of a to b ndash Apply an x to each

Ex Two acute angles of a right triangle are in a ratio of 513 What is the measure of the larger acute angle

Proportions Cross multiply Ex Tommy types 35 words per minute How long would it take Tommy to type 987 words

5 13 90 x x

18 90x

5x 13 13 5 65 x

35 987

1

x

35 987x

282x28 min 12 secx

Direct Variation vs Inverse Variation orDirectly Proportional vs Inversely Proportional

x uarr y uarr x uarr y darrx darr y darr x darr y uarr

y = kx y = kx or k = xy

Ex If y is directly proportional to x and y = 7 when x = 2 find the value of y when x is 5

35 k

y kx

7 2 k175y

35y x

35 5y

Ex If it takes 4 workers 2 hours to complete a certain job how many minutes would it take 6 workers to complete the same job

480k

k

yx

120(4)k

80y1204

k

480y

x

480

6y

III AVERAGES

A) Average = Mean = Sumcount

Know the average then sum = average x count Ex After 5 tests Tony has an 85 average If Tony had an 83

average after his first three tests what was his average on the last two tests

5 5 85 425T 425 24987

2A

3 3 83 249T

B) Median = Middle

ARRANGE THEM IN ORDER FIRST

Odd of scores - Find middle Even of scores - Find average of middle 2 rsquos

C) Mode = Number that occurs the MOST

The End

• Week 1 BASIC MATH REVIEW
• I BASIC ARITHMETIC
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• II RATIONAL NUMBERS
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• III AVERAGES
• Slide 24
• The End

D) FACTORS

Factors ndash Finite set of values - Know your ldquogoes intosrdquoMultiples ndash Infinite set of values

GCF and LCM ndash use product of primes

GCF = product of common primes(1 time)LCM = product of common primes(1 time) and

uncommon primes

Ex Find the GCF and the LCM of 32 and 44

32

2 16

2 8

2 4

2 2

44

11 4

2 2

32 2 2 2 2 2

44 2 2 11

2 2 4 GCF

2 2 2 2 2 11 352 LCM

E) EXPONENTS and ROOTS

Rules of exponents 3 + 3 + 3 + 3 = 4(3)3(3)(3)(3) = 34

0

1

1

b c b c

cb bc

bb c

c

a

a a

a a a

a a

aa

a

Ex If find the value of x

52 2

5

x

x

2 32x

Ex Which of the following if any are true

10

10

10 10

I -2 0

II - -2 0

III 2 (-2 ) 0

Always Negative ---FALSE

Always Positive ---TRUE

Always Positive ---TRUE

II and III

F) SQUARES and SQUARE ROOTS

Know your squaressquare roots 1-151-225Know exact values always + 2 answers +-

2aa

Ex Find the circumference of a circle whose area is 20π

2A r2

2

20

20

20

2 5

r

r

r

r

2

2 2 5 4 5

C r

C

Rules of radicals

Ex Evaluate the following

A) B)

1

3832

1

1nn

nn

ab a b

a a

b b

aa

a a

3

1 1

2 8 3 8 2

G) PEMDAS

Careful with negatives on calculator

H) INEQUALITIES

or x a - SWITCH SIGN

Ex Solve for a if 5 ndash 3a lt 10

5 3 10a 3 5a

3 5

3 3

a

5

3a

Properties of Inequalities between 0 and 1

1 1 if

if 0 1

1 if 0 1

b c

b ca a

a a a

a aa

A) Fractions and Decimals

ComparingDecimals ndash same of places ndash larger is

larger number

Fractions ndash same denom ndash bigger numer is larger fraction

same numer ndash smaller denom is smaller fraction

II RATIONAL NUMBERS

Powers of 10 - move decimal place ndash + exponent ndash move to right

ndash exponent ndash move to the left

Rounding - know rules- do not need to round grid-ins

Operations with fractionsAddsub like denominatorsMultiply numerators and denominatorsDivide multiply by reciprocals

ldquoofrdquo means multiply

B) Percents

Ex Find the following

1) 45 of 200

is

of 100

45

200 100

x

100 45(200)x

90x

90

2) 90 is 45 of what number

3) 90 is what percent of 200

90

200 100

x

90 45

100

x 45 90 100x

200x

200

200 90 100x

45x

45

Percent increasedecrease IncreaseDecrease = ldquoisrdquoOriginal = ldquoofrdquo

C) Ratio and Proportion

Part Part compared to Part Whole

73 710 or 310

Two numbers in a ratio of a to b ndash Apply an x to each

Ex Two acute angles of a right triangle are in a ratio of 513 What is the measure of the larger acute angle

Proportions Cross multiply Ex Tommy types 35 words per minute How long would it take Tommy to type 987 words

5 13 90 x x

18 90x

5x 13 13 5 65 x

35 987

1

x

35 987x

282x28 min 12 secx

Direct Variation vs Inverse Variation orDirectly Proportional vs Inversely Proportional

x uarr y uarr x uarr y darrx darr y darr x darr y uarr

y = kx y = kx or k = xy

Ex If y is directly proportional to x and y = 7 when x = 2 find the value of y when x is 5

35 k

y kx

7 2 k175y

35y x

35 5y

Ex If it takes 4 workers 2 hours to complete a certain job how many minutes would it take 6 workers to complete the same job

480k

k

yx

120(4)k

80y1204

k

480y

x

480

6y

III AVERAGES

A) Average = Mean = Sumcount

Know the average then sum = average x count Ex After 5 tests Tony has an 85 average If Tony had an 83

average after his first three tests what was his average on the last two tests

5 5 85 425T 425 24987

2A

3 3 83 249T

B) Median = Middle

ARRANGE THEM IN ORDER FIRST

Odd of scores - Find middle Even of scores - Find average of middle 2 rsquos

C) Mode = Number that occurs the MOST

The End

• Week 1 BASIC MATH REVIEW
• I BASIC ARITHMETIC
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• II RATIONAL NUMBERS
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• III AVERAGES
• Slide 24
• The End

