HOW TO USE YOUR TI-GRAPHING CALCULATOR 1. What does the blue 2ND button do? 2. What does the ALPHA button do? TURNING OFF YOUR CALCULATOR Hit the 2ND button and the ON button NEGATIVE NUMBERS Use (-) EX: -10 3. -239 + 1093 = 4. 120 (-4029) = 5. -294 (-5019) = CLEAR To clear the line you are typing hit the CLEAR button, hit CLEAR twice to clear the entire screen
EXPONENTS There are several ways to enter in exponents EX: 16 2 EX: 3 2
6. 3 16 = 7. 4 4 = 2 8. ( 8) = 2 9. 8 = SQUARE ROOTS Use the 2ND button and x 2 to get a square root EX: 4 10. 121 = 11. 93 =
INSERT/DELETE You can insert and delete if you miss type something. EX: INSERT Type 10938631. You want to insert a 4 in between the 0 and 9. Arrow to the left until the cursor is on the 9. Hit 2ND and DEL and insert the 4. Arrow to the right or left to get out of the insert option. This helps you so you don t waste time retyping expressions into your calculator. EX: DELETE Type 987654321. You want to delete the number 6. Arrow to the left until your cursor is on the 6. Hit the DEL button.
RETRIEVE PREVIOUSLY ENTRIES Keep hitting 2ND and ENTER for previous entries. Keep hitting 2ND and ENTER to see other previous entries. PARANTHESES ( ) EX: 2 (790 198) 1031 12. 2 ( 8 10) 4(12 18) = 13. (312) (4(16 19)) ( 3) = 14. 2 3 (32(23) 10 ) =
ABSOLUTE VALUE Hit 2ND and 0 for the catalog. Absolute value is the first one in the list. Hit ENTER. Input the value in the absolute value bars and hit ENTER. EX: 12 15. 192 = 16. 13 = 17. 29 18 =
USE PREVIOUS ANSWERS Your calculator automatically stores the last answer you entered. This can help you enter things quickly. EX: Type 12 87 and ENTER then multiplied by 3. ANS will appear automatically. ANS will store the previous entry s answer. EX: You can also access ANS by 2ND (-). You will see 297 should appear since it was the last answer.
FRACTIONS - Use ALPHA and Y= or you will need to put the fractions in ( ). EX: 4 23 3 108 OR Now, your answer here isn t in a fraction. You can turn the answer into a fraction. TURN DECIMALS TO FRACTIONS Hit MATH and then ENTER and ENTER.
18. 12 3 23 7 = 19. 12 3 = (Hint: You can use 2ND ENTER to make this faster) 23 7 20. 12 3 23 7 = 21. 12 3 23 7 = MODE This is your settings for different things. QUIT If want to get back to the home screen you can hit, 2ND MODE to quit. Or, you can hit CLEAR twice.
Sec. 1.1 Variables and Expressions Consider the following: the population of Florida the area of Colorado the flight time from Philadelphia to San Francisco Which of these has a value which varies? Algebra uses symbols to represent quantities that are unknown or that vary. VOCABULARY: quantity - variable - algebraic expression - numerical expression - Translating between Math and English Math Symbols What does it look like? Addition Subtraction Multiplication Division In English What words do I use?
What is the algebraic expression for the word phrase? EX 1: Three more than twice a number x EX 2: 9 less than the quotient of 6 and a number x EX 3: The produce of 4 and the sum of a number x and 7 What word phrase can you use the represent the algebraic expression? EX 4: 20 EX 5: 10 9 EX 6: EX 7: EX 8: 5 1 EX 9: 3 1)
Name Date Class SEC. 1.1 PRACTICE WORKSHEET Write an algebraic expression for each word phrase. 1. 10 less than x 2. 5 more than d 3. 7 minus f 4. the sum of 11 and k 5. x multiplied by 6 6. a number t divided by 3 7. one fourth of a number n 8. the product of 2.5 and a number t 9. the quotient of 15 and y 10. a number q tripled 11. 3 plus the product of 2 and h 12. 3 less than the quotient of 20 and x Write a word phrase for each algebraic expression. 13. n + 6 14. 5 c 15. 11.5 + y x 16. 17 17. 3x + 10 18. 10x + 7z 4
Name Date Class Write an algebraic expression for each word phrase. 21. 8 minus the quotient of 15 and y 22. a number q tripled plus z doubled 23. the product of 8 and z plus the product of 6.5 and y 24. the quotient of 5 plus d and 12 minus w 25. Error Analysis A student writes 5y 3 to model the relationship the sum of 5y and 3. Explain the error. 26. Error Analysis A student writes the difference between 15 and the product of 5 and y to describe the expression 5y 15. Explain the error.
