Math Final mid
2(4+6)
(2x4)+(2x6)
no solution
3(x + 2) - (x - 3) = x - 5 - 3(x + 1) + 4x
3(5+8)
(3x5)+(3x8)
4(1+3)
(4x1)+(4x3)
4(2+3)
(4x2)+(4x3)
5(1+3)
(5x1)+(5x3)
6(3+2)
(6x3)+(6x2)
7(10+2)
(7x10)+(7x2)
7(9+2)
(7x9)+(7x2)
8(2+1)
(8x2)+(8x1)
8(2+6)
(8x2)+(8x6)
9(1+2)
(9x1)+(9x2)
-2⁰
-1
-8(3 + 2b)
-16b − 24
-9b + 5b + 7
-4b + 7
13 − b − 4b
-5b + 13
2⁰
1
a⁷/a⁷
1
7b + (4 + 3b)
10b + 4
18b + 3(4 − 6b)
12
3b(4) + 5
12b + 5
18 + 5b − 12 + 7b
12b + 6
x= - 10/14
2(3x+7)=4(-2x+1)
x=2/9
2(5 - 3x) = 6(2x + 1)
x=6
2x + 5 = 3x - 1
x=-7/3
2x - 1 = 4(x - 2) + x
(2²)²
2⁴
2³ ⋅ 2³
2⁶
x=1
3 - (5 - x) = 3 - 4x
x=1
3(5x-2) +4x = 9x +6 -2x
12 − 4b + 7b − 3
3b + 9
x=4
3x + 2 = 14
x=13
3x - 4 = 2x + 9
3⁵/ 3³
3²
3⁰ ⋅ 3³
3³
x=-7
4(3x - 2) - 10x = 3x - 1
x=-11
4+x=-7
x=1
4x+7-6x=5-4x+4
x=3
4x-2=10
4³ ⋅ 4²
4⁵
x = -4
5(2x+3) = 3 (4x+1) -2(3x+2)
2b(3 − 1) + b
5b
x=2
5x + 7 = -5 + 11x
x=3/2
5x - 4 = 8 - 3x
x=5/3
5x+2=8x-3
x=-7
6-x=13
5b − (-2b) + 6
7b + 6
x=3/10
7x - 1 = - 3x + 2
Negative Exponent Property
A nonzero base raised to a negative exponent is equal to the reciprocal of the base raised to the opposite, positive exponent
Zero power property
ANYTHING raised to the power of zero is 1 or -1
23.5
Ann's volleyball scores- 23,24,25,6,77,45,23,23. Find the median
6
Ariana has been playing 10 games, find her outlier(s) of all the games, here they are: 20, 18, 17, 19, 19, 18, 20, 16, 19, 6
65
Basketball scores: 12.3, 12, 45, 66, 77, 66. Find the range
86
Betha's test scores. Find the median: 79, 86, 86, 97 100, 95, 67
34.5
Find the mean: 39,34,35,42,45,12,
28.5
Find the median: 21, 32, 45, 60, 13, 25
44
Find the mode: 44,29,13,44,15
4.5 and 34
Find the mode: 64,77,4.5,67,4.5,34,34,,23,12,69,65
64
Find the mode: 89,72,34,35,35,35,64,64,77,88,64,88,64
100 and 13.5
Find the mode: 92, 100, 100, 23, 24, 99, 13.5, 13.5
23
Find the mode:87,56,45,23,23,34,64,23,54
88
Find the range: 56, 79, 80, 80, 93, 16, 16, 17, 5
96
Find the range: 67, 35, 67, 67, 13, 108, 109
53
Find the range:73,45,67,87,98
≤ and ≥
Graphed with a CLOSED circle
< and >
Graphed with an OPEN circle
91
Hikaru's test scores- 75, 86, 97, 100, 100, 88. Find the Mean
Product of powers
If you are multiplying powers with the same base add the exponents and keep the base
Exponent Form
The exponent tells how many times the base multiplies itself
Power to a power
To find a power of a power, multiply the exponents
x < -3
What is the inequality for the graph?
x > -3
What is the inequality for the graph?
x ≤ -3
What is the inequality for the graph?
x ≥ -3
What is the inequality for the graph?
2x > 10
Which inequality has the solution represented by the given graph?
x + 3 ≥ 5
Which inequality has the solution represented by the given graph?
x - 6 < -1
Which inequality has the solution represented by the given graph?
Mean
add up all the numbers then divide by the number of items you added
a⁶⋅a⁶
a¹²
(a³)⁵
a¹⁵
c⁶/c³
c³
c⁹⋅c⁻⁴
c⁵
91
find the mean: 96, 62, 34, 09, 220, 17, 212, 78
0.8
find the median: 0.1, 0.4, 0.8, 0.14, 0.23
62, 56
find the mode: 62, 43, 41, 56, 76, 23, 62, 90, 84, 65, 56
76, 52
find the outlier(s): 98, 102, 104, 76, 96, 57, 97, 99
543
find the range 64, 90, 87, 42, 12, 234, 548, 5
p⁹/p⁷
p²
p⁷/p³
p⁴
Range
subtract the smallest and the biggest number
Median
the number in the middle
Mode
the number that occurs most often
Outliers
the one that doesn't fit in with the rest
Quotient of powers
when dividing powers with the same base KEEP base and SUBTRACT the exponents
x²⋅x³
x⁵
x⁵⋅x
x⁶