Ex Find the GCF and the LCM of 32 and 44

32

2 16

2 8

2 4

2 2

44

11 4

2 2

32 2 2 2 2 2

44 2 2 11

2 2 4 GCF

2 2 2 2 2 11 352 LCM

E) EXPONENTS and ROOTS

Rules of exponents 3 + 3 + 3 + 3 = 4(3)3(3)(3)(3) = 34

0

1

1

b c b c

cb bc

bb c

c

a

a a

a a a

a a

aa

a

Ex If find the value of x

52 2

5

x

x

2 32x

Ex Which of the following if any are true

10

10

10 10

I -2 0

II - -2 0

III 2 (-2 ) 0

Always Negative ---FALSE

Always Positive ---TRUE

Always Positive ---TRUE

II and III

F) SQUARES and SQUARE ROOTS

Know your squaressquare roots 1-151-225Know exact values always + 2 answers +-

2aa

Ex Find the circumference of a circle whose area is 20π

2A r2

2

20

20

20

2 5

r

r

r

r

2

2 2 5 4 5

C r

C

Rules of radicals

Ex Evaluate the following

A) B)

1

3832

1

1nn

nn

ab a b

a a

b b

aa

a a

3

1 1

2 8 3 8 2

G) PEMDAS

Careful with negatives on calculator

H) INEQUALITIES

or x a - SWITCH SIGN

Ex Solve for a if 5 ndash 3a lt 10

5 3 10a 3 5a

3 5

3 3

a

5

3a

Properties of Inequalities between 0 and 1

1 1 if

if 0 1

1 if 0 1

b c

b ca a

a a a

a aa

A) Fractions and Decimals

ComparingDecimals ndash same of places ndash larger is

larger number

Fractions ndash same denom ndash bigger numer is larger fraction

same numer ndash smaller denom is smaller fraction

II RATIONAL NUMBERS

Powers of 10 - move decimal place ndash + exponent ndash move to right

ndash exponent ndash move to the left

Rounding - know rules- do not need to round grid-ins

Operations with fractionsAddsub like denominatorsMultiply numerators and denominatorsDivide multiply by reciprocals

ldquoofrdquo means multiply

B) Percents

Ex Find the following

1) 45 of 200

is

of 100

45

200 100

x

100 45(200)x

90x

90

2) 90 is 45 of what number

3) 90 is what percent of 200

90

200 100

x

90 45

100

x 45 90 100x

200x

200

200 90 100x

45x

45

Percent increasedecrease IncreaseDecrease = ldquoisrdquoOriginal = ldquoofrdquo

C) Ratio and Proportion

Part Part compared to Part Whole

73 710 or 310

Two numbers in a ratio of a to b ndash Apply an x to each

Ex Two acute angles of a right triangle are in a ratio of 513 What is the measure of the larger acute angle

Proportions Cross multiply Ex Tommy types 35 words per minute How long would it take Tommy to type 987 words

5 13 90 x x

18 90x

5x 13 13 5 65 x

35 987

1

x

35 987x

282x28 min 12 secx

Direct Variation vs Inverse Variation orDirectly Proportional vs Inversely Proportional

x uarr y uarr x uarr y darrx darr y darr x darr y uarr

y = kx y = kx or k = xy

Ex If y is directly proportional to x and y = 7 when x = 2 find the value of y when x is 5

35 k

y kx

7 2 k175y

35y x

35 5y

Ex If it takes 4 workers 2 hours to complete a certain job how many minutes would it take 6 workers to complete the same job

480k

k

yx

120(4)k

80y1204

k

480y

x

480

6y

III AVERAGES

A) Average = Mean = Sumcount

Know the average then sum = average x count Ex After 5 tests Tony has an 85 average If Tony had an 83

average after his first three tests what was his average on the last two tests

5 5 85 425T 425 24987

2A

3 3 83 249T

B) Median = Middle

ARRANGE THEM IN ORDER FIRST

Odd of scores - Find middle Even of scores - Find average of middle 2 rsquos

C) Mode = Number that occurs the MOST

The End

• Week 1 BASIC MATH REVIEW
• I BASIC ARITHMETIC
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• II RATIONAL NUMBERS
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• III AVERAGES
• Slide 24
• The End

E) EXPONENTS and ROOTS

Rules of exponents 3 + 3 + 3 + 3 = 4(3)3(3)(3)(3) = 34

0

1

1

b c b c

cb bc

bb c

c

a

a a

a a a

a a

aa

a

Ex If find the value of x

52 2

5

x

x

2 32x

Ex Which of the following if any are true

10

10

10 10

I -2 0

II - -2 0

III 2 (-2 ) 0

Always Negative ---FALSE

Always Positive ---TRUE

Always Positive ---TRUE

II and III

F) SQUARES and SQUARE ROOTS

Know your squaressquare roots 1-151-225Know exact values always + 2 answers +-

2aa

Ex Find the circumference of a circle whose area is 20π

2A r2

2

20

20

20

2 5

r

r

r

r

2

2 2 5 4 5

C r

C

Rules of radicals

Ex Evaluate the following

A) B)

