Download MCAS Grade 8

MCAS Grade 8
Approved Supplemental Mathematics Reference Sheet
(For use by students on the MCAS Mathematics test who have this accommodation)
Symbols
General problem-solving strategies
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Reread question for clarity
Circle or highlight key terms
Calculate and solve
Circle my answer
See if my answer makes sense
> is greater than
< is less than
= is equal to
|absolute value|
≤ is less than or equal to
≥ is greater than or equal to
Place Value
Ht
Whole Numbers
Tt Th H T
O
Divisibility Rules
.
Decimals
T
H Th
2
If the last digit is even
3
If the sum of the digits can be
divided by 3
5
If the last digit is 0 or 5
6
If the number is divisible by both 2
and 3
If the sum of the digits can be
divided by 9
9
10
Volume (V ) Formulas
If the last digit is 0
Area (A ) Formulas
3
Cube... 𝑉 = 𝑠
(𝑠 = 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑎𝑛 𝑒𝑑𝑔𝑒)
4
Sphere... 𝑉 = 3 𝜋𝑟 3
(𝑟 = 𝑟𝑎𝑑𝑖𝑢𝑠)
1
Cone… 𝑉 = 𝜋𝑟 2 ℎ
Square… 𝐴 = 𝑠 2
(𝑠 = length of a side)
Rectangle... 𝐴 = 𝑏ℎ
(𝑏 = 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑏𝑎𝑠𝑒; ℎ = ℎ𝑒𝑖𝑔ℎ𝑡)
3
Right Circular Cylinder… 𝑉 = 𝜋𝑟 2 ℎ
Right prism… 𝑉 = 𝐵ℎ
(𝐵 = 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑏𝑎𝑠𝑒; ℎ = ℎ𝑒𝑖𝑔ℎ𝑡)
Circle Formulas
Area.... 𝐴 = 𝜋𝑟 2
(𝑟 = 𝑟𝑎𝑑𝑖𝑢𝑠)
Circumference…𝐶 = 2𝜋𝑟
OR
𝐶 = 𝜋𝑑
(𝑑 = 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟)
OR
𝐴 = 𝑙𝑤
(𝑙 = 𝑙𝑒𝑛𝑔𝑡ℎ; 𝑤 = 𝑤𝑖𝑑𝑡ℎ)
Circle… 𝐴 = 𝜋𝑟 2
Parallelogram... 𝐴 = 𝑏ℎ
1
Triangle... 𝐴 = 2 𝑏ℎ
1
Trapezoid... 𝐴 = 2 ℎ( 𝑏1 + 𝑏2 )
Spring 2017 MCAS Grade 8
Approved Supplemental Mathematics Reference Sheet
Total Surface Area (SA ) Formulas
Pythagorean Theorem
𝑎2 + 𝑏 2 = 𝑐 2
𝑐
𝑎
Right Rectangular Prism…
𝑆𝐴 = 2(𝑙𝑤) + 2(ℎ𝑤) + 2(𝑙ℎ)
(𝑙 = 𝑙𝑒𝑛𝑔𝑡ℎ; 𝑤 = 𝑤𝑖𝑑𝑡ℎ; ℎ = ℎ𝑒𝑖𝑔ℎ𝑡)
Right Circular Cylinder… 𝑆𝐴 = 2𝜋𝑟 2 + 2𝜋𝑟ℎ
Sphere… 𝑆𝐴 = 4𝜋𝑟 2
𝑏
Devices and Operations
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PEMDAS
Same sign – sum
Different sign - difference
Percentages and Proportions
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𝑖𝑠
𝑜𝑓
= 100
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𝑎
𝑏
𝑐
𝑑
=
%
𝑡ℎ𝑒𝑛 𝑎𝑑 = 𝑏𝑐
Coordinate Plane
Transformations
y
II
I
x
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roTation
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reFLection
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𝐴𝑥 + 𝐵𝑦 = 𝐶
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tranSLation
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𝑚 = 𝑥2 −𝑥1
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𝑦 = 𝑚𝑥 + 𝑏
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𝑦 − 𝑦 1 = 𝑚(𝑥 − 𝑥1 )
III
𝑦 −𝑦
2
Statistics
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meAn
MOde
meDIan
RangE
IV
1
Probability
𝑃=
𝑓𝑎𝑣𝑜𝑟𝑎𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
Spring 2017 MCAS Grade 8
Approved Supplemental Mathematics Reference Sheet
Properties
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𝑎(𝑏 + 𝑐) = 𝑎𝑏 + 𝑎𝑐
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𝑎 + (𝑏 + 𝑐) = (𝑎 + 𝑏) + 𝑐
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𝑎 ⦁(𝑏⦁𝑐) = (𝑎⦁𝑏)⦁ 𝑐
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𝑎⦁𝑏 =𝑏⦁𝑎
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𝑎+𝑏 =𝑏+𝑎
Fractions
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𝑎
𝑏
+𝑑 =

𝑎
𝑏
−𝑑 =

𝑎
𝑏
· 𝑑 = 𝑏𝑑
1
11
21
31
41
51
61
71
81
91
2
12
22
32
42
52
62
72
82
92
3
13
23
33
43
53
63
73
83
93
4
14
24
34
44
54
64
74
84
94
5
15
25
35
45
55
65
75
85
95
6
16
26
36
46
56
66
76
86
96
𝑎𝑑+𝑏𝑐
𝑏𝑑
𝑐
𝑎𝑑−𝑏𝑐
𝑏𝑑

𝑎
𝑏
÷𝑑 =
𝑐
Number Table
0
10
20
30
40
50
60
70
80
90
𝑐
𝑎𝑐
𝑐
𝑎𝑑
𝑏𝑐
Number Line
7
17
27
37
47
57
67
77
87
97
8
18
28
38
48
58
68
78
88
98
9
19
29
39
49
59
69
79
89
99
Conversions
1 cup = 8 fluid ounces
1 pint = 2 cups
1 quart = 2 pints
1 gallon = 4 quarts
1 gallon ≈ 3.785 liters
1 liter ≈ 0.264 gallon
1 liter = 1000 cubic centimeters
1 inch = 2.54 centimeters
1 meter ≈ 39.37 inches
1 mile = 5280 feet
1 mile = 1760 yards
1 mile ≈ 1.609 kilometers
1 kilometer ≈ 0.62 mile
1 pound = 16 ounces
1 pound ≈ 0.454 kilogram
1 kilogram ≈ 2.2 pounds
1 ton = 2000 pounds
Spring 2017 MCAS Grade 8
Approved Supplemental Mathematics Reference Sheet