Chapter 1 Review

1. Chapter 1 Review

2. What is the area of a rectangle? Length times Width If the length is 3 meters and the width is 2 meters, what is the area? A = L x WA = 3 x 2 = 6 meters2 A, L and W are the variables. It is any letter that represents an unknown number.

3. An algebraic expressioncontains: 1) one or more numbers or variables, and 2) one or more arithmetic operations. Examples: x - 3 3 • 2n

4. In expressions, there are many different ways to write multiplication. • 1) ab • 2) a • b • 3) a(b) or (a)b • 4) (a)(b) • 5) a x b We are not going to use the multiplication symbol any more. Why?

5. Division, on the other hand, is written as: 1) 2) x ÷ 3

6. Throughout this year, you will hear many words that mean addition, subtraction, multiplication, and division. Complete the table with as many as you know.

7. Here are some phrases you may have listed. The terms with * are ones that are often used.

8. Write an algebraic expression for1) m increased by 5. m + 5 2) 7 times the product of x and t. 7xt or 7(x)(t) or 7 • x • t

9. 3) 11 less than 4 times a number. 4n - 11 4) two more than 6 times a number. 6n + 2 5) the quotient of a number and 12.

10. Answer Now Which of the following expressions represents 7 times a number decreased by 13? • 7x + 13 • 7x - 13 • 13 - 7x • 13 + 7x

11. Answer Now Which one of the following expressions represents 28 less than three times a number? • 28 - 3x • 3x - 28 • 28 + 3x • 3x + 28

12. 2) Write a verbal expression for: 1) 8 + a. The sum of 8 and a The ratio of m to r Do you have a different way of writing these?

13. Answer Now Which of the following verbal expressions represents 2x + 9? • 9 increased by twice a number • a number increased by nine • twice a number decreased by 9 • 9 less than twice a number

14. Answer Now Which of the following expressions represents the sum of 16 and five times a number? • 5x - 16 • 16x + 5 • 16 + 5x • 16 - 5x

15. When looking at the expression 103, 10 is called the base and 3 is called the exponentor power. 103 means 10 • 10 • 10 103 = 1000

16. How is it said?21 Two to the first power 22 Two to the second power or two squared 23 Two to the third power or two cubed 2n7 Two times n to the seventh power

17. Answer Now Which of the following verbal expressions represents x2 + 2x? • the sum of a number squared and twice a number • the sum of a number and twice the number • twice a number less than the number squared • the sum of a number and twice the number squared

18. Answer Now Which of the following expressions represents four less than the cube of a number? • 4 – x3 • 4 – 3x • 3x – 4 • x3 – 4

19. Evaluate.21 2 22 2 • 2 = 4 23 2 • 2 • 2 = 8 2n7 We can’t evaluate because we don’t know what n equals to!!

20. Is 35 the same as 53?Evaluate each and find out! 35 = 3 • 3 • 3 • 3 • 3 = 243 53 = 5 • 5 • 5 = 125 243 ≠ 125 They are not the same!

21. Evaluate the variable expression when y=3 and x=5

22. Write the expression in exponential form. Nine cubed Six to the nth power

23. Insert grouping symbols into this equation so the expression is 50

24. Solve this word problem and also write the expression you would use to solve it. • If you can travel only 35 miles per hour, is 3 hours enough time to get to a concert that is 100 miles away??

25. Write the phrases as variable expressions or equations. • 7 time a number n • x is at least 90 • quotient of m and 2 • y decreased by 3 • 8 minus s is 4 • 9 is less than t

26. Decide whether the statement is true or false FALSE FALSE TRUE FALSE TRUE When x = 2 When x = 3 When y = 3

27. Mnemonic • Please • Parenthesis • Excuse • Exponents • My Dear • Multiply or Divide – Left to Right • Aunt Sally • Add or Subtract – Left to Right

28. Parenthesis Multiplication Exponents Addition Subtraction Example 1: 2 3 - (4-2) + 32

29. 2 3 - (4-2) + 32 Parenthesis 2 3 - 2 + 32 Exponents 2 3 - 2 + 9 Multiply 6 - 2 + 9 Add or Subtract – Left to Right 4 + 9 13

30. Parenthesis Multiplication Exponents Addition Subtraction Example 2: 4 6 – (3 + 4) + 22

31. 4 6 – (3 + 4) + 22 Parenthesis 4 6 - 7 + 22 Exponents 4 6 – 7 + 4 Multiply 24 – 7 + 4 Add or Subtract – Left to Right 17 + 4 21

32. 3+23- (9+1) PEMDAS 3+23- 10 3+8-10 11-10 1

33. 3 (9+1) + 62 PEMDAS 3(10)+62 3(10)+36 30+36 66

34. 4+5 (6-2) PEMDAS 4+5 4 4+20 24

35. 4+ 10 23 -16 PEMDAS 4+10 8 -16 4+ 80 -16 84-16 68

36. 21 + 102 10 PEMDAS 21+10010 21 + 10 31

37. 10+72-2 5 PEMDAS 10+49–2 5 10+49- 10 59 - 10 49

38. PEMDAS 64  (9 3-19) 64(27 –19) 64 8 8

39. Solve this word problem and also write the expression you would use to solve it. • The senior class is planning a trip that will cost $35 per student. If $3,920 has been collected, how many seniors have paid for the trip??? s = # of students s = 112 So 112 students have already paid

40. To find the perimeter of a rectangle: 18 Add up all the sides: P= length + width + length + width P= 18 + 15 + 18 + 15 P= 66 15

41. To find the perimeter of a rectangle: 5a Add up all the sides: P= length + width + length + width P= 5a + 3a + 5a + 3a P= 16a 3a JUST ADD UP THE COEFFICENTS

42. VOLUME VOLUMEis the amount of liquid or solid that will FILLa3-Dimensional object! *Always measured in units cubed (u3)

43. QUICK DEFINITION • 3-Dimensionalobjects are NOT FLAT. • They have 3 measurements: • Length • Width • Height

44. FIND THE VOLUME OF THIS RECTANGULAR PRISM: 3 mm 2 mm 12 mm

45. FIND THE VOLUME OF THIS RECTANGULAR PRISM: 4 in 10 in 3 in

46. FIND THE VOLUME OF THIS RECTANGULAR PRISM: 5 cm 5 cm 5 cm

47. A cereal box has a length of 8 inches, a width of 1.75 inches, and a height of 12.125 inches? How much cereal will the box hold?

48. Functions A function is a relation in which each element of the domain is paired with exactly one element of the range. Another way of saying it is that there is one and only one output (y) with each input (x). f(x) y x

49. Function Notation Input Name of Function Output

50. 2 3 5 4 3 0 2 3 f(x) f(x) f(x) f(x) Determine whether each relation is a function. 1. {(2, 3), (3, 0), (5, 2), (4, 3)} YES, every domain is different!