1

3832

1

1nn

nn

ab a b

a a

b b

aa

a a

3

1 1

2 8 3 8 2

G) PEMDAS

Careful with negatives on calculator

H) INEQUALITIES

or x a - SWITCH SIGN

Ex Solve for a if 5 ndash 3a lt 10

5 3 10a 3 5a

3 5

3 3

a

5

3a

Properties of Inequalities between 0 and 1

1 1 if

if 0 1

1 if 0 1

b c

b ca a

a a a

a aa

A) Fractions and Decimals

ComparingDecimals ndash same of places ndash larger is

larger number

Fractions ndash same denom ndash bigger numer is larger fraction

same numer ndash smaller denom is smaller fraction

II RATIONAL NUMBERS

Powers of 10 - move decimal place ndash + exponent ndash move to right

ndash exponent ndash move to the left

Rounding - know rules- do not need to round grid-ins

Operations with fractionsAddsub like denominatorsMultiply numerators and denominatorsDivide multiply by reciprocals

ldquoofrdquo means multiply

B) Percents

Ex Find the following

1) 45 of 200

is

of 100

45

200 100

x

100 45(200)x

90x

90

2) 90 is 45 of what number

3) 90 is what percent of 200

90

200 100

x

90 45

100

x 45 90 100x

200x

200

200 90 100x

45x

45

Percent increasedecrease IncreaseDecrease = ldquoisrdquoOriginal = ldquoofrdquo

C) Ratio and Proportion

Part Part compared to Part Whole

73 710 or 310

Two numbers in a ratio of a to b ndash Apply an x to each

Ex Two acute angles of a right triangle are in a ratio of 513 What is the measure of the larger acute angle

Proportions Cross multiply Ex Tommy types 35 words per minute How long would it take Tommy to type 987 words

5 13 90 x x

18 90x

5x 13 13 5 65 x

35 987

1

x

35 987x

282x28 min 12 secx

Direct Variation vs Inverse Variation orDirectly Proportional vs Inversely Proportional

x uarr y uarr x uarr y darrx darr y darr x darr y uarr

y = kx y = kx or k = xy

Ex If y is directly proportional to x and y = 7 when x = 2 find the value of y when x is 5

35 k

y kx

7 2 k175y

35y x

35 5y

Ex If it takes 4 workers 2 hours to complete a certain job how many minutes would it take 6 workers to complete the same job

480k

k

yx

120(4)k

80y1204

k

480y

x

480

6y

III AVERAGES

A) Average = Mean = Sumcount

Know the average then sum = average x count Ex After 5 tests Tony has an 85 average If Tony had an 83

average after his first three tests what was his average on the last two tests

5 5 85 425T 425 24987

2A

3 3 83 249T

B) Median = Middle

ARRANGE THEM IN ORDER FIRST

Odd of scores - Find middle Even of scores - Find average of middle 2 rsquos

C) Mode = Number that occurs the MOST

The End

• Week 1 BASIC MATH REVIEW
• I BASIC ARITHMETIC
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• II RATIONAL NUMBERS
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• III AVERAGES
• Slide 24
• The End

Ex If find the value of x

52 2

5

x

x

2 32x

Ex Which of the following if any are true

10

10

10 10

I -2 0

II - -2 0

III 2 (-2 ) 0

Always Negative ---FALSE

Always Positive ---TRUE

Always Positive ---TRUE

II and III

F) SQUARES and SQUARE ROOTS

Know your squaressquare roots 1-151-225Know exact values always + 2 answers +-

2aa

Ex Find the circumference of a circle whose area is 20π

2A r2

2

20

20

20

2 5

r

r

r

r

2

2 2 5 4 5

C r

C

Rules of radicals

Ex Evaluate the following

A) B)

1

3832

1

1nn

nn

ab a b

a a

b b

aa

a a

3

1 1

2 8 3 8 2

G) PEMDAS

Careful with negatives on calculator

H) INEQUALITIES

or x a - SWITCH SIGN

Ex Solve for a if 5 ndash 3a lt 10

5 3 10a 3 5a

3 5

3 3

a

5

3a

Properties of Inequalities between 0 and 1

1 1 if

if 0 1

1 if 0 1

b c

b ca a

a a a

a aa

A) Fractions and Decimals

ComparingDecimals ndash same of places ndash larger is

larger number

Fractions ndash same denom ndash bigger numer is larger fraction

same numer ndash smaller denom is smaller fraction

II RATIONAL NUMBERS

Powers of 10 - move decimal place ndash + exponent ndash move to right

ndash exponent ndash move to the left

Rounding - know rules- do not need to round grid-ins

Operations with fractionsAddsub like denominatorsMultiply numerators and denominatorsDivide multiply by reciprocals

ldquoofrdquo means multiply

B) Percents

Ex Find the following

1) 45 of 200

is

of 100

45

200 100

x

100 45(200)x

90x

90

2) 90 is 45 of what number

3) 90 is what percent of 200

90

200 100

x

90 45

100

x 45 90 100x

200x

200

200 90 100x

45x

45

Percent increasedecrease IncreaseDecrease = ldquoisrdquoOriginal = ldquoofrdquo

C) Ratio and Proportion

Part Part compared to Part Whole

73 710 or 310

Two numbers in a ratio of a to b ndash Apply an x to each

Ex Two acute angles of a right triangle are in a ratio of 513 What is the measure of the larger acute angle

Proportions Cross multiply Ex Tommy types 35 words per minute How long would it take Tommy to type 987 words

5 13 90 x x

18 90x

5x 13 13 5 65 x

35 987

1

x

35 987x

282x28 min 12 secx

Direct Variation vs Inverse Variation orDirectly Proportional vs Inversely Proportional

x uarr y uarr x uarr y darrx darr y darr x darr y uarr

y = kx y = kx or k = xy

Ex If y is directly proportional to x and y = 7 when x = 2 find the value of y when x is 5

35 k

y kx

7 2 k175y

35y x

35 5y

Ex If it takes 4 workers 2 hours to complete a certain job how many minutes would it take 6 workers to complete the same job

