Download Math 7 SOL Fact Sheet

Math 7 SOL Review
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KEY FACT: Most IMPORTANT facts to study and know for the SOL test
Scientific Notation  Decimal – move decimal number of times of exponent (pos – right, neg – left)
KEY FACT: 5.2 x 105 = 520,000
3.04 x 10-6 = 0.00000304
Decimal Scientific Notation – move decimal so that coefficient is 1≤ C < 10
KEY FACT: 60,100 = 6.01 x 104
0.000000976 = 9.76 x 10-7
ORDER numbers – change all to one form (decimals) and then compare
KEY FACT: Add zeros to compare with numbers that have different number of decimal places
0.66 , 0.06, and 0.6  0.66 , 0.06, and 0.60
 0.06, 0.6 , 0.66
Order of Operations:
Groupings ( ), Exponents 23, Multiply (∙) OR Divide (), Add(+) OR Subtract()
KEY FACT: If looks like a big fraction, just do the top, the bottom, and finally DIVIDE!
KEY FACT: Use the
button on the calculator to simplify all exponents 34  3
4 = 81
Properties –
KEY FACT: LOOK carefully about how the numbers change from one side to the other:
Commutative Add/Multiply
Numbers move and change the order
2+5=5+2
-3 ∙ 4 = 4 ∙ -3
Associative Add/Multiply
Parentheses move to group numbers differently 2 + (-5 + 6) = (2 + -5) + 6
Distributive
Number on outside MULTIPLIES by BOTH on the inside
9(23) = 9(20) + 9(3) Break large numbers into base 10.
Inverse Add/Subtract
Opposite numbers cancel out
Add (+/)
Multiply (fraction)
9 + -9 = 0
4∙¼=1
Identity
Start and END with SAME number Add (0)
Multiply (1)
x+0=x
¾y = ¾
Consumer Applications:
part
%
KEY FACT: Use total = 100
Totals with Tax/Tip – find % then ADD back
Sales Price with Discount – find % then SUBTRACT
Integer Rules – write word problems out and THINK about a number line!
KEY FACT: THINK the pos/neg chips adding or canceling out when adding
KEY FACT: Re-Write the problem by adding the opposite
KEY FACT: THINK about MAD BOB when multiplying/dividing:
KEY FACT: Absolute Value: POSITIVE distance from zero. (ALWAYS POSITIVE!!!)
Proportions – Use these to solve word problems when comparing different values, Ratio/Rates Problems, Scale
Models, PERCENT problems, SIMILAR TRIANGLES, Probability when finding # of times, etc.
KEY FACT: Check to see if true by CROSS multiplying
___in
___in
___yellow ___yellow
%
part
KEY FACT: Set up 2 fractions with labels: ___mi = ___mi OR ___total = ___total OR 100 = total
Measurement – Use the formula sheet!
KEY FACT: FIND all missing parts of a polygon first!
Perimeter – 2D figures OUTSIDE – ADD all the parts
(Circumference for circles)
Area – 2D figuresINSIDE – USE FORMULA Sheet and/or SUBDIVIDE into smaller rectangles
Surface Area – COVER a 3-D shape – USE FORMULA Sheet
Volume – FILL a 3-D shape – FORMULA Sheet
Quadrilaterals –
Parallelogram
2 sets of parallel
sides
Rectangle
90 angles
OR
Trapezoid
1 parallel sides
Rhombus
= sides
Ordered pairs:
(x, y)
KEY FACT: Start at the origin then
+ x move  or x move 
+y move  or y move 
Square
90 angles
= sides
Similar Figures – Same shape, but different Sides
KEY FACT: Angles that match up in both are CONGRUENT ()
KEY FACT: Sides that match up in both are Similar – USE A PROPORTION
Probability: - Theoretical – what should happen and
Experimental is based on trials.
how many
KEY FACT: Make into a fraction: TOTAL
then convert if necessary
KEY FACT: How many
outfits/arrangements/combinations, etc. = counting =
MULTIPLY
Sequences – Arithmetic: ADD same numbe
Geometric: MULTIPLY same number
KEY FACTS: Find the common difference by
SUBTRACTING BACKWARDS:
2nd number – 1st number:
54 , 50 , 46 , 42 , ….
42 – 46 = 4,
and
46 – 50 = 4, and
50 – 54 = 4
KEY FACTS: Find the common ratio by Dividing
BACKWARDS: 2nd number – 1st number:
400 , 100 , 25 , …
25  100 = 0.25= ¼ and
100  400 = 0.25= ¼
Transformations: PLOT on GRAPH paper …
KEY FACT: Translation – just count
Horizontal: + x move  or x move 
Vertical:
+y move  or y move 
KEY FACT: Rotation – trace on patty paper
Clockwise:
90 - 1 turn
Counter-clockwise:
180 - 2 turns
KEY FACT: Reflection –
x-axis: y values change to the opposite
y-axis: x values change to the opposite
KEY FACT: Dilation – bigger or smaller
Scale Factor of 2, 3 or 4 means multiply values by 2,
3 or 4
Scale Factor of ½ or ¼ means divide values by 2 or 4.
Algebraic Terms: expression – made up of only
terms (#s or variables) with operations, equation – 2
equal expressions, inequality – comparison of 2
quantities
Statistics and Graphs – Write the data set down in ORDER on your paper … look at SCALE of graphs
KEY FACTS: Frequency – how many
KEY FACTS:
Mean: add up then divide
Median: Middle (if 2 add/divide by2)
Mode: most often
KEY FACTS: Histograms:
Range: SUBTRACT
Shows equal intervals Ex: 1-9, 10-19, 20–29, etc.,..
KEY FACTS:
Expression - JUST numbers/variables
3ab
4x + 2
Equations - =
Inequality - > , < , ≥ , ≤
2x = 9
x<8
3=9–6
9a ≤ 20
x
-8
3
x + 3 = 8