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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
Natural
0,7,sq.rt.16,20/4 7,sq.rt16,20/4
Integers
0, -4, 7,
-30, 16,20/4
Rational
Irrational
Everything but
pi and sq rt 2 Pi and sq rt 2
Place the following numbers in order from least to greatest:
{4, -8, 0, 16, -14, -21, 2, 7}
( -21, -14, -8, 0, 2, 4, 7, 16)
Place the following numbers in order from greatest to least
{19, -12, -45, -3, -4, 17, -22, 22}
( 22, 19, 17, -3, -4, -12, -22, -45)
Round
- to the nearest tenth.
6.435
6.4
- to the nearest hundredth. 23.8613
23.86
- to the nearest thousandth. 17.42667
17.427
Absolute Value
| 19 – 25 |
6
Exponents
Simplify
28
256
|-3| + |2|
5
45
1024
|-5 – 10 |
15
62
36
Scientific Notation
Express in scientific notation
0.00074
643,000
0.00354
7,000,000
7.4 x 10 ^-4
6.43 x 10 ^5
3.54 x 10 ^-3
7 x 10 ^6
Express in standard form
4 x 107
4.32 x 10-4
40,000,000
.000432
8.9 x 10 5
890,000
6 x 10-2
.006
Scientific Notation
Add, Subtract, Multiply and Divide
**Express your final answer in scientific notation!!
(6.3 x 104 ) • (4.6 x 10
-2
)
63000 x .046 = 2.898 x 10 ^3
(5x 105 ) ÷ (2 x 102 )
(4.2 x 105 ) + (3.41 x 10
500000 / 200 = 2.5 x 10 ^3
2
)
(4.58 x 10-3 ) - (4 x 10 -2)
Substitution
a=3
b = -9
420000 + 341 = 4.20341 x 10 ^5
.00458 - .004 = 5.8 x 10 ^-4
c=5
a+b+c
3 + -9 + 5 = -6 + 5 = -1
b2 + c2
81 + 25 = 106
(c – a)
2
5 – 3) ^2 = 2 ^2 = 4
Square Roots
324
=18
144
256
= 12
16
25 =5
81 9
Is the sq. root of 66 closer to 8 or 9? _____8______
If the area of a square is 225 square feet, what is the side length of the square? Sq. root 225
= 15 feet
What is the perimeter?
4 x 15 = 60 feet
Written Expressions
Write the following expressions.
Five less than a number
n - 5
Twice as many pencils
2p
The quotient of a number and 4
n
4
A number increased by 7
n + 7
Order of Operations
(42 + 4) ÷ 4
20 ÷ (-2 – 2) + 22
( 16 + 4) / 4 = 5
20 / -4 + 4 = -5 + 4 = -1
Combine Like Terms
-3n + 12 – 4n
-7n + 12
23x – 7x + 4x
16x + 4x = 20x
Distributive property (multiply everything inside parenthesis)
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
= -8r + 24y -3r – 2y = -11r +22y
-9(2x + 8) + 21
= -18x – 72 + 21 = -18x - 51
2(3p – 5p)
= 6p – 10p = -4p
Equations
½ x = 20
a = -28
13
42 = -14p
-33 = x + 16
X = 40
a = -364
p = -3
-49 = x
22 = 2y + 8
6x – 4 = -10
7 = y
x = -1
Distribute, Combine Like Terms AND Solve
5(x +7) – 2x = 44
-4(2y + 7) - 10 = 2
x = 3
y = -5
Solving Equations with variables on both sides
41 – 2n = 2 + n
n = 13
6x – 9x – 4 = -2x – 2
x = -2
Express each percent as a fraction
73%
73
100
18%
9
50
4%
1
25
Express each decimal as a percent
.7
70 %
.324
32.4 %
.65
65 %
Express each fraction as a percent
14/15
93.3 %
2/5
40 %
18/93
19.4 %
Find the values of a when the perimeter is 279
17 - a
7a
32a + 13 = 279 (solve)
a = 8.3125
5a - 2
9a
12a-2
Find the value of y
15y – 10 + 14y – 7 + 3y + 3 = 180
5(3y-2)
22y -14 = 180 (solve)
Y = 8.82
7(2y – 1)
3(y + 1)
Rates
$330 for 3 days
Cost per day
432 beats per minute
number of beats per second
Divide = $110 per day
Divide by 60 = 7.2
Ratio
Write in simplest form
2 cups to 18 cups
1/9
12 boys : 18 girls
2/3
Proportions
Solve
4 = 12
5
n
n = 15
Is
Of
=
8 = n
3
27
n = 72
8 = 5
n 2.45
n = 3.92
%
100
19% of 400
73 is what percent of 400
96 is 30% of what number
19 = x
100 400
x = 73
100 400
30 = 96
100
x
x = 76
x = 18.25
x = 320
Discounts and Sales Tax
A $159.99 TV is on sale for 20% off. Find the sale price of the TV.
Show your work!
160 x .20 = 32 , 160 – 32 = $128
Michelle bought a new car for $10, 599. A sales tax of 6% is applied to the price.
Find the price of the car after the sales tax.
Show your work!
10,600 x .06 = 636, 10600 + 636 = $11,236
Best Buy is advertising a CD player for $79.99 at 30% off. Find the total cost after
the discount and 5% sales tax is applied.
80 x .30 = 24, 80 – 24 = $56
56 x .05 = 2.80, 56 + 2.80 = $58.80 final price.
Graphing
Name the quadrant or the axis the point lies on.
U ____(-6, 8)______________
K _____(-4, -8)_____________
L ____(2, 0)______________
Q ___(0, 0)_______________
J _____(0, -1)______________
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
y = -3x + 7
x
-2
-1
0
1
2
y
13 10
7
4
1
*can you use slope-intercept ??
Slope
Determine the slope of the following points.
(9, 1) and (6, 3)
1 – 3
9 – 6
-2
= 3
(3, 2) and (-7, -8))
2 - -8
3 - -7
10
10
=
1
What is the slope and y – intercept of the following equations?
y = -3x + 5
m = -3
y-intercept = 5
-5 + ½ x = y
m = 1/2
y-intercept = -5