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Name _____________
Place the following numbers in the correct category.
{1/3, 0, Π , 2/9, -4, 7, -30, √16, √2, 20/4 }
Whole
O,7,√16,20/4
Natural
7, √16, 20/4
Integers
0,-4,7,
-30,√16,20/4
Writing Expressions – Verbal to Algebraic
1. “seven divided by the product of x and y”
Rational
Everything but
√2 and ∏
Irrational
∏ and √2
7
xy
2. “six times a number y is equal to one-third of the sum of x and y” 6y = 1/3(x+y)
3. “the difference of x and three is six” x – 3 = 6
Order of Operations
(42 + 4) ÷ 4 = 5
(12 + 3) ÷ 5 • 4 = 12
20 ÷ (-2 – 2) + 22
=-1
4 • 32 – 5(2 • 3)
= 3
4÷2
Substitution
a=3
b = -9
a+b+c
= -1
b2 + c2
= 106
(c – a)
2
= 4
c=5
Square Roots
√324
144
256
= 18
= 12
16
25
81
=5
9
Is the √66 closer to 8 or 9? ___8________
The square root of some number is 4.898989… What is the number?
24
If the area of a square is 225 square feet, what is the side length of the square? 15
What is the perimeter of that square? 15 x 4 = 60
Explain how to estimate the √24 WITHOUT using a calculator. √25 is 5, so the answer needs
to be around 4.9 or so.
Combine Like Terms
4x + 10xy + 2y – 3xy
= 7xy +4x +2y
12 + 4x – 3y + 14xy – 10 + y = 14xy +4x -2y + 2
Distributive property
8(y - 2x) = 8y – 16x
5(n + 13y) = 5n + 65y
3(w – 4)
= 3w - 12
Distributive Property and Combine Like Terms
4(2r + 6y) – 3r – 2y = 5r +22y
-9(2x + 8) + 21
= -18x - 51
2(3p – 5p)
= -4p
Equations
½ x = 20
a = -28
13
42 = -14p
-33 = x + 16
a = -364
p = -3
x = -49
22 = 2y + 8
6x – 4 = -10
3x + 5 = 2x – 1
Y= 7
x = -1
x = -6
x= 40
x – 1 = 2(3x + 4)
6x + 10x – 4 = 20
5x – 10 = 2x + 3
x = -1
x = -6
x = 4.3…
5(x +7) – 2x = 44
-4(2y + 7) - 10 = 2
3x + 7 = 5(2x – 7)
X = 3
y = -5
x = 6
Properties
1. What is the additive inverse of 2?
-2
2. What is the multiplicative inverse of –¼?
-4
3. T or F: This is an example of the associative property: (3+4) + 6 = 3 + (4+6) true
4. Put parenthesis in this equation to represent the associative property:
(7 • 5) • y = 7 • (5 • y )
5. T or F: This is an example of the commutative property: (6+3) + 9 = (3+6) + 9 true
6. Put parenthesis in this equation to represent the commutative property:
(5 + 4 )+ 9 = (4 + 5) + 9
Graphing
Name the quadrant or the axis the point lies on.
U ________2__________
K ________3_________
L ________x__________
Q ____origin______________
J ________y___________
Complete the (x,y) tables and graph the coordinates. Be sure you connect your
points to make a straight line!!
y = 2x - 8
x
y
0
-8
2
-4
5
2
8
8
*use slope-intercept ?!?
y = -3x + 7
x
-2
-1
0
1
2
y
13 10 -7
4
1
Slope
Determine the slope of the following points.
(9, 1) and (6, 3) = 2
3
(3, 2) and (-7, -8)) = 10
10
= 1
What is the slope and y – intercept of the following equations?
y = -3x + 5
-5 + ½ x = y
m = -3
y-intercept = 5
m= ½
y-intercept = -5
Graph the following equations.
Y = ½x + 3
positive slope
y = -¾x – 1
negative slope
y=4
zero slope
x = -6
undefined slope
Match these equations with
parallel equations.
*Need the same slope
y = ½x – 6
y = 7x + 4
Match these equations with
perpendicular equations.
Need opposite sign and reciprocal
y = 1/3x + 4
y = 4x + 1
y = 8x + 9
y = ¾x – 2
y = - ¼x + 6
y = -3x + 10
y = 7x – 1
y = ½x + 9
y = 5x + 2
y = ½x + 3
y = ¾x + 3
y = 8x – 5
y -2x + 7
y = -1/5x
Functions
1. Find f(-3) given f(x) = 4x2 – 2x + 1 = 36 + 6 + 1 = 43
2. Find g(2) given g(x) = 2x + 10 = 4 + 10 = 14
3. If the domain of f(x) = x – 4 is {0, 1, 2, 3, …} what is the range?
( -4, -3, -2, -1, …)
Function Word Problem
Suppose you decide to shovel driveways to make some extra money around the holidays
and you charge $5 per driveway.
a. Create a function for the total amount of money you could have at any given
moment. Y = 5x
b. Identify your independent and dependent variables.
Independent = driveways
Dependent = $
c. Graph your function for part (a) and be sure to label your x and y-axis
accordingly.
money $
by 5’s
15
10
5
Driveways