480k

k

yx

120(4)k

80y1204

k

480y

x

480

6y

III AVERAGES

A) Average = Mean = Sumcount

Know the average then sum = average x count Ex After 5 tests Tony has an 85 average If Tony had an 83

average after his first three tests what was his average on the last two tests

5 5 85 425T 425 24987

2A

3 3 83 249T

B) Median = Middle

ARRANGE THEM IN ORDER FIRST

Odd of scores - Find middle Even of scores - Find average of middle 2 rsquos

C) Mode = Number that occurs the MOST

The End

• Week 1 BASIC MATH REVIEW
• I BASIC ARITHMETIC
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• II RATIONAL NUMBERS
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• III AVERAGES
• Slide 24
• The End

F) SQUARES and SQUARE ROOTS

Know your squaressquare roots 1-151-225Know exact values always + 2 answers +-

2aa

Ex Find the circumference of a circle whose area is 20π

2A r2

2

20

20

20

2 5

r

r

r

r

2

2 2 5 4 5

C r

C

Rules of radicals

Ex Evaluate the following

A) B)

1

3832

1

1nn

nn

ab a b

a a

b b

aa

a a

3

1 1

2 8 3 8 2

G) PEMDAS

Careful with negatives on calculator

H) INEQUALITIES

or x a - SWITCH SIGN

Ex Solve for a if 5 ndash 3a lt 10

5 3 10a 3 5a

3 5

3 3

a

5

3a

Properties of Inequalities between 0 and 1

1 1 if

if 0 1

1 if 0 1

b c

b ca a

a a a

a aa

A) Fractions and Decimals

ComparingDecimals ndash same of places ndash larger is

larger number

Fractions ndash same denom ndash bigger numer is larger fraction

same numer ndash smaller denom is smaller fraction

II RATIONAL NUMBERS

Powers of 10 - move decimal place ndash + exponent ndash move to right

ndash exponent ndash move to the left

Rounding - know rules- do not need to round grid-ins

Operations with fractionsAddsub like denominatorsMultiply numerators and denominatorsDivide multiply by reciprocals

ldquoofrdquo means multiply

B) Percents

Ex Find the following

1) 45 of 200

is

of 100

45

200 100

x

100 45(200)x

90x

90

2) 90 is 45 of what number

3) 90 is what percent of 200

90

200 100

x

90 45

100

x 45 90 100x

200x

200

200 90 100x

45x

45

Percent increasedecrease IncreaseDecrease = ldquoisrdquoOriginal = ldquoofrdquo

C) Ratio and Proportion

Part Part compared to Part Whole

73 710 or 310

Two numbers in a ratio of a to b ndash Apply an x to each

Ex Two acute angles of a right triangle are in a ratio of 513 What is the measure of the larger acute angle

Proportions Cross multiply Ex Tommy types 35 words per minute How long would it take Tommy to type 987 words

5 13 90 x x

18 90x

5x 13 13 5 65 x

35 987

1

x

35 987x

282x28 min 12 secx

Direct Variation vs Inverse Variation orDirectly Proportional vs Inversely Proportional

x uarr y uarr x uarr y darrx darr y darr x darr y uarr

y = kx y = kx or k = xy

Ex If y is directly proportional to x and y = 7 when x = 2 find the value of y when x is 5

35 k

y kx

7 2 k175y

35y x

35 5y

Ex If it takes 4 workers 2 hours to complete a certain job how many minutes would it take 6 workers to complete the same job

480k

k

yx

120(4)k

80y1204

k

480y

x

480

6y

III AVERAGES

A) Average = Mean = Sumcount

Know the average then sum = average x count Ex After 5 tests Tony has an 85 average If Tony had an 83

average after his first three tests what was his average on the last two tests

5 5 85 425T 425 24987

2A

3 3 83 249T

B) Median = Middle

ARRANGE THEM IN ORDER FIRST

Odd of scores - Find middle Even of scores - Find average of middle 2 rsquos

C) Mode = Number that occurs the MOST

The End

• Week 1 BASIC MATH REVIEW
• I BASIC ARITHMETIC
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• II RATIONAL NUMBERS
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• III AVERAGES
• Slide 24
• The End

Rules of radicals

Ex Evaluate the following

A) B)

1

3832

1

1nn

nn

ab a b

a a

b b

aa

a a

3

1 1

2 8 3 8 2

G) PEMDAS

Careful with negatives on calculator

H) INEQUALITIES

or x a - SWITCH SIGN

Ex Solve for a if 5 ndash 3a lt 10

5 3 10a 3 5a

3 5

3 3

a

5

3a

Properties of Inequalities between 0 and 1

1 1 if

if 0 1

1 if 0 1

b c

b ca a

a a a

a aa

A) Fractions and Decimals

ComparingDecimals ndash same of places ndash larger is

larger number

Fractions ndash same denom ndash bigger numer is larger fraction

same numer ndash smaller denom is smaller fraction

II RATIONAL NUMBERS

Powers of 10 - move decimal place ndash + exponent ndash move to right

ndash exponent ndash move to the left

Rounding - know rules- do not need to round grid-ins

Operations with fractionsAddsub like denominatorsMultiply numerators and denominatorsDivide multiply by reciprocals

ldquoofrdquo means multiply

B) Percents

Ex Find the following

1) 45 of 200

is

of 100

45

200 100

x

100 45(200)x

90x

90

2) 90 is 45 of what number

3) 90 is what percent of 200

90

200 100

x

90 45

100

x 45 90 100x

200x

200

200 90 100x

45x

45

Percent increasedecrease IncreaseDecrease = ldquoisrdquoOriginal = ldquoofrdquo

C) Ratio and Proportion

Part Part compared to Part Whole

73 710 or 310

Two numbers in a ratio of a to b ndash Apply an x to each

Ex Two acute angles of a right triangle are in a ratio of 513 What is the measure of the larger acute angle

