Study Tips 1- Read chapter BEFORE class 2- Do the end of the chapter exercises BEFORE class. 3- To understand a concept: (a) Read the book very carefully, (a) Come to class to hear the professor’s explanation, (3) Talk to the TA, (4) Check on the internet (only the good sources!) 1- Read chapter BEFORE class 2- Do the end of the chapter exercises BEFORE class. 3- To understand a concept: (a) Read the book very carefully, (a) Come to class to hear the professor’s explanation, (3) Talk to the TA, (4) Check on the internet (only the good sources!)

Study Tips 1- As soon as you have a question, please send an to your TA asap! 2- If you can’t solve a problem, take a picture of what you did and send it to the TA. 3- Before coming to the office hour (Tuesdays 1:00 to 2:00 pm at BSB 402), please your TA to let her know that you will be attending (as hours will be extended when needed). Also, please e- mail your questions in advance (to allow for better preparation). 1- As soon as you have a question, please send an to your TA asap! 2- If you can’t solve a problem, take a picture of what you did and send it to the TA. 3- Before coming to the office hour (Tuesdays 1:00 to 2:00 pm at BSB 402), please your TA to let her know that you will be attending (as hours will be extended when needed). Also, please e- mail your questions in advance (to allow for better preparation).

What should you bring to every class 1- Calculator (not your phone) 2- The textbook 3- Paper and pen/pencil 4- A separate sheet with all the formulas you have learned so far (including the ones you will need for that day’s lecture!) 5- If you have an electronic copy of the book, consider making a copy of the tables (as it will make things much easier!) 1- Calculator (not your phone) 2- The textbook 3- Paper and pen/pencil 4- A separate sheet with all the formulas you have learned so far (including the ones you will need for that day’s lecture!) 5- If you have an electronic copy of the book, consider making a copy of the tables (as it will make things much easier!)

Symbols and Notations a- (5+3) X 2= b- 5 + (3x2)= c- (3+1) 2 – 4 x 7/2= d- 12/2 x 3= e- 6 x (3+8) 2 – 50= f- (3+8) – 5= or 3 + (8-5)= g- 2 x 3 2 = h- (2x3) 2 = 1- Parentheses 2- Squaring/Exponents 3- Multiplication/Division (left to right) 4- Addition/ Subtraction

Symbols and Notations a- (5+3) X 2= 16 b- 5 + (3x2)= 11 c- (3+1) 2 – 4 x 7/2= 2 d- 12/2 x 3= 18 e- 6 x (3+8) 2 – 50= 676 f- (3+8) – 5= or 3 + (8-5)= 6 g- 2 x 3 2 = 18 h- (2x3) 2 = Parentheses 2- Squaring/Exponents 3- Multiplication/Division (left to right) 4- Addition/ Subtraction

Proportions: fractions, decimals and percentages FractionDecimalPercentage ¾0.7575% ¼ ½ 1/10 FractionDecimalPercentage ¾0.7575% ¼ ½ 1/10 1- Fraction to decimal= Divide 2- Decimal to percentage = Multiply by 100

Proportions: fractions, decimals and percentages FractionDecimalPercentage ¾0.7575% ¼0.2525% ½0.5050% 1/ % FractionDecimalPercentage ¾0.7575% ¼0.2525% ½0.5050% 1/ % 1- Fraction to decimal= Divide 2- Decimal to percentage = Multiply by 100

Finding equivalent fractions

Multiplying Fractions

Dividing Fractions Invert second fraction and multiply: 1 ÷ 1 = 1 x 4 = 4 = 2 = Invert second fraction and multiply: 1 ÷ 1 = 1 x 4 = 4 = 2 =

Dividing and Multiplying Fractions 9 ÷ 2 = x 7 = ÷ 2 = x 7 = 6 10

Dividing and Multiplying Fractions 9 ÷ 2 = 9 x 3 = x 7 = ÷ 2 = 9 x 3 = x 7 =

Adding and Subtracting Fractions Same denominator: = Different denominator: = 2 x 10 1 x 3 = = x x = 1 x 1 1 x 2 = = x 1 2 x /22 + 2/3 = 7/8 – ½ = 1/8 + 2/3 = Same denominator: = Different denominator: = 2 x 10 1 x 3 = = x x = 1 x 1 1 x 2 = = x 1 2 x /22 + 2/3 = 7/8 – ½ = 1/8 + 2/3 =

Adding and Subtracting Fractions Same denominator: = Different denominator: = 2 x 10 1 x 3 = = x x = 1 x 1 1 x 2 = = x 1 2 x /22 + 2/3 = 65/66 7/8 – ½ = 3/8 1/8 + 2/3 = 19/24 Same denominator: = Different denominator: = 2 x 10 1 x 3 = = x x = 1 x 1 1 x 2 = = x 1 2 x /22 + 2/3 = 65/66 7/8 – ½ = 3/8 1/8 + 2/3 = 19/24

