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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