Proportions Cross multiply Ex Tommy types 35 words per minute How long would it take Tommy to type 987 words

5 13 90 x x

18 90x

5x 13 13 5 65 x

35 987

1

x

35 987x

282x28 min 12 secx

Direct Variation vs Inverse Variation orDirectly Proportional vs Inversely Proportional

x uarr y uarr x uarr y darrx darr y darr x darr y uarr

y = kx y = kx or k = xy

Ex If y is directly proportional to x and y = 7 when x = 2 find the value of y when x is 5

35 k

y kx

7 2 k175y

35y x

35 5y

Ex If it takes 4 workers 2 hours to complete a certain job how many minutes would it take 6 workers to complete the same job

480k

k

yx

120(4)k

80y1204

k

480y

x

480

6y

III AVERAGES

A) Average = Mean = Sumcount

Know the average then sum = average x count Ex After 5 tests Tony has an 85 average If Tony had an 83

average after his first three tests what was his average on the last two tests

5 5 85 425T 425 24987

2A

3 3 83 249T

B) Median = Middle

ARRANGE THEM IN ORDER FIRST

Odd of scores - Find middle Even of scores - Find average of middle 2 rsquos

C) Mode = Number that occurs the MOST

The End

• Week 1 BASIC MATH REVIEW
• I BASIC ARITHMETIC
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• II RATIONAL NUMBERS
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• III AVERAGES
• Slide 24
• The End

G) PEMDAS

Careful with negatives on calculator

H) INEQUALITIES

or x a - SWITCH SIGN

Ex Solve for a if 5 ndash 3a lt 10

5 3 10a 3 5a

3 5

3 3

a

5

3a

Properties of Inequalities between 0 and 1

1 1 if

if 0 1

1 if 0 1

b c

b ca a

a a a

a aa

A) Fractions and Decimals

ComparingDecimals ndash same of places ndash larger is

larger number

Fractions ndash same denom ndash bigger numer is larger fraction

same numer ndash smaller denom is smaller fraction

II RATIONAL NUMBERS

Powers of 10 - move decimal place ndash + exponent ndash move to right

ndash exponent ndash move to the left

Rounding - know rules- do not need to round grid-ins

Operations with fractionsAddsub like denominatorsMultiply numerators and denominatorsDivide multiply by reciprocals

ldquoofrdquo means multiply

B) Percents

Ex Find the following

1) 45 of 200

is

of 100

45

200 100

x

100 45(200)x

90x

90

2) 90 is 45 of what number

3) 90 is what percent of 200

90

200 100

x

90 45

100

x 45 90 100x

200x

200

200 90 100x

45x

45

Percent increasedecrease IncreaseDecrease = ldquoisrdquoOriginal = ldquoofrdquo

C) Ratio and Proportion

Part Part compared to Part Whole

73 710 or 310

Two numbers in a ratio of a to b ndash Apply an x to each

Ex Two acute angles of a right triangle are in a ratio of 513 What is the measure of the larger acute angle

Proportions Cross multiply Ex Tommy types 35 words per minute How long would it take Tommy to type 987 words

5 13 90 x x

18 90x

5x 13 13 5 65 x

35 987

1

x

35 987x

282x28 min 12 secx

Direct Variation vs Inverse Variation orDirectly Proportional vs Inversely Proportional

x uarr y uarr x uarr y darrx darr y darr x darr y uarr

y = kx y = kx or k = xy

Ex If y is directly proportional to x and y = 7 when x = 2 find the value of y when x is 5

35 k

y kx

7 2 k175y

35y x

35 5y

Ex If it takes 4 workers 2 hours to complete a certain job how many minutes would it take 6 workers to complete the same job

480k

k

yx

120(4)k

80y1204

k

480y

x

480

6y

III AVERAGES

A) Average = Mean = Sumcount

Know the average then sum = average x count Ex After 5 tests Tony has an 85 average If Tony had an 83

average after his first three tests what was his average on the last two tests

5 5 85 425T 425 24987

2A

3 3 83 249T

B) Median = Middle

ARRANGE THEM IN ORDER FIRST

Odd of scores - Find middle Even of scores - Find average of middle 2 rsquos

C) Mode = Number that occurs the MOST

The End

• Week 1 BASIC MATH REVIEW
• I BASIC ARITHMETIC
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• II RATIONAL NUMBERS
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• III AVERAGES
• Slide 24
• The End

Properties of Inequalities between 0 and 1

1 1 if

if 0 1

1 if 0 1

b c

b ca a

a a a

a aa

A) Fractions and Decimals

ComparingDecimals ndash same of places ndash larger is

larger number

Fractions ndash same denom ndash bigger numer is larger fraction

same numer ndash smaller denom is smaller fraction

II RATIONAL NUMBERS

Powers of 10 - move decimal place ndash + exponent ndash move to right

ndash exponent ndash move to the left

Rounding - know rules- do not need to round grid-ins

Operations with fractionsAddsub like denominatorsMultiply numerators and denominatorsDivide multiply by reciprocals

ldquoofrdquo means multiply

B) Percents

Ex Find the following

1) 45 of 200

is

of 100

45

200 100

x

100 45(200)x

90x

90

2) 90 is 45 of what number

3) 90 is what percent of 200

90

200 100

x

90 45

100

x 45 90 100x

200x

200

200 90 100x

45x

45

Percent increasedecrease IncreaseDecrease = ldquoisrdquoOriginal = ldquoofrdquo

C) Ratio and Proportion

Part Part compared to Part Whole

73 710 or 310

Two numbers in a ratio of a to b ndash Apply an x to each

Ex Two acute angles of a right triangle are in a ratio of 513 What is the measure of the larger acute angle