Sec. 1.2 Order of Operations & Evaluating Expressions Why do we need a rule (order of operations) to perform calculations? EX: 321 1025 P PARENTHESES ( ) [ ] Operations in the group symbols EX: 343 5 Order of Operations Large fraction bars are included in grouping symbols EX: Start at the innermost grouping and work outwards EX: 28432 E EXPONENTS We can use powers to shorten a such as: 22222. 2 22222 powers exponents base
EX: 3 EX: 3 to the 4 th power Two thirds to the third power CALCULATOR: M/D MULTIPLY & DIVIDE LEFT TO RIGHT EX: 34 3 4 34 34 variables: A/S ADD & SUBTRACT LEFT TO RIGHT EX: 34 Order of Operations EX 1: EX 2: 57 4 2 EX 3: Evaluating Expressions What is the value of the expression for x = 5 and y = -2? EX 4: 12 EX 5:
Sec. 1.3 Square Roots and Perfect Squares PERFECT SQUARES the square of a number is called a EX: 4 4 squared or 4 to the 2 nd power Why do we call it a perfect square? SQUARE ROOTS a number a is a of a number b if EX: 16 the square root of 16 ROOT (side dimension) PERFECT SQUARE (number of squares) ROOT (side dimension) PERFECT SQUARE (number of squares) ON TI-CALCULATOR: 36 = 386 =
CLASSIFYING NUMBERS Natural Numbers - Whole Numbers - Integers - Rational Number - EX: Irrational Number - EX: Real Numbers EX: Classify the following numbers. GRAPHING AND ORDERING REAL NUMBERS
COMMUTATIVE PROPERTY Applies only to addition and multiplication 1.4 PROPERTIES OF REAL NUMBERS 7 + 4 = 4 + 7 5 * 2 = 2 * 5 ASSOCIATIVE PROPERTY: Applies only to addition and multiplication Examples: 1 + (2 + 3) = (1 + 2) + 3 2 * (4 * 6) = (2 * 4) * 6 DISTRIBUTIVE PROPERTY: Multiplication over addition or subtraction Examples: 3 (a + 4) = 5 (9 - b) = ADDITIVE IDENTIY: 0 + any number = that number Example: 6 + 0 = MULTIPLICATIVE IDENTITY: 1 * any number = that number Example: 4 * 1 =
ZERO PROPERTY 0 * any number = 0 Examples: 0 * 2 = 0 * -8 = ADDITIVE INVERSE: any number + additive inverse = 0 additive inverse of a number = opposite sign on that number 6 + = 0-9 + = 0 MULTIPLICATIVE INVERSE: any number * multiplicative inverse = 1 (multiplicative inverse = reciprocal) 6 * = 1-7 * = 1
Algebra Properties Worksheet Name: Date: Per: For #1-27, name the property illustrated by each statement. 1. x y y x + = + 2. 6( mn ) = ( 6 ) mn 3. k+ 0 = k 4. 3t+ 2r = 2r+ 3t 5. ( ) 6 u+ 2v = 6u+ 12v 6. 0 = 100 0 7. ( 2a 3b) 4c 2a ( 3b 4c) + + = + + 8. pq + n = qp + n 9. gx xg = 10. 15c+ 15d = 15( c+ d) 11. 0 + b= b 12. If x + y = 3, then 3 = x+ y 13. x = x 14. 41 = 4 15. 1 y = y 16. 6= 6 17. 0= 0 12 18. 5= 5+ 0 19. If 12 17 5, then 17 5 12 = = 20. 78 ( 3) = 75 ( ) 21. w ( ) + 4+ 6 = w+ 10 22. x + 2= x + 2
