Download 5 + (-8) + 10

2nd Interim Study Guide (SOL’s 7.1-3, 7.12-15)
1
Solve: 5m – 6 = - 44
+6
(Find the letter)
(Add or subtract 1st)
+6
5m – 0 = - 38
÷5
÷5
(Mult. or Div. 2nd)
Name:______________________________
5 Simplify: 5 – 82 + 24 ÷ 3 ● -4
5 – 64 + 8 ● -4
5 – 64 + -32
-59 + -32
m = - 7.6
-91
- Object is to get the variable by itself.
- The 2 numbers with the variable must go!
-What is done to 1 side you must do to the other
2 Graph a solution to:
1
a  -16
4
- 1st Parenthesis,
2nd Exponents,
3rd Left to Right Divide or Multiply
4th Left to Right Subtract or Add
6 Simplify: -3 – 6(-8 – 3)2
-3 – 6(-11)
-3 – -6●121
-3 - -726
723
2
1
a ( 4) < -28 ( 4)
4
a < -112
P
E
M/D
A/S
-116
-114
-112
-110
-108
- Open circle for < or >, closed for ≤ or ≥
3 Solve and graph below: -3x ≥ 51
(÷ -3)
(÷ -3)
x ≤ -17
If you multiply (or divide) both sides by a
negative number you must reverse the
inequality sign!
-22 -21 -20 -19 -18 -17 -16 -15 -14
4
5 + (-8) – -10
5 + (-8) + 10
-3 + 10
7
-6 ÷ -2  -5 - -8
-6 ÷ -2  -5 + 8
3  -5 + 8
-15 + 8
-7
7 Solve: b – 2(7b – 2c)2
(Substitute 1st)
where b = -4 and c = -12
-4 – 2(7●- 4 – 2●-12)2
-4 – 2(-28 + 24)2
-4 – 2(- 4)2
-4 – 2●16
-4 – 32
-36
P (Mult/Div)
P (Add/Sub)
Exponent
L 2 R D/M
L 2 R S/A
-9x – 3w2 – 5xw
when x = -5 and w = 2
8 Simplify:
9●(-5) – 3●(24)
9●(-5) – 3●(16)
(-45) – (48)
-93
= -93
2nd Interim Study Guide (SOL’s 7.1-3, 7.12-15)
Name:______________________________
9 Which of the following is ordered L to G?
.025 .045 .090 .085
1
a) 0.025, 4.5% , , 8.5x10 2
11
1
, 8.5x102 , 4.5% , 0.025
b)
11
1
c) 0.025, 4.5% , 8.5x10 2 ,
ANSWER!
11
1
, 8.5x102 , 0.025, 4.5%
d)
11
13 Recognize powers of ten
10 Convert the following to a decimal:
14 Multiplying or Dividing Integers - When
the sign of the numbers being multiplied are
the same, multiply the numbers--The sign of
the answer is positive
-9 • -8 = -72
4.35 x 10-3 = _.00435____(Put in calculator)
312.5% = ___3.125____ (Divide by 100)
1
= ___.0833333____(1 ÷ 12)
12
0.30 = __0.3__ _(Do not do anything)_
103 = 1000.
102 = 100.
101 = 10.
100 = 1.
10-1 = .1
10-2 = .01
10-3 = .001
= 1 ÷ 10 = 1 ÷ 101
= 1 ÷ 100 = 1 ÷ 102
= 1 ÷ 1000 = 1 ÷ 103
Multiplying or Dividing Integers - When the
sign of the numbers being multiplies are
different, multiply the numbers--The sign of
the answer is negative
-7 • 4 = -28
11 Which of the following is true?
15 What are all the perfect square numbers?
12
 150%
15 = 1.5 = 1.5
8
12
8.0 x 102 
 80%
0.08 = 0.80 = 0.80
15
2
4.0 x 101 
 40%
0.4 = 0.4 = 0.4
5
3
3.75 x 102 
 3.75% .0375=.375=.0375
8
To find them: 1•1 = 1,
4•4 = 16
5•5 = 25,
12 Put these in descending order:
16 What decimal number could x be?
1.5 x 101 
2.1 x 1011,
2.95 x 1010,
2.1 x 1011
3.09 x 1010
2.95 x 1010
Order exponents 1st – largest!
Order 1st # (3.09) - Middle
Lowest 1st # (2.95) - Lowest!
2.1 x 1011
3.09 x 1010
3.09 x 1010
2•2 = 4,
6•6 = 36,
3•3 = 9,
7•7 = 49
1 =1, 4 =2, 9 =3, 16 =4, 25 =5,
36 =6, 49 =7, 64 =8, 81 =9, 100 =10,
121 =11, 144 =12, 169 =13, 196 =14,
225 =15, 256 =16, 289 =17, 324 =18,
361 =19, 400 =20
85%
<
x
<
9
10
Convert 85% by dividing by 100......