Comparing the size of fractions

Converting Decimals to Fractions 0.1 = = = = = = = = = = 100

Converting Decimals to Fractions 0.1 = = = , = = , = = = , = = ,000

Converting Percentages Percentage to fraction (use 100 as nominator) 52% = 52 5% = 100 Percentage to decimal (divide by 100 or move decimal point two places to left) 83% = % = 5% = Percentage to fraction (use 100 as nominator) 52% = 52 5% = 100 Percentage to decimal (divide by 100 or move decimal point two places to left) 83% = % = 5% =

Converting Percentages Percentage to fraction (use 100 as nominator) 52% = 52 5% = Percentage to decimal (divide by 100 or move decimal point two places to left) 83% = % = % = 0.05 Percentage to fraction (use 100 as nominator) 52% = 52 5% = Percentage to decimal (divide by 100 or move decimal point two places to left) 83% = % = % = 0.05

Negative Numbers How good were you at math before and after the review with the TA? Participant Before After Change How good were you at math before and after the review with the TA? Participant Before After Change

Negative Numbers How good were you at math before and after the review with the TA? Participant Before After Change How good were you at math before and after the review with the TA? Participant Before After Change

Negative Numbers Adding negative numbers 3 + (-2) + 5 = (-4) (-6) + (-2) Positive sum = 6 Negative sum = 13 Subtract negative from positive (i.e. positive first) 6-13 = (-8) (-1) + (-3) = 5 – (-9) + 2 – (-3) – (-1) = 3 – 7 – (-21) + (-5) – (-9) = Adding negative numbers 3 + (-2) + 5 = (-4) (-6) + (-2) Positive sum = 6 Negative sum = 13 Subtract negative from positive (i.e. positive first) 6-13 = (-8) (-1) + (-3) = 5 – (-9) + 2 – (-3) – (-1) = 3 – 7 – (-21) + (-5) – (-9) =

Negative Numbers Adding negative numbers 3 + (-2) + 5 = (-4) (-6) + (-2) Positive sum = 6 Negative sum = 13 Subtract negative from positive (i.e. positive first) 6-13 = (-8) (-1) + (-3) = 3 5 – (-9) + 2 – (-3) – (-1) = 20 3 – 7 – (-21) + (-5) – (-9) = 21 Adding negative numbers 3 + (-2) + 5 = (-4) (-6) + (-2) Positive sum = 6 Negative sum = 13 Subtract negative from positive (i.e. positive first) 6-13 = (-8) (-1) + (-3) = 3 5 – (-9) + 2 – (-3) – (-1) = 20 3 – 7 – (-21) + (-5) – (-9) = 21

Negative Numbers Subtracting negative numbers 4 – (-3) = Multiplying negative numbers 3 x (-2) = -4 x (-2) = Dividing negative numbers -6 ÷ 3 = 8 ÷ (-4) = -8 ÷ (-4) = Subtracting negative numbers 4 – (-3) = Multiplying negative numbers 3 x (-2) = -4 x (-2) = Dividing negative numbers -6 ÷ 3 = 8 ÷ (-4) = -8 ÷ (-4) =

Negative Numbers Subtracting negative numbers 4 – (-3) = = 7 Multiplying negative numbers 3 x (-2) = -6 >>> -2 + (-2) + (-2) -4 x (-2) = +8 >>> - (-2) - (-2) – (-2) – (-2) Dividing negative numbers -6 ÷ 3 = -2 8 ÷ (-4) = ÷ (-4) = 2 Subtracting negative numbers 4 – (-3) = = 7 Multiplying negative numbers 3 x (-2) = -6 >>> -2 + (-2) + (-2) -4 x (-2) = +8 >>> - (-2) - (-2) – (-2) – (-2) Dividing negative numbers -6 ÷ 3 = -2 8 ÷ (-4) = ÷ (-4) = 2

Basic Algebra: Solving Equations Equation: Math statement indicating two quantities are identical 12 = It may have an unknown value 12 = 8 + X To solve equation: 1- Isolate unknown value 2- Keep both sides of equation balanced Equation: Math statement indicating two quantities are identical 12 = It may have an unknown value 12 = 8 + X To solve equation: 1- Isolate unknown value 2- Keep both sides of equation balanced

Basic Algebra: Solving Equations Value added to X: X + 3 = 7 X + 3 – 3 = 7 – 3 X= 4 Value added to X: X + 3 = 7 X + 3 – 3 = 7 – 3 X= 4 Value Sub. From X: X – 8 = 12 X – = X = 20 Value Sub. From X: X – 8 = 12 X – = X = 20 Value multiplied: 4 X = 24 4 X/4 = 24/4 X = 6 Value multiplied: 4 X = 24 4 X/4 = 24/4 X = 6 Value divided: X/3 = 9 3 (X/3) = 9 x 3 X = 27 Value divided: X/3 = 9 3 (X/3) = 9 x 3 X = 27

