study tips 1- read chapter before class 2- do the end of the chapter exercises before class. 3- to...
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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