Use a calculator to compute the two quantities above. Use the caret button ^ or the y x

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1 Section.1A What is an Exponent? Squares and Cubes A square is... A cube is... Find the area of the square model shown in class. Find the volume of the cube model shown in class To find areas and volumes, we used repeated multiplication. Here s the notation: 4 = It is called a power of 4 - the power of 4 4 is called the. It is... is called the. It tells us... Formulas for Area of a Square and Volume of a Cube: A = V = Find (a) 6 (b) 10 (c) 6 4 Powers of negative numbers. What is the difference between ( ) 4 and 4? ( ) 4 = 4 = When taking powers of negative numbers, always... Use a calculator to compute the two quantities above. Use the caret button ^ or the y x button. Compute. and ( 6.) 4 Write out all of the powers of 10 up to What are the word names for 10, 10 6 and 10 9? 1

2 Section.1B and Supplement Scientific Notation Very large and very small numbers are often written using scientific notation. This consists of a number between 1 and 10, multiplied by a power of ten: e.g To write these numbers in standard notation, move the decimal point the number of places equal to the exponent on the power of 10. Fill in with zeros as necessary. Examples 1. Write these numbers in standard notation = = To Write a Very Large Number in Scientific Notation: 1. Move the decimal point so that there is exactly one non-zero digit to the left of the decimal point.. Multiply by a power of 10, so that the exponent is equal to the number of places that you moved the decimal point. Examples. Write in Scientific Notation: a.,00,000,000 b. 10,67,000 Using a Calculator: To enter the number,00,000,000 into a calculator, 1. Convert to scientific notation. Enter the numeric part,., press the EE or EXP key, then enter the exponent on the 10. You should see. EE 10 (or similar) Repeat the process for 10,67,000. Performing Operations on Numbers in Scientific Notation: Use a Calculator! Multiply the two numbers above, then divide,00,000,000 10,67,000. Very Small Numbers Numbers close to zero (i. e. between 1 and 1)written using scientific notation, have a negative exponent on the power of 10 6 e.g

3 To write these numbers in standard notation, move the decimal point to the left the number of places equal to the exponent on the power of 10. Fill in with zeros as necessary. Examples. Write these numbers in standard notation = = To Write a Very Small Number in Scientific Notation: 1. Move the decimal point so that there is exactly one non-zero digit to the left of the decimal point.. Multiply by a power of 10, so that the exponent is the opposite of the number of places that you moved the decimal point. The exponent will be negative Examples 4. Write in Scientific Notation: a b Using a Calculator: To enter the number into a calculator, 1. Convert to scientific notation (see above).. Enter the numeric part, 6.78, press the EE or EXP key, then enter the exponent on the 10. You should see 6.78 EE -4 (or similar) Repeat the process for Remember: Numbers between 1 and 1 are written with negative exponents on the powers of ten. Mixed calculations in Scientific Notation, using a Calculator. Express your answer in scientific notation. a. 8 (4. 10 )( ) b. 6 4 ( )( ) 7 10 ( )( )

4 MTH 60 Module Section. A. ORDER OF OPERATIONS AGAIN P E M A / D / S Example Notes Evaluate Evaluate ( )( ) Evaluate the expressions below for x = : (a) (x) (b) x (c) x 4 (d) ( x) 4 Evaluate the expression xy(x y) for x =, y = 4. 4

5 .B CIRCLES AND SPHERES Terminology: Circle, radius, r, diameter, D, circumference, C, Circumference, C, is the... Formula: C = or Examples: 1. Find the circumference of the circle with diameter 1 feet.. Find the circumference of a circle with radius.1 inches.. Use the tape measure to measure the circumference of the basketball, then calculate its diameter and radius. Area of a Circle Formula: A = 4. Find the area of a circular garden plot with diameter meters. Volume of a Sphere Volume, V =. Find the volume of a therapy ball of radius 0. meters.

6 Section.A Like Terms What are terms? Like terms have exactly the same variables. (...with the same exponents covered later.) Examples: Like terms: We can add and subtract them exactly like numbers Unlike Terms: Examples: 1. 4y + y 4. 8xy + 11xy. 7x 9x. w 4w + w. 8b + 8b x.x 7. b 11b ( b) + b 8. 7a ( 8a) 9. x 7 x ab + a ( 4ab) 8a x (.x) 1. 9(r) (800x) 14. 7(h) (6h 9h) 1. x ( x x) (x x) 6

7 Section. Like Terms.B Simplifying Expressions I. Adding & subtracting Combining Like Terms. Examples Thinking 1. 4x + 7 x Like terms:. x + x x x. 6pq pq p q 6pq 4. hk 4h + 4k hk II. Multiplying variable expressions. 1. x x Thinking. 4 ( y )( 4 y ). 4p q w p( p w ) 7

