Chapter 1 Review

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.

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

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?

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

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

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.

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

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.

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

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

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?

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

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

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

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

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

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

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!!

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!

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

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

Insert grouping symbols into this equation so the expression is 50

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??

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

Decide whether the statement is true or false When x = 2 When x = 3 When y = 3

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

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

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

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

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

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

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

PEMDAS 4+5  (6-2) 4+5  4 4+20 24

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

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

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

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

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

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

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

*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)

QUICK DEFINITION 3-Dimensional objects are NOT FLAT. They have 3 measurements: Length Width Height

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

FIND THE VOLUME OF THIS RECTANGULAR PRISM:

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

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 12.125 inches? How much cereal will the box hold?

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

Function Notation Input Name of Function Output

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

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

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

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

Given h(z) = z2 - 4z + 9, find h(-3) (-3)2-4(-3)+9 -3 30 9 + 12 + 9 h(-3) = 30

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

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

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

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

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 + 1 6.) y = 2x + 1 Input Output 1 7 2 13 3 19 Input Output 1 3 2 5 7

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 + 4 8.) y = 3x Input Output 4 1 5 2 6 3 7 Input Output 1 3 2 6 9