Proportions Cross multiply Ex Tommy types 35 words per minute How long would it take Tommy to type 987 words

5 13 90 x x

18 90x

5x 13 13 5 65 x

35 987

1

x

35 987x

282x28 min 12 secx

Direct Variation vs Inverse Variation orDirectly Proportional vs Inversely Proportional

x uarr y uarr x uarr y darrx darr y darr x darr y uarr

y = kx y = kx or k = xy

Ex If y is directly proportional to x and y = 7 when x = 2 find the value of y when x is 5

35 k

y kx

7 2 k175y

35y x

35 5y

Ex If it takes 4 workers 2 hours to complete a certain job how many minutes would it take 6 workers to complete the same job

480k

k

yx

120(4)k

80y1204

k

480y

x

480

6y

III AVERAGES

A) Average = Mean = Sumcount

Know the average then sum = average x count Ex After 5 tests Tony has an 85 average If Tony had an 83

average after his first three tests what was his average on the last two tests

5 5 85 425T 425 24987

2A

3 3 83 249T

B) Median = Middle

ARRANGE THEM IN ORDER FIRST

Odd of scores - Find middle Even of scores - Find average of middle 2 rsquos

C) Mode = Number that occurs the MOST

The End

• Week 1 BASIC MATH REVIEW
• I BASIC ARITHMETIC
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• II RATIONAL NUMBERS
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• III AVERAGES
• Slide 24
• The End

A) Fractions and Decimals

ComparingDecimals ndash same of places ndash larger is

larger number

Fractions ndash same denom ndash bigger numer is larger fraction

same numer ndash smaller denom is smaller fraction

II RATIONAL NUMBERS

Powers of 10 - move decimal place ndash + exponent ndash move to right

ndash exponent ndash move to the left

Rounding - know rules- do not need to round grid-ins

Operations with fractionsAddsub like denominatorsMultiply numerators and denominatorsDivide multiply by reciprocals

ldquoofrdquo means multiply

B) Percents

Ex Find the following

1) 45 of 200

is

of 100

45

200 100

x

100 45(200)x

90x

90

2) 90 is 45 of what number

3) 90 is what percent of 200

90

200 100

x

90 45

100

x 45 90 100x

200x

200

200 90 100x

45x

45

Percent increasedecrease IncreaseDecrease = ldquoisrdquoOriginal = ldquoofrdquo

C) Ratio and Proportion

Part Part compared to Part Whole

73 710 or 310

Two numbers in a ratio of a to b ndash Apply an x to each

Ex Two acute angles of a right triangle are in a ratio of 513 What is the measure of the larger acute angle

Proportions Cross multiply Ex Tommy types 35 words per minute How long would it take Tommy to type 987 words

5 13 90 x x

18 90x

5x 13 13 5 65 x

35 987

1

x

35 987x

282x28 min 12 secx

Direct Variation vs Inverse Variation orDirectly Proportional vs Inversely Proportional

x uarr y uarr x uarr y darrx darr y darr x darr y uarr

y = kx y = kx or k = xy

Ex If y is directly proportional to x and y = 7 when x = 2 find the value of y when x is 5

35 k

y kx

7 2 k175y

35y x

35 5y

Ex If it takes 4 workers 2 hours to complete a certain job how many minutes would it take 6 workers to complete the same job

480k

k

yx

120(4)k

80y1204

k

480y

x

480

6y

III AVERAGES

A) Average = Mean = Sumcount

Know the average then sum = average x count Ex After 5 tests Tony has an 85 average If Tony had an 83

average after his first three tests what was his average on the last two tests

5 5 85 425T 425 24987

2A

3 3 83 249T

B) Median = Middle

ARRANGE THEM IN ORDER FIRST

Odd of scores - Find middle Even of scores - Find average of middle 2 rsquos

C) Mode = Number that occurs the MOST

The End

• Week 1 BASIC MATH REVIEW
• I BASIC ARITHMETIC
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• II RATIONAL NUMBERS
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• III AVERAGES
• Slide 24
• The End

Powers of 10 - move decimal place ndash + exponent ndash move to right

ndash exponent ndash move to the left

Rounding - know rules- do not need to round grid-ins

Operations with fractionsAddsub like denominatorsMultiply numerators and denominatorsDivide multiply by reciprocals

ldquoofrdquo means multiply

B) Percents

Ex Find the following

1) 45 of 200

is

of 100

45

200 100

x

100 45(200)x

90x

90

2) 90 is 45 of what number

3) 90 is what percent of 200

90

200 100

x

90 45

100

x 45 90 100x

200x

200

200 90 100x

45x

45

Percent increasedecrease IncreaseDecrease = ldquoisrdquoOriginal = ldquoofrdquo

C) Ratio and Proportion

Part Part compared to Part Whole

73 710 or 310

Two numbers in a ratio of a to b ndash Apply an x to each

Ex Two acute angles of a right triangle are in a ratio of 513 What is the measure of the larger acute angle

Proportions Cross multiply Ex Tommy types 35 words per minute How long would it take Tommy to type 987 words

5 13 90 x x

18 90x

5x 13 13 5 65 x

35 987

1

x

35 987x

282x28 min 12 secx

Direct Variation vs Inverse Variation orDirectly Proportional vs Inversely Proportional

x uarr y uarr x uarr y darrx darr y darr x darr y uarr

y = kx y = kx or k = xy

Ex If y is directly proportional to x and y = 7 when x = 2 find the value of y when x is 5

35 k

y kx

7 2 k175y

35y x

35 5y

Ex If it takes 4 workers 2 hours to complete a certain job how many minutes would it take 6 workers to complete the same job