8 III. Solving Equations with Variables on Both Sides Solve the equations: 1. 6x 1 = x + 19 Thinking:. (y + 1) = 4(y + 1). (4 w) + 7w = 9w (w ) 8

9 Sec. 9.A The Distributive Property Simplify (i) (4 9) (ii) ( + )( 4) Another way to look at (i) and (ii): Kim and Amanda are selling raffle tickets for a quilt for $0.0 each. Amanda sold 1 tickets, and Kim sold 0 tickets. Show two ways to compute the total amount of money they brought in. The Distributive Property says: If a, b, and c are algebraic expressions, then... How would we simplify (4x 9) or ( + y)( 4)? (i) (4x 9) (ii) ( + y)( 4) Practice: 1. 4(x + ). (x 4). 8(z 6) 4. (x + 1). (w 7) 6. ( 8z ) (Be careful!) 7. (m + )7 8. (q + )( 4) 9. (y )() 10. (z 4)( ) 11. ( 4p + 6)( ) 1. ( m )( 7) Simplify and combine like terms: 1. 6(x + 1) + x 14. (t ) + t (t + ) 1. (1 y) y 16. 8(1 z) + z 4(z ) 17. 7w (6 + 4w) 18. ( 9)x 9x ( 9x) 9

10 Section 6.A Graphs of Equations #, page 41: Softek bought a new photocopying machine for $0,000. Every year, the Photocopier depreciates in value by $000. Its value, V after t years is given by V = 0 t, where V is measured in... Fill in the table of values: (Show the calculation!) t V Answer the questions: 1. What is the value of the copier after years? Locate this point on your graph.. When will the copier s value be $8000? Locate this point on your graph. #4, page 416 :While hiking, Beau drops a stone of the edge of a 400-foot cliff. After falling for t seconds, the height h of the stone above the base of the cliff is given by h = t. Fill in the table of values: (Show the calculation!) t h Plot the graph on the graph paper provided. Answer the questions: 1. What is the height of the stone seconds after being dropped? Locate this point on your graph.. How long will it take for the stone to hit the ground? Locate this point on your graph. 10

11 Section 6. B The Cartesian Coordinate System Number Lines: The Cartesian Coordinate System x-axis: positive, right negative, left y-axis: positive, up negative, down origin, quadrants, coordinates, ordered pair: (x-coordinate, y-coordinate). Plot and label the points (, 1), (, ), ( 4, ), (, 6) Now plot the points A ( 4, 0) and B (0, ). Point A lies... Point B lies... Note the error on page 49, (Ex. 6) If the x-coordinate is zero, then the point lies... If the y-coordinate is zero, then the point lies... Make a table and graph the x y = equation y = 4 x : 11

12 MTH 60 Section 6.4 Notes - Lines A linear equation looks like... Graph the equation y = x. Make a table: (You may choose any convenient values for x, but it s wise to choose some positive, some negative, and 0 for easy calculation!) x y Calculation x-intercept: y-intercept: For the graph of y = x, the x-intercept is and the y-intercept is Graphing an equation where the coefficient of x is a fraction. Graph the equation y x Choose values of x that are divisible by the denominator. x y Calculation Find the x-intercept and the y-intercept for the graph of y x. x-intercept: y-intercept: 1

13 Module Section 6. - Equations Again! Thinking like a mathematician: To evaluate , think... When we see two terms like this 4 x, think... To solve the equation 4 x = 19 set up the table Operations done to x Undo in the reverse order Check: Practice: 1. Name the operations that have been performed on x, in the correct order. x x (a) (b) How would you undo these operations?. Solve the equations: x (a) 9 11 (b) x 8 7 (c) Jean-Paul started a tab at the Common Grounds coffee house by paying the owner $0. One month later, Jean-Paul owed the owner $7.40. If a cup of coffee costs $0.8, how many cups did he drink? 1

14 Section 7. Equations with Fractions Fraction review: Multiply: 4 4 Thinking: Divide: When dividing two fractions... Multiply: Divide: 4 4 Solving Equations the Module Way Solve A. x = 0 Thinking: B. 0 x Undo in two steps: 1. C. 0 x. Undo in one step: Divide by... or D. w 4 Multiply by... The Disappearing Fraction Trick: What happened to the equation in example B after the first step in the solution? 14

15 Least Common Denominator: What is the least common denominator of,, 1 8 4? Describe the least common denominator in your own words. E. Solve the equation Thinking: y, the usual way: 8 Now solve the easy way!! y CLEAR FRACTIONS! 8 Find the LCD of all the fractions: Multiply both sides of the equation by the LCD. Use the distributive law. Note: we multiplied every term in the equation by the LCD! Result: Solve by undoing, as usual. F. Solve p 6 Clear fractions first! G. Solve 4 m H. Solve w