Basic Algebra: Solving Equations A- 3X = 18 B- X – 4 = 18 C- X = 5 9 D- X = -5 5 A- 3X = 18 B- X – 4 = 18 C- X = 5 9 D- X = -5 5

Basic Algebra: Solving Equations A- 3X = 18 X = 6 B- X – 4 = 18 X = 22 C- X = 5 X = 45 9 D- X = -5 X = A- 3X = 18 X = 6 B- X – 4 = 18 X = 22 C- X = 5 X = 45 9 D- X = -5 X = -25 5

More Equations 3X + 7 = 22 3X + 7 – 7 = 22 – 7 3X = 15 3X/3 = 15/3 X = 5 3X + 7 = 22 3X + 7 – 7 = 22 – 7 3X = 15 3X/3 = 15/3 X = 5 X + 3 = (X+3/4) = 2 x 4 X + 3 = 8 X + 3 – 3 = 8 – 3 X = 5 X + 3 = (X+3/4) = 2 x 4 X + 3 = 8 X + 3 – 3 = 8 – 3 X = 5 2X = 12 3 X + 1 = 3 3 2X = 12 3 X + 1 = 3 3

More Equations 3X + 7 = 22 3X + 7 – 7 = 22 – 7 3X = 15 3X/3 = 15/3 X = 5 3X + 7 = 22 3X + 7 – 7 = 22 – 7 3X = 15 3X/3 = 15/3 X = 5 X + 3 = (X+3/4) = 2 x 4 X + 3 = 8 X + 3 – 3 = 8 – 3 X = 5 X + 3 = (X+3/4) = 2 x 4 X + 3 = 8 X + 3 – 3 = 8 – 3 X = 5 2X = 12 X = 18 3 X + 1 = 3 X = 6 3 2X = 12 X = 18 3 X + 1 = 3 X = 6 3

Exponents 5 3 =125 (5x5x5) (“3 cubed”) 4 2 = (“4 squared”) 2 4 = (“2 raised to the fourth power”) 6 1 = 9 0 = XY 2 = X 2 Y 2 = 5 3 =125 (5x5x5) (“3 cubed”) 4 2 = (“4 squared”) 2 4 = (“2 raised to the fourth power”) 6 1 = 9 0 = XY 2 = X 2 Y 2 =

Exponents 5 3 =125 (5x5x5) (“3 cubed”) 4 2 = 16 (“4 squared”) 2 4 = 16 (“2 raised to the fourth power”) 6 1 = = 1 XY 2 = XYY X 2 Y 2 = XXYY 5 3 =125 (5x5x5) (“3 cubed”) 4 2 = 16 (“4 squared”) 2 4 = 16 (“2 raised to the fourth power”) 6 1 = = 1 XY 2 = XYY X 2 Y 2 = XXYY

Exponents (-3) 2 = (-6) 3 = (3 + 5) 2 = Careful! Not the same!! = 3 2 = 4 2 Same result (3/4) 2 = (-3) 2 = (-6) 3 = (3 + 5) 2 = Careful! Not the same!! = 3 2 = 4 2 Same result (3/4) 2 =

Exponents -3 2 = 9 (-3) (-3) ///// (-6) 3 = -216 (-6)(-6)(-6) (3 + 5) 2 = 64 Careful! Not the same!! = = 9/ Same result (3/4) 2 = (3/4) x (3/4) = 9/ = 9 (-3) (-3) ///// (-6) 3 = -216 (-6)(-6)(-6) (3 + 5) 2 = 64 Careful! Not the same!! = = 9/ Same result (3/4) 2 = (3/4) x (3/4) = 9/16

Square Roots What value multiplied by itself gives you the value underneath the radical? √4 = 2 √16 = √3 2 = (√64) 2 = √ = Careful! Not the same!! √9 + √16 = What value multiplied by itself gives you the value underneath the radical? √4 = 2 √16 = √3 2 = (√64) 2 = √ = Careful! Not the same!! √9 + √16 =

Square Roots What value multiplied by itself gives you the value underneath the radical? √4 = 2 √16 = 4 √3 2 = √9 = 3 (√64) 2 = 8 2 = 64 √ = 5 Careful! Not the same!! √9 + √16 = 7 What value multiplied by itself gives you the value underneath the radical? √4 = 2 √16 = 4 √3 2 = √9 = 3 (√64) 2 = 8 2 = 64 √ = 5 Careful! Not the same!! √9 + √16 = 7

Square Roots √16 = √4 Same result √16/4 = √9 x √16 = Same result √9 x 16 = √16 = √4 Same result √16/4 = √9 x √16 = Same result √9 x 16 =

Square Roots √16 = 4 = 2 √4 2 Same result √16/4 = √4 = 2 √9 x √16 = 3 x 4 = 12 Same result √9 x 16 = √144 = 12 √16 = 4 = 2 √4 2 Same result √16/4 = √4 = 2 √9 x √16 = 3 x 4 = 12 Same result √9 x 16 = √144 = 12