.85
Convert 9/10 by dividing top # by bottom #
Need a number between .85 and .90
2.95 x 1010
.86
.87
.88
.89
.90
2nd Interim Study Guide (SOL’s 7.1-3, 7.12-15)
17 Adding Integers - When the signs of the
numbers being added are the same, add their
absolute values--The sign of the answer is the
same as the sign of the numbers added together
-8 + - 5 = -13
Adding Integers- When the signs of the numbers
being added are different, subtract their
absolute values--The sign of the answer is the
same as the number with the largest absolute
value
-4 + 6 = 2
Subtracting Integers - Add the opposite and
refer to the addition rules (change the
subtraction to addition and change the sign of
the number being subtracted)
-8 – - 5 = -8 + 5 = -3
18 Graph this on a number line: -2 + (8) = +6
-8
-6 -4
-2
0
2
4
6
8
Graph this on a number line: -2 • (4) = -8
-8
-6 -4
-2
0
2
4
6
8
19 Wesley opened a checking account with
$37.50 and he saves $5.25 per week. After how
many weeks will Wesley have more than $230 to
buy an ipod?
37.50 + 5.25 • w
-37.50
5.25 • w
5.25
w
37
> 230.00
-37.50
> 192.50
5.25
_
> 36.6 weeks
Name:______________________________
20 On Monday UPS delivers 3 checks
for $5 each and 2 bills for $2 each. If you
had a starting balance of $25, what is the
ending balance?
25 + 3(5) - 2(2)
25 + 15 - 4
40 - 4
36
21 Write the expression for 14 minus the product
of 3 and a number.
14 – 3n
Write the expression for negative sixteen plus a
number divided by 2.
-16 + n/2
Write the equation for twice a number less six is
forty.
2n – 6 = 40
Write the equation for twenty-two is seven less
than a number.
22 = n – 7
22 Convert the following algebraic
expressions/sentences to verbal expressions or
equations.
9 - ½•k
One-half of k is subtracted from nine
6(3 + m)
Six times the sum of three and m
8 + 3/5w
Three-fifths of w is added to eight
9n – 2 = 12
Two less than nine times a number is twelve.
2nd Interim Study Guide (SOL’s 7.1-3, 7.12-15)
23 For each quadrant state whether x or y is
negative or positive.
Name:______________________________
27 Absolute values is distance on # line
66 - |22| = 44
(-x, +y)
(+x, +y)
(-x, -y)
(+x, -y)
24 Which of the following makes this equation
true?
y = -2x + 5
a (0, -5)
-2•(0) + 5 = 5
b (4, 3)
-2•(4) + 5 = -3
c (-2, 9)
-2•(-2) + 5 = 9
d (5, 5)
-2•(5) + 5 = -5
18 - |-16 - 8|
18 - |-24|
18 - 24
-6
|-9| = 9
|9| = 9
28 If it -5°C outside, and the temperature drops
19 degrees, what is temperature now?
-5° – 19° = -24°
If a submarine is 100 feet below sea level, and the
submarine rises 35 feet to periscope depth, then
dives down 700 feet, what is depth of the sub?
-100 + 35 – 700 = -65 – 700 = -765 ft
25 Which of the following equations make this
table true?
-2
3
29 Suppose you go two blocks east, then nine
blocks west, then fifteen blocks east again.
How far and in what direction did you go
compared to where you started?
b) y = 2x - 2
1
c) y  x  1
2
1
0
+2E – 9W + 15E
4
-3
d) y = -3x + 3
7
-6
a)
y  x 1
x
y
–7W + 15E
8 blocks East
26 John received 26 dollars from his mother
and he spent 7 dollars in Walmart and another 6
dollars at Subway. When he got home he
received his allowance of 10 dollars. Write an
algebraic expression to represent this and state
how much he has now.
+26 – 7 – 6 + 10
19 – 6 + 10
13 + 10 =
23
30
-4 + -8 • -8
-4 + 64
60
-3(-5 +13) ÷ 2
-3(8) ÷ 2
-24 ÷ 2
-12
2nd Interim Study Guide (SOL’s 7.1-3, 7.12-15)
Name:______________________________
31 Jim pays $0.25 per minute plus the $7 a
month fee for his phone. If Jim spent $34.75
this month, then how many minutes did he talk
on the phone?
m = minutes talked
33 Write the algebraic equation that is
represented here:

0.25 • m + 7 = 34.75
- 7
-7
0.25 • m
.25
m
= 27.75
.25
= 111 minutes
Always add or subtract first then multiply or divide
second in a 2-step equation.
