Redlands High School

Transcription

1 Redlands High School Dear Math I Honors Students, Familiarity with pre high school math topics is essential for success in Integrated Math I Honors class. The majority of the questions in Math I require a working knowledge of Pre Algebra and Algebra topics as well as an understanding of basic mathematical operations including decimals and fractions. Print this packet and read through the following review, making notes on topics that you do not understand. Memorize and have a working knowledge of all definitions and formulas that are given if you don t already know them. Understanding basic mathematics and linear algebra concepts are VERY important to your success in this class; make sure you understand these topics. Your job: Read the review and make notes as needed. Work out the problems on lined paper. Make sure your work is legible. Leave at least one space between problems. Turn in all work to your teacher on the 1 st day of school. It is vital that you complete this packet before the beginning of the school year if you are going to be able to keep up with the pace and rigor of the Integrated Math I Honors curriculum. This is not meant to be busy work. You absolutely need these skills to be successful. See you then, Mrs. Casey and Mr. Comadena Redlands High School Math I Honors teachers Mathematics Department

2 VOCABULARY: Match the given words to the correct definition. Write the answers on this page. absolute value equation area prime number sum base exponent integers counter example variable composite numbers expression perimeter quotient difference factors ordered pair rational number function median irrational number opposites inverse operations coefficient mean mode domain range product conjecture congruent volume 1. a mathematical sentence that contains an equal sign 2. made up of quantities and the operations performed on them 3. symbol that is used to represent a number 4. used to locate points (x,y) in the coordinate plane 5. the amount of square units required to fill a two dimensional space 6. found by taking the sum of all the values and dividing by the number of values 7. the solution to an addition problem 8. the solution to a subtraction problem 9. the solution to a multiplication problem 10. the solution to a division problem 11. whole numbers and their opposites ( 3, 2, 1, 0, 1, 2, 3 ) symbol is Z 12. the number that appears most often in a set of numbers 13. the distance around the outside of an object 14. a number that can be expressed in the form a/b, in which a and b are integers and b 0 (Symbol is Q) 15. a number s distance away from the middle number in a set of numbers when the numbers are arranged from least to greatest 17. the quantities that are multiplied in a multiplication expression 18. a whole number greater than one, with exactly two factors, 1 and itself 19. a whole number greater than 1 that has more than 2 factors 20. x in an expression of the form xⁿ 21. two numbers that are the same number from zero on the number line, but on opposite sides 22. two operations that undo each other, such as addition and subtraction 23. if a term of an expression consists of a number multiplied by one or more variables, the number is called 24. the n in an expression of the form xⁿ 25. the collection of all input values of a function 26. a rule that establishes a relationship between two quantities, the input and output 27. the collection of all output values of a function 28. any number that cannot be written in the form a/b, such as π 29. an example that shows a conjecture false 30. an unproven statement based on observations 31. the amount of cubic units required to fill a 3 dimensional space 32. the same, used for geometric figures

3 GEOMETRY FORMULAS Reminders: pi ( ) 3.14 units MUST be written Practice: (assume all units are cm) 5 cm 1) 2) 3) 2 cm Area Perimeter 1) rectangle A = LW = P = 2L + 2W = 2) triangle A = ½ bh = P = add sides = 3) circle A = r 2 = Circumference = 2 r or d = Find the volume of the given shape: (assume all units are cm) Volume (units 3 ) 1) Rectangular Prism V = lwh Cube = lwh = s 3 2) Cylinder V = πr 2 h= PYTHAGOREAN THEOREM a 2 + b 2 = c 2 (RIGHT TRIANGLES ONLY!) 5 cm Find the length of the hypotenuse 12 cm

4 PLACE VALUE REVIEW You MUST know place value. If you have trouble with this, go to the web site to practice Be familiar with the Symbols and words that describe the sets of Real Numbers

5 IDENTITY AND EQUALITY PROPERTIES (used to simplify expressions) For any numbers a, b, c Additive Identity Property Multiplicative Identity Property a + 0 = 0 + a = a a 1 = 1 a = a Multiplicative Property of Zero a 0 = 0 a = 0 Substitution Property Reflexive Property Symmetric Property Transitive Property Distributive Property Commutative Property Associative property If a = b, then a may be replaced by b a = a If a = b, then b = a If a = b and b = c, then a = c a(b+c) = ab + ac and a(b-c) = ab - ac a + b = b + a and a b = b a (a+b)+c = a+(b+c) and (ab)c = a(bc) PRACTICE: Name the property illustrated by each statement 1) = 21 2) 0 (15) = 0 3) x 3 1 = x 3 4) = ) 6x + 2y = 2y + 6x 6) (14 6) + 3 = ) If x + y = 9 then 9 = x + y 8) 9(r 2 + s 2 ) = 9r 2 + 9s 2 9) If = 6 and 6 = 3 2, then = ) (2c + 6) + 10 = 2c + (6 + 10)

6

7

8 Simplify. 9.

9

10 9. Graph the following lines: a. y = 2x + 1 b. y = -2x - 1 c. y = -x + 3 d. y = 2/3x 4

11

12 *linear combinations is the same as elimination. *

13 Problem-Based Task #1 Rafting and Hiking Trip: To celebrate graduation, you and 4 of your closest friends have decided to take a 5-day white-water rafting and hiking trip. During your 5-day trip, 2 days are spent rafting. If the rafting trip covers a distance of 60 miles and you are expected to raft 8 hours each day, how many miles must you raft each hour? For the hiking portion of your trip, you and your friends carry the same amount of equipment, which works out to 35 pounds of equipment each. For extra money, you can hire an assistant, who will carry 50 pounds of equipment. Each assistant charges a flat fee of $50 and an additional $22 for each mile. The total amount you would have to pay the assistant is $512. How many miles will your group be hiking? Is it worth hiring two assistants to help you and your friends carry the equipment? Justify your answers. Here are some questions to help you get started: 1. If the rafting trip covers a distance of 60 miles and you are expected to raft 8 hours each day, how many miles must you raft each hour? 2. What is the ratio of miles to days? 3. What is the ratio you are looking for? 4. What is the ratio of days to hours? 5. How do you convert the original ratio of miles to days into miles per hour? 6. How many miles will your group be hiking? 7. What is the equation of the cost of hiring an assistant? 8. What is the solution to this equation? 9. Is it worth hiring two assistants to help you and your friends carry the equipment? 10. How much weight will each of you carry without assistants? 11. How much weight will each of you carry with two assistants? 12. What is the difference in the cost per day? 13. Are you willing to pay more money to have someone carry your equipment? Why?