480k

k

yx

120(4)k

80y1204

k

480y

x

480

6y

III AVERAGES

A) Average = Mean = Sumcount

Know the average then sum = average x count Ex After 5 tests Tony has an 85 average If Tony had an 83

average after his first three tests what was his average on the last two tests

5 5 85 425T 425 24987

2A

3 3 83 249T

B) Median = Middle

ARRANGE THEM IN ORDER FIRST

Odd of scores - Find middle Even of scores - Find average of middle 2 rsquos

C) Mode = Number that occurs the MOST

The End

• Week 1 BASIC MATH REVIEW
• I BASIC ARITHMETIC
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• II RATIONAL NUMBERS
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• III AVERAGES
• Slide 24
• The End

B) Percents

Ex Find the following

1) 45 of 200

is

of 100

45

200 100

x

100 45(200)x

90x

90

2) 90 is 45 of what number

3) 90 is what percent of 200

90

200 100

x

90 45

100

x 45 90 100x

200x

200

200 90 100x

45x

45

Percent increasedecrease IncreaseDecrease = ldquoisrdquoOriginal = ldquoofrdquo

C) Ratio and Proportion

Part Part compared to Part Whole

73 710 or 310

Two numbers in a ratio of a to b ndash Apply an x to each

Ex Two acute angles of a right triangle are in a ratio of 513 What is the measure of the larger acute angle

Proportions Cross multiply Ex Tommy types 35 words per minute How long would it take Tommy to type 987 words

5 13 90 x x

18 90x

5x 13 13 5 65 x

35 987

1

x

35 987x

282x28 min 12 secx

Direct Variation vs Inverse Variation orDirectly Proportional vs Inversely Proportional

x uarr y uarr x uarr y darrx darr y darr x darr y uarr

y = kx y = kx or k = xy

Ex If y is directly proportional to x and y = 7 when x = 2 find the value of y when x is 5

35 k

y kx

7 2 k175y

35y x

35 5y

Ex If it takes 4 workers 2 hours to complete a certain job how many minutes would it take 6 workers to complete the same job

480k

k

yx

120(4)k

80y1204

k

480y

x

480

6y

III AVERAGES

A) Average = Mean = Sumcount

Know the average then sum = average x count Ex After 5 tests Tony has an 85 average If Tony had an 83

average after his first three tests what was his average on the last two tests

5 5 85 425T 425 24987

2A

3 3 83 249T

B) Median = Middle

ARRANGE THEM IN ORDER FIRST

Odd of scores - Find middle Even of scores - Find average of middle 2 rsquos

C) Mode = Number that occurs the MOST

The End

• Week 1 BASIC MATH REVIEW
• I BASIC ARITHMETIC
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• II RATIONAL NUMBERS
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• III AVERAGES
• Slide 24
• The End

2) 90 is 45 of what number

3) 90 is what percent of 200

90

200 100

x

90 45

100

x 45 90 100x

200x

200

200 90 100x

45x

45

Percent increasedecrease IncreaseDecrease = ldquoisrdquoOriginal = ldquoofrdquo

C) Ratio and Proportion

Part Part compared to Part Whole

73 710 or 310

Two numbers in a ratio of a to b ndash Apply an x to each

Ex Two acute angles of a right triangle are in a ratio of 513 What is the measure of the larger acute angle

Proportions Cross multiply Ex Tommy types 35 words per minute How long would it take Tommy to type 987 words

5 13 90 x x

18 90x

5x 13 13 5 65 x

35 987

1

x

35 987x

282x28 min 12 secx

Direct Variation vs Inverse Variation orDirectly Proportional vs Inversely Proportional

x uarr y uarr x uarr y darrx darr y darr x darr y uarr

y = kx y = kx or k = xy

Ex If y is directly proportional to x and y = 7 when x = 2 find the value of y when x is 5

35 k

y kx

7 2 k175y

35y x

35 5y

Ex If it takes 4 workers 2 hours to complete a certain job how many minutes would it take 6 workers to complete the same job

480k

k

yx

120(4)k

80y1204

k

480y

x

480

6y

III AVERAGES

A) Average = Mean = Sumcount

Know the average then sum = average x count Ex After 5 tests Tony has an 85 average If Tony had an 83

average after his first three tests what was his average on the last two tests

5 5 85 425T 425 24987

2A

3 3 83 249T

B) Median = Middle

ARRANGE THEM IN ORDER FIRST

Odd of scores - Find middle Even of scores - Find average of middle 2 rsquos

C) Mode = Number that occurs the MOST

The End

• Week 1 BASIC MATH REVIEW
• I BASIC ARITHMETIC
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• II RATIONAL NUMBERS
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• III AVERAGES
• Slide 24
• The End

Percent increasedecrease IncreaseDecrease = ldquoisrdquoOriginal = ldquoofrdquo

C) Ratio and Proportion

Part Part compared to Part Whole

73 710 or 310

Two numbers in a ratio of a to b ndash Apply an x to each

Ex Two acute angles of a right triangle are in a ratio of 513 What is the measure of the larger acute angle

Proportions Cross multiply Ex Tommy types 35 words per minute How long would it take Tommy to type 987 words

5 13 90 x x

18 90x

5x 13 13 5 65 x

35 987

1

x

35 987x

282x28 min 12 secx

Direct Variation vs Inverse Variation orDirectly Proportional vs Inversely Proportional

x uarr y uarr x uarr y darrx darr y darr x darr y uarr

y = kx y = kx or k = xy

Ex If y is directly proportional to x and y = 7 when x = 2 find the value of y when x is 5

35 k

y kx

7 2 k175y

35y x

35 5y

Ex If it takes 4 workers 2 hours to complete a certain job how many minutes would it take 6 workers to complete the same job

