Chapter 1 Review. What is the area of a rectangle? Length times Width If the length is 3 meters and...

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 WA = 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

41

m

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

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.

Addition Subtraction Multiplication Division

Here are some phrases you may have listed. The terms with * are

ones that are often used.Addition Subtraction Multiplication Division

sum* difference* product* quotient*

increase decrease times divided

plus minus multiplied ratio

add subtract

more than less than

total

Write an algebraic expression for

1) m increased by 5.m + 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.

4n - 11

4) two more than 6 times a number.

6n + 2

5) the quotient of a number and 12.

12

x

Which of the following expressions represents

7 times a number decreased by 13? 1. 7x + 13

2. 7x - 13

3. 13 - 7x

4. 13 + 7x

Answer Now

Which one of the following expressions represents 28 less than three times a

number? 1. 28 - 3x

2. 3x - 28

3. 28 + 3x

4. 3x + 28

Answer Now

Write a verbal expression for:

1) 8 + a.

The ratio of m to rDo you have a different way of writing these?

The sum of 8 and a

2)

m

r.

Which of the following verbal expressions represents 2x + 9?

Answer Now

1. 9 increased by twice a number

2. a number increased by nine

3. twice a number decreased by 9

4. 9 less than twice a number

Which of the following expressions represents the sum of 16 and five

times a number?

Answer Now

1. 5x - 16

2. 16x + 5

3. 16 + 5x

4. 16 - 5x

baseand 3 is called the

exponent or power.103 means 10 • 10 • 10

103 = 1000

When looking at the expression 103, 10 is

called the

How is it said?21

Two to the first power22

Two to the second power or two squared

23

Two to the third power or two cubed2n7

Two times n to the seventh power

Which of the following verbal expressions represents x2 + 2x?

Answer Now

1. the sum of a number squared and twice a number

2. the sum of a number and twice the number

3. twice a number less than the number squared

4. the sum of a number and twice the number squared

Which of the following expressions represents four less than the cube

of a number?

Answer Now

1. 4 – x3

2. 4 – 3x

3. 3x – 4

4. x3 – 4

Evaluate.21

222

2 • 2 = 423

2 • 2 • 2 = 82n7

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 = 125243 ≠ 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

FALSE

FALSE

TRUE

FALSE

TRUE

Mnemonic• Please

• Parenthesis

• Excuse• Exponents

• My Dear• Multiply or Divide – Left to Right

• Aunt Sally• Add or Subtract – Left to Right

Example 1:2 3 - (4-2) + 32

MultiplicationParenthesis

Subtraction Addition

Exponents

2 3 - (4-2) + 32

2 3 - 2 + 32

Parenthesis

Exponents

6 - 2 + 9Multiply

2 3 - 2 + 9

Add or Subtract – Left to Right

4 + 913

Example 2:

4 6 – (3 + 4) + 22

MultiplicationParenthesis

Subtraction Addition

Exponents

4 6 – (3 + 4) + 22

4 6 - 7 + 22

Parenthesis

Exponents

24 – 7 + 4Multiply

4 6 – 7 + 4

Add or Subtract – Left to Right

17 + 421

PEMDAS3+23- (9+1)

3+23- 10

3+8-10

11-10

1

PEMDAS3 (9+1) + 62

3(10)+62

3(10)+36

30+36

66

PEMDAS4+5 (6-2)

4+5 4

4+20

24

PEMDAS4+ 10 23 -16

4+10 8 -16

4+ 80 -16

84-1668

PEMDAS 21 + 102 10

21+10010

21 + 10

31

PEMDAS10+72-2 5

10+49–2 5

10+49- 10

59 - 10

49

PEMDAS

64 (9 3-19)

64(27 –19)

64 8

8

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

15

Add up all the sides:

P= length + width + length + widthP= 18 + 15 + 18 + 15P= 66

To find the perimeter of a rectangle:

5a

3a

Add up all the sides:

P= length + width + length + widthP= 5a + 3a + 5a + 3aP= 16a

JUST ADD UP THE COEFFICENTS

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 WidthHeight

FIND THE VOLUME OF THIS RECTANGULAR PRISM:

3 mm 2

mm12 mm

FIND THE VOLUME OF THIS RECTANGULAR PRISM:

10 in

3 in

4 in

FIND THE VOLUME OF THIS RECTANGULAR PRISM:

5 cm

5 cm5 cm

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?

FunctionsA 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)x y

Function Notation

Output

InputName of Function

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 0

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

f(x)5 3

f(x)6 6

f(x)1 9

NO, 5 is paired with 2 numbers!

Is this relation a function?{(1,3), (2,3), (3,3)}

1. Yes

2. No

Answer Now

Given f(x) = 3x - 2, find:1) f(3)

2) f(-2)

3(3)-23 7

3(-2)-2-2 -8

= 7

= -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)

Answer Now

1. 2

2. 6

3. 14

4. 18

Example1. y = 3x + 2

Input Output

y = 3(0) + 2y = 0 + 2

y = 2

2. y = 3x + 2y = 3(1) +

2y = 3 + 2

y = 5

3. y = 3x + 2y = 3(2) +

2y = 6 + 2

y = 8

4. y = 3x + 2y = 3(3) +

2y = 9 + 2

y = 11

0

1

2

3

2

5

8

11

Your Turn – Identifying a Function

Does the table represent a function? Explain

Input Output

1 3

1 4

2 5

3 6

Input Output

1 12 33 64 10

Input Output

1 32 63 114 18

Input Output

5 94 83 92 7

1.

2.

3.

4.

YESNO

YES

YES

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

0 21

1 19

2 17

3 15

Input Output

0 0

1 5

2 10

3 15

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

0 1

1 7

2 13

3 19

Input Output

0 1

1 3

2 5

3 7

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

0 4

1 5

2 6

3 7

Input Output

0 0

1 3

2 6

3 9