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Math 7 SOL Review Name: 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