Study Tips

1- Read chapter BEFORE class2- 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 e-mail 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 e-mail 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 textbook3- Paper and pen/pencil4- 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 Notationsa- (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 32= h- (2x3)2=

1- Parentheses2- Squaring/Exponents3- Multiplication/Division (left to right)4- Addition/ Subtraction

Symbols and Notationsa- (5+3) X 2= 16b- 5 + (3x2)= 11c- (3+1)2 – 4 x 7/2= 2d- 12/2 x 3= 18e- 6 x (3+8)2 – 50= 676f- (3+8) – 5= or 3 + (8-5)= 6g- 2 x 32= 18h- (2x3)2= 36

1- Parentheses2- Squaring/Exponents3- Multiplication/Division (left to right)4- Addition/ Subtraction

Proportions: fractions, decimals and percentages

Fraction DecimalPercentage¾ 0.75

75%¼½1/10

1- Fraction to decimal= Divide2- Decimal to percentage = Multiply by 100

Proportions: fractions, decimals and percentages

Fraction DecimalPercentage¾ 0.75

75%¼ 0.25

25%½ 0.50

50%1/10 0.1010%

1- Fraction to decimal= Divide2- 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 = 22 4 2 1 2 1

Dividing and Multiplying Fractions

9 ÷ 2 = 10 3 1 x 7 = 6 10

Dividing and Multiplying Fractions

9 ÷ 2 = 9 x 3 = 2710 3 10 2 201 x 7 = 76 10 60

Adding and Subtracting Fractions

Same denominator:2 + 1 = 35 5 5Different denominator:2 + 1 = 2 x 10 1 x 3 = 20 + 3 = 236 10 3 x 10 10 x 3 30 30 301 + 1 = 1 x 1 1 x 2 = 1 + 2 = 34 2 4 x 1 2 x 2 4 4 4

7/22 + 2/3 =7/8 – ½ =1/8 + 2/3 =

Adding and Subtracting Fractions

Same denominator:2 + 1 = 35 5 5Different denominator:2 + 1 = 2 x 10 1 x 3 = 20 + 3 = 236 10 3 x 10 10 x 3 30 30 301 + 1 = 1 x 1 1 x 2 = 1 + 2 = 34 2 4 x 1 2 x 2 4 4 4

7/22 + 2/3 = 65/667/8 – ½ = 3/81/8 + 2/3 = 19/24

Comparing the size of fractions

Converting Decimals to Fractions

0.1 = 1 0.32 = 32 0.5234 = 10 100

0.05 = 5 0.001 = 100

Converting Decimals to Fractions

0.1 = 1 0.32 = 32 0.5234 = 5234 10 100 10,000

0.05 = 5 0.001 = 1 100 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% = 0.8314.5% = 5% =

Converting Percentages

Percentage to fraction (use 100 as nominator)

52% = 52 5% = 5 100 100

Percentage to decimal (divide by 100 or move decimal point two places to left)

83% = 0.8314.5% = 0.1455% = 0.05

Negative Numbers

How good were you at math before and after the review with the TA?

Participant Before After Change001 6 7

+1002 7 6

003 2 4

004 9 6

Negative Numbers

How good were you at math before and after the review with the TA?

Participant Before After Change001 6 7

+1002 7 6

-1003 2 4

+2004 9 6

-3

Negative Numbers

Adding negative numbers3 + (-2) + 5 = 6-1 + 3 + (-4) + 3 + (-6) + (-2)Positive sum = 6 Negative sum = 13Subtract negative from positive (i.e. positive first)6-13 = -73 + (-8) + 5 + 7 + (-1) + (-3) = 5 – (-9) + 2 – (-3) – (-1) = 3 – 7 – (-21) + (-5) – (-9) =

Negative Numbers

Adding negative numbers3 + (-2) + 5 = 6-1 + 3 + (-4) + 3 + (-6) + (-2)Positive sum = 6 Negative sum = 13Subtract negative from positive (i.e. positive first)6-13 = -73 + (-8) + 5 + 7 + (-1) + (-3) = 35 – (-9) + 2 – (-3) – (-1) = 203 – 7 – (-21) + (-5) – (-9) = 21

Negative Numbers

Subtracting negative numbers4 – (-3) = Multiplying negative numbers3 x (-2) =-4 x (-2) = Dividing negative numbers-6 ÷ 3 = 8 ÷ (-4) = -8 ÷ (-4) =

Negative Numbers

Subtracting negative numbers4 – (-3) = 4 + 3 = 7Multiplying negative numbers3 x (-2) = -6 >>> -2 + (-2) + (-2) -4 x (-2) = +8 >>> - (-2) - (-2) – (-2) – (-2) Dividing negative numbers-6 ÷ 3 = -28 ÷ (-4) = -2-8 ÷ (-4) = 2

Basic Algebra: Solving Equations

Equation: Math statement indicating two quantities are identical12 = 8 + 4It may have an unknown value12 = 8 + X

To solve equation:1- Isolate unknown value2- Keep both sides of equation balanced

Basic Algebra: Solving Equations

Value added to X:X + 3 = 7X + 3 – 3 = 7 – 3 X= 4

Value Sub. From X:X – 8 = 12X – 8 + 8 = 12 + 8X = 20

Value multiplied:4 X = 244 X/4 = 24/4X = 6

Value divided:X/3 = 93 (X/3) = 9 x 3X = 27

Basic Algebra: Solving Equations

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 = -25 5

More Equations

3X + 7 = 223X + 7 – 7 = 22 – 73X = 153X/3 = 15/3X = 5

X + 3 = 2 44 (X+3/4) = 2 x 4X + 3 = 8X + 3 – 3 = 8 – 3X = 5

2X = 12 3X + 1 = 3 3

More Equations

3X + 7 = 223X + 7 – 7 = 22 – 73X = 153X/3 = 15/3X = 5

X + 3 = 2 44 (X+3/4) = 2 x 4X + 3 = 8X + 3 – 3 = 8 – 3X = 5

2X = 12 X = 18 3X + 1 = 3 X = 63

Exponents

53 =125 (5x5x5) (“3 cubed”)42 = (“4 squared”)24 = (“2 raised to the fourth power”)61= 90 = XY2 = X2Y2 =

Exponents

53 =125 (5x5x5) (“3 cubed”)42 = 16 (“4 squared”)24 = 16 (“2 raised to the fourth power”)61= 690 = 1XY2 = XYYX2Y2 = XXYY

Exponents

(-3)2 = (-6)3 =

(3 + 5) 2 = Careful! Not the same!! 32 + 52 =

32 = 42 Same result(3/4)2 =

Exponents

-32 = 9 (-3) (-3) ///// (-6)3 = -216 (-6)(-6)(-6)

(3 + 5) 2 = 64 Careful! Not the same!! 32 + 52 = 34

32 = 9/16 42 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 = √32 = (√64)2 = √9 + 16 = Careful! Not the same!!√9 + √16 =

Square Roots

What value multiplied by itself gives you the value underneath the radical?√4 = 2√16 = 4√32 = √9 = 3(√64)2 = 82 = 64√9 + 16 = 5 Careful! Not the same!!√9 + √16 = 7

Square Roots

√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