32
Represent: 3x - 2 = -8

x
 1
 -1
-12 = 4 +2n
x
 1
 -1
34 Arithmetic Sequence - The pattern is adding
or subtracting AND it must have a common
difference (same # added or subtracted) between
any two consecutive terms.
Example: 4, 1, -2, -5…
The common difference between terms is -3:
(4 – 1 = 1, 1 – -3 = -2, -2 – -3 = -5)
An expression for the sequence above is: n – 3
where n is any term and subtracting any term by
three gets the next consecutive term in the
sequence.
Geometric Sequence - The pattern is multiplying
or dividing AND it must have a common ratio
(same # multiplied or divided) between any two
consecutive terms.
Example: 3, 6, 12, 24…
The common ratio between terms is •2:
(3 • 2 = 6, 6 • 2 = 12, 12 • 2 = 24)
An expression for the example above is: n • 2
where n is any term and multiplying any term by
two gets the next consecutive term in the
sequence.
2nd Interim Study Guide (SOL’s 7.1-3, 7.12-15)
35 Graph this table:
x y
Name:______________________________
37 Graph these ordered pairs:
(2, -1), (0, -5), (6,7)
5 3
1 1
-3 -1
-7 -3
36 Which equation represents this line?
1
a) y   x  2
2
b) y  2 x  2
1
c) y   x  1
2
d) y  2 x  1
3
38 Graph y   x  1
4
Create table 1st
x
y
0 1
4 -2
8 -5
2nd Interim Study Guide (SOL’s 7.1-3, 7.12-15)
39 Graph this equation: x
2
y   x4
0
3
3
6
y
Name:______________________________
41 Graph the line that includes these ordered
pairs: (-1, 4), (2, 0), (5,-4)
-4
Make sure you know how to graph points on a
coordinate grid !
-6
-8
40 What is the equation that represents this
line?
42 Graph y  2 x  2
x
y
2 -2
-1 4
-3 8
Create a table of points from the line
Then figure out which equation fits the points.
(4,1) (5,3) (6, 5)
y = 2x – 7
2nd Interim Study Guide (SOL’s 7.1-3, 7.12-15)
43 Which table makes y = -3x true?
x
0
1
2
3
y
-3
-6
-9
-12
x
0
1
2
3
y
-3
3
6
9
x
0
1
2
3
y
0
-3
-6
-9
x
0
1
2
3
Y
0
3
6
9
x
-4
-1
2
4
x
-3
-2
0
3
y
-1
5
11
15
y
20
15
7
-10
x
-4
-1
2
4
46 If it is -25°F in Rantoul and it is 75°F in
Honolulu, what is the temperature
difference between the two cities?
75 - -25 = 75 + 25 = 100°F
A monkey sits on a limb that is 25 ft
above the ground. He swings up 10 ft,
climbs up 6 ft more then jumps down 13
ft. How far off the ground is the monkey
now?
+25 +10 +6
44 Which table makes y = -2x + 7 true?
x
-5
-3
1
3
Name:______________________________
y
17
13
5
1
y
-15
-7
-3
-1
45 Graphing linear equations
A linear equation is an equation whose graph is a line.
Next plot the ordered pairs in the coordinate plane
(x moves first, then y) –x is to the left and +x is to the
right, then +y is up and –y is down. (-3, 5) 3 left, 5 up
Once all points are plotted you may connect the dots to
form a straight line.
= 41 – 13 = 28
47) Equations/Inequalities - Whatever operation is
performed on one side of an equation must be
performed on the other side.
1) Find the variable! You need to get rid of the
numbers on that side to get variable alone.
2) Add or subtract to get rid of any number added or
subtracted to the variable; 3x – 5 = 2 (Add to get rid
of 5)
3) Multiply or divide to get rid of the number with the
variable. (Ex: If you see fraction bar...multiply)
4) Reverse inequality sign if you had to multiply or
divide by a negative number on both sides.
5) To graph an inequality: 1) the ≥ ≤ symbols must
use a circle filled in and < > symbols use a circle not
filled in; 2) Substitute a number into your solution
and ask yourself...Is it true....if yes...arrow goes
towards that #. If false....arrow goes the other way.
48 Order of Operations (PEMDAS) –
1st, do all operations that lie inside parentheses ( ), [ ],
{ }, | |,
Graphing a linear equation requires a table of ordered
pairs by first, substituting into the equation the x-values
(0,1,2…) and solving for the y values. If there is a
fraction remember to use multiples of the bottom
number if at all possible.
-13
until there is a single # inside them.
2nd, do any exponents. Remember that -52 = -25
but (-5)2 = 25. Do not do exponents outside a grouping
symbol until you have the single number inside them.
3rd, working from left to right, do just multiplication
and division.
4th, working from left to right, do just addition and
subtraction.
Note: If you have a fraction bar everything must be
done before dividing.