480k

k

yx

120(4)k

80y1204

k

480y

x

480

6y

III AVERAGES

A) Average = Mean = Sumcount

Know the average then sum = average x count Ex After 5 tests Tony has an 85 average If Tony had an 83

average after his first three tests what was his average on the last two tests

5 5 85 425T 425 24987

2A

3 3 83 249T

B) Median = Middle

ARRANGE THEM IN ORDER FIRST

Odd of scores - Find middle Even of scores - Find average of middle 2 rsquos

C) Mode = Number that occurs the MOST

The End

• Week 1 BASIC MATH REVIEW
• I BASIC ARITHMETIC
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• II RATIONAL NUMBERS
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• III AVERAGES
• Slide 24
• The End

Ex Two acute angles of a right triangle are in a ratio of 513 What is the measure of the larger acute angle

Proportions Cross multiply Ex Tommy types 35 words per minute How long would it take Tommy to type 987 words

5 13 90 x x

18 90x

5x 13 13 5 65 x

35 987

1

x

35 987x

282x28 min 12 secx

Direct Variation vs Inverse Variation orDirectly Proportional vs Inversely Proportional

x uarr y uarr x uarr y darrx darr y darr x darr y uarr

y = kx y = kx or k = xy

Ex If y is directly proportional to x and y = 7 when x = 2 find the value of y when x is 5

35 k

y kx

7 2 k175y

35y x

35 5y

Ex If it takes 4 workers 2 hours to complete a certain job how many minutes would it take 6 workers to complete the same job

480k

k

yx

120(4)k

80y1204

k

480y

x

480

6y

III AVERAGES

A) Average = Mean = Sumcount

Know the average then sum = average x count Ex After 5 tests Tony has an 85 average If Tony had an 83

average after his first three tests what was his average on the last two tests

5 5 85 425T 425 24987

2A

3 3 83 249T

B) Median = Middle

ARRANGE THEM IN ORDER FIRST

Odd of scores - Find middle Even of scores - Find average of middle 2 rsquos

C) Mode = Number that occurs the MOST

The End

• Week 1 BASIC MATH REVIEW
• I BASIC ARITHMETIC
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• II RATIONAL NUMBERS
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• III AVERAGES
• Slide 24
• The End

Direct Variation vs Inverse Variation orDirectly Proportional vs Inversely Proportional

x uarr y uarr x uarr y darrx darr y darr x darr y uarr

y = kx y = kx or k = xy

Ex If y is directly proportional to x and y = 7 when x = 2 find the value of y when x is 5

35 k

y kx

7 2 k175y

35y x

35 5y

Ex If it takes 4 workers 2 hours to complete a certain job how many minutes would it take 6 workers to complete the same job

480k

k

yx

120(4)k

80y1204

k

480y

x

480

6y

III AVERAGES

A) Average = Mean = Sumcount

Know the average then sum = average x count Ex After 5 tests Tony has an 85 average If Tony had an 83

average after his first three tests what was his average on the last two tests

5 5 85 425T 425 24987

2A

3 3 83 249T

B) Median = Middle

ARRANGE THEM IN ORDER FIRST

Odd of scores - Find middle Even of scores - Find average of middle 2 rsquos

C) Mode = Number that occurs the MOST

The End

• Week 1 BASIC MATH REVIEW
• I BASIC ARITHMETIC
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• II RATIONAL NUMBERS
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• III AVERAGES
• Slide 24
• The End

Ex If it takes 4 workers 2 hours to complete a certain job how many minutes would it take 6 workers to complete the same job

480k

k

yx

120(4)k

80y1204

k

480y

x

480

6y

III AVERAGES

A) Average = Mean = Sumcount

Know the average then sum = average x count Ex After 5 tests Tony has an 85 average If Tony had an 83

average after his first three tests what was his average on the last two tests

5 5 85 425T 425 24987

2A

3 3 83 249T

B) Median = Middle

ARRANGE THEM IN ORDER FIRST

Odd of scores - Find middle Even of scores - Find average of middle 2 rsquos

C) Mode = Number that occurs the MOST

The End

• Week 1 BASIC MATH REVIEW
• I BASIC ARITHMETIC
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• II RATIONAL NUMBERS
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• III AVERAGES
• Slide 24
• The End

III AVERAGES

A) Average = Mean = Sumcount

Know the average then sum = average x count Ex After 5 tests Tony has an 85 average If Tony had an 83

average after his first three tests what was his average on the last two tests

5 5 85 425T 425 24987

2A

3 3 83 249T

B) Median = Middle

ARRANGE THEM IN ORDER FIRST

Odd of scores - Find middle Even of scores - Find average of middle 2 rsquos

C) Mode = Number that occurs the MOST

The End

• Week 1 BASIC MATH REVIEW
• I BASIC ARITHMETIC
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• II RATIONAL NUMBERS
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• III AVERAGES
• Slide 24
• The End

B) Median = Middle

ARRANGE THEM IN ORDER FIRST

Odd of scores - Find middle Even of scores - Find average of middle 2 rsquos

C) Mode = Number that occurs the MOST

The End

• Week 1 BASIC MATH REVIEW
• I BASIC ARITHMETIC
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• II RATIONAL NUMBERS
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• III AVERAGES
• Slide 24
• The End

The End

• Week 1 BASIC MATH REVIEW
• I BASIC ARITHMETIC
• Slide 3
• Slide 4
• Slide 5
• Slide 6
• Slide 7
• Slide 8
• Slide 9
• Slide 10
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• II RATIONAL NUMBERS
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Slide 20
• Slide 21
• Slide 22
• III AVERAGES
• Slide 24
• The End