23. ( 6+ 9) x = 15x 24. ( 7 4)( 6) = 3( 6) 25. If 6+ 3= 9 and 9= 3( 3 ), then 6+ 3= 3( 3) 26. ( ) 8+ 5= 4+ 4 + 5 For #27-28, name the property used in each step. 27. ab( a + b) = ( ab) a + ( ab) b a( ab) ( ab) b ( aa) b a( bb) = + = i + i 2 2 = ab+ ab 28. ( ) ( ) 3c 5c 5( 2) ( 3c 5c) 5( 2) ( 3 5) c 5( 2) 3c+ 5 2+ c = 3c+ 5 2 + 5c = + + = + + = + + = 8c + 10 For #29-30, evaluate the expression and name the property used in each step. 2 29. ( ) 2+ 6 9 3 2 30. 513 ( 39 3) + 71
ADDITION (both are positive) Examples: 10+23 = 1.5 & 1.6 OPERATIONS WITH REAL NUMBERS 3+7 = 14+27 = 2+9 = ADDITION (1 positive, 1 negative) 1) Determine which number is greater - the answer will have that number's sign 2) Answer = largest smallest Examples: 3 + (-6) = (-2) + 9 = 9 + (-9) = ADDITION (both are negative) 1) Sign on answer is always negative 2) Add 2 numbers as if both are positive Examples: (-3) + (-10) = (-7) + (-4) =
SUBTRACTION (1 positive, 1 negative) 1) Turn subtraction sign into adding a negative number 2) Follow addition steps Examples: 3-9 = 1-4 = (-8) - 5 = (-6) - 10 = MULTIPLICATION If both signs are the same, answer will be positive. + * + = + - * - = + If signs are different, answer will be negative. + * - = - - * + = - Examples: 9 * 7 = 12 * 7 = (-9) * (-5) = (-9) * 8 = DIVISION WITH INTEGERS (SAME RULES AS MULT.) If both signs are the same, answer will be positive. + / + = + - / - = + If signs are different, answer will be negative. + / - = - - / + = - Examples: 28 / 7 = (-48) / (-4) = (-18) / 2 =
ADDING/SUBTRACTING FRACTIONS Scenario #1: Denominators are identical 1) Keep denominator the same 2) Add/subtract numerators 3) Cancel/reduce/simplify 1 3 2 3 Examples: 4 7 1 7 2 10 4 10 Scenario #2: Denominators are different First find the Least Common Multiple (LCM) (or sometimes called Least Common Denominator (LCD)) 1) Find the prime factors of the denominators 2) Find the greatest power of every prime 3) Multiply these together 1 3 3 7 Prime factors 3 = 7 = Greatest power of each prime factor Example: 3 24 1 18
MULTIPLYING FRACTIONS 1) Cancel/reduce/simplify: any numerator with any denominator ONLY 2) Multiply across: numerator * numerator and denominator * denominator 3 7 5 9 Example: 3 4 8 9 DIVIDING FRACTIONS 1) Change the division sign to multiplication 2) Turn the 2nd fraction into its reciprocal 3) Follow multiplication rules Reciprocal = flip fraction upside down Examples: 5 4 3 10 7 2 9 8 15 4 5
Sec. 1.7 The Distributive Property THE DISTRIBUTIVE PROPERTY Let a, b, and c be real numbers. Which expression can we use the Distributive Property? In an algebraic, there is a term - 6 35312 constant - 6 35312 coefficient - What are the like terms? 6 35312 6 35312 EX 1: 3 8 EX 2: EX 3: 3 EX 4: 232