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 W A = 3 x 2 = 6 meters2
A, L and W are the variables. It is any letter that represents an unknown number.

3. An algebraic expression contains:
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
Here are some phrases you may have listed. The terms with * are ones that are often used.

8. Write an algebraic expression for 1) m increased by 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.
4) two more than 6 times a number.
6n + 2
5) the quotient of a number and 12.

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

11. Which one of the following expressions represents 28 less than three times a number?
Answer Now

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

13. 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
Answer Now

14. Which of the following expressions represents the sum of 16 and five times a number?
Answer Now

15. When looking at the expression 103, 10 is called the
base
and 3 is called the
exponent or 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. 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
Answer Now

18. Which of the following expressions represents four less than the cube of a number?
Answer Now

19. We can’t evaluate because we don’t know what n equals to!!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
When x = 2
When x = 3
When y = 3

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

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

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

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

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

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

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

34. PEMDAS
4+5  (6-2)
4+5  4
4+20 24

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

36. PEMDAS
 10
21+10010 31

37. PEMDAS
 5
10+49–2  5 49

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

39. So 112 students have already paid
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=
P= 66 15

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

42. *Always measured in units cubed (u3)
VOLUME
VOLUME is the amount of liquid or solid that will FILL a 3-Dimensional object!
*Always measured in units cubed (u3)

43. QUICK DEFINITION 3-Dimensional objects 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:

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
A cereal box has a length of 8 inches, a width of 1.75 inches, and a height of 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. Determine whether each relation is a function.
1. {(2, 3), (3, 0), (5, 2), (4, 3)}
YES, every domain is different!
f(x) 2 3
f(x) 3
f(x) 5 2
f(x) 4 3

51. Determine whether the relation is a function.
2. {(4, 1), (5, 2), (5, 3), (6, 6), (1, 9)}
f(x) 4 1
f(x) 5 2
NO, 5 is paired with 2 numbers!
f(x) 5 3
f(x) 6
f(x) 1 9

52. Is this relation a function? {(1,3), (2,3), (3,3)}
Yes No
Answer Now

53. 3(3)-2 3 7 -2 -8 3(-2)-2 Given f(x) = 3x - 2, find: 1) f(3) = 7
= -8
3(-2)-2 -2 -8

54. Given h(z) = z2 - 4z + 9, find h(-3)
(-3)2-4(-3)+9 -3 30
h(-3) = 30

55. Given g(x) = x2 – 2, find g(4) 2 6 14 18
Answer Now

56. Example 2 1 5 2 8 3 11 Input Output 1. y = 3x + 2 3. y = 3x + 2
y = 0 + 2
y = 6 + 2 2
y = 2
y = 8 1 5
2. y = 3x + 2
4. y = 3x + 2
y = 3(1) + 2
y = 3(3) + 2 2 8
y = 3 + 2
y = 9 + 2
y = 5
y = 11 3 11

57. Your Turn – Identifying a Function
Does the table represent a function? Explain 3. 1.
Input
Output 1 2 3 6 4 10
Input
Output 1 3 2 6 11 4 18 2. 4.
Input
Output 1 3 4 2 5 6
Input
Output 5 9 4 8 3 2 7
YES
YES NO
YES

58. Make an input/output table for each function
Make an input/output table for each function. Use 0, 1, 2, 3 as the domain (input).
1.) y = 21 – 2x 2.) y = 5x
Input
Output 21 1 19 2 17 3 15
Input
Output 1 5 2 10 3 15

59. Make an input/output table for each function
Make an input/output table for each function. Use 0, 1, 2, 3 as the domain (input).
5.) y = 6x ) y = 2x + 1
Input
Output 1 7 2 13 3 19
Input
Output 1 3 2 5 7

60. Make an input/output table for each function
Make an input/output table for each function. Use 0, 1, 2, 3 as the domain (input).
7.) y = x ) y = 3x
Input
Output 4 1 5 2 6 3 7
Input
Output 1 3 2 6 9