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Math-7 SOL Review Blitz

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Quadrilaterals Trapezoid -- must have . . . Parallelogram ONE set of parallel sides! Parallelogram -- must have . . . TWO sets of parallel sides! Rectangle -- must have . . . FOUR right angles! Rhombus -- must have . . . FOUR equal (congruent) sides! Square -- must have . . . FOUR right angles AND FOUR = sides!

Transformations Translation Rotation Reflection Dilation

This means two units to the RIGHT and four units DOWN! Translations (slides): Translate the figure (2, -4): A is at (-7,2) . Where will AI be?? This means two units to the RIGHT and four units DOWN! AI A AI = (-5,-2)

Reflections (flips): Reflect the figure over the x axis: A is at (-8,2) . Where will AI be?? The reflected point must be the same distance from the x axis! A AI AI = (-8,-2)

Dilations (re-sizing): Dilate the figure by a scale factor of ½ : A is at (6, 2) . Where will AI be?? Multiply by the scale factor! AI A AI = (3, 1)

The x and y coordinates switch with each turn! Rotations (turns): Rotate the figure 90⁰ counter- clockwise: A is at (2,1) . Where will AI be?? The x and y coordinates switch with each turn! AI BI CI A B C AI = (-1, 2)

VOLUME or SURFACE AREA? Key Words: Key Words: Cover Wrap Paint Outside _________ UNITS Square² Key Words: Fill Hold Pour Inside VOLUME: ________ UNITS Cubic³

Changing a Dimension/ Attribute . . . For the Prism ONLY: If we double ONE dimension (length, width, or height) in a prism, the volume also _______________. Does the surface area also double? DOUBLES NO!!! Surface Area would increase, but not double. 8 in. 3 in. V = ____ in.3 4 in. 3 in. V = 36 in.3 72

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ABSOLUTE VALUE Absolute Value measures distance from _____________ on a number line! Absolute Value is ALWAYS ____________! On a number line . . . zero positive TRUE or FALSE ?? │2/3 │ = -2/3 false false -2.5 = │2.5 │ true │-40 │ = 40 true 8 = │- 8 │

Keep Sign of Larger Absolute Value ADDING INTEGERS SIGNS SAME SIGNS DIFFERENT ADD SUBTRACT Keep Sign of Larger Absolute Value Keep Sign 4 + 3 = -4 + -3 = 4 + -3 = -4 + 3 = 7 1 -7 -1

Draw a line, Change the Sign! SUBTRACTING INTEGERS Draw a line, Change the Sign! 3 - 5 can be re-written as . . . 3 + (-5) = -2

MULTIPLYING or DIVIDING INTEGERS Piece of Cake!

MODELING INTEGERS Adding Integers: Multiplying Integers: 3(-3) = -9 -2 + 6 = ? Answer: -2 + 6 = 4 Answer: 2 + (-7) = -5 Multiplying Integers: Three groups of -3 . . . 3(-3) = -9 3(-2) = -6 Three groups of -2 . . .

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HIGHLIGHT KEY WORDS!!!

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Turn Fraction CLOCKWISE It’s as easy as riding a bike! Fraction to Decimal Turn Fraction CLOCKWISE to the RIGHT!! 3 8 8 3 Remember: Take the TOP number, ________ by the _________ number! It’s as easy as riding a bike! divide bottom

To the Left OR to the Right ? 7.5% = “To the left, to the left!” “P to D” Percent to Decimal 0.075 .014 = “To the right, to the right!” “D to P” Decimal to Percent 1.4%

What about NEGATIVE exponents? . . . Whew! Glad that’s settled! You Heard it Here. . . 10² is NOT !! 20 The RIGHT way . . . 10² = 10 x 10 = __ 100 What about NEGATIVE exponents? . . . 𝟏 𝟏𝟎𝟎 𝟏 𝟏𝟎 x 𝟏 𝟏𝟎 10-² =____ =__ =__ .01 What about . . . 100 = ____ 1 Whew! Glad that’s settled!

NOT

SQUARE NUMBER MODEL 4 16 un² 4 16 = 4 AREA SIDE

Scientific Notation Is it really Big or really Small?? Positive Exponent– Crazy Big # !! 4.56 x 105 = __________ (move decimal to the right ___ spaces) Negative Exponent– Crazy Small # !! 5.15 x 10-4 = __________ (move decimal to the left ____ spaces) 456,000 5 0.000515 4

Sequences Arithmetic Sequences: Add or Subtract by Same #!! 2, 5, 8, 11 . . . + 3 Rule, so COMMON ___________ is 3 difference 14, 10, 6, 2 . . . - 4 Rule, so COMMON DIFFERENCE is - 4 Geometric Sequences: Multiply/ Divide by Same #!! 3, 9, 27, 81. . . x 3 Rule, so COMMON ___________ is 3 ratio 40, 20, 10, 5 , 𝟓 𝟐 . . . ÷ 2 Rule, so COMMON RATIO is ½

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THEORETICAL PROBABILITY EXPERIMENTAL PROBABILITY is what happen (based on math). EXPERIMENTAL PROBABILITY happens (do the experiment)! SHOULD ACTUALLY

Fundamental Counting Principle How Many Total Outcomes? MULTIPLY, MULTIPLY, MULTIPLY!! Two Number Cubes: Two Coins and One Number Cube: Choice of these letters for a four-letter code: A, B, C, D, E, F 6 = 36 x 2 = 24 x 6 That’s SIX letter choices . . . 6 = 1,296 x

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PLUG “2” BACK INTO EQUATION! Equations Goal: Get x by itself!!! Golden Rule: Whatever you do to one side of the equation , you MUST do to the _______________. other side 6x – 4 = 8 +4 + 4 6x = 12 6 6 x = 2 PLUG “2” BACK INTO EQUATION! 6(2) – 4 = 8 It works!

Does the bird get the worm? Inequalities When multiplying or dividing by a __________, we switch the inequality sign! Do you switch? (Yes or No) 2x > -5 - x + (2) < 5 𝒙 −𝟒 < 2 x + (-2) > -17 Open or Closed Circle?? x > 6 x ≥ 3 Ask yourself . . . Does the bird get the worm?? negative # no yes yes no Does the bird get the worm? open closed

Check ALL ordered pairs! Plug in ALL x values into equation! Linear Functions Which Table Matches? x y -2 -1 -5 4 x y -2 1 3 x y -2 1 2 -1 x y -2 3 -5 Check ALL ordered pairs! Which Equation Matches? x y 1 9 2 17 3 25 y = x + 8 y = 9x C. y = 8x + 1 D. y = 7x + 2 Plug in ALL x values into equation!

y = mx + b Slope-Intercept Form slope y- intercept POSITIVE y = 2x - 5 y = -2x + 5 y = -5x + 𝟏 𝟐 y = -2x - 5 UPHILLS have ______________ SLOPES! DOWNHILLS have ______________ SLOPES! POSITIVE NEGATIVE

Percent Proportion % 100 = 𝑝𝑎𝑟𝑡 𝑤ℎ𝑜𝑙𝑒 20 100 = 𝑥 19.50 % 100 = 𝑝𝑎𝑟𝑡 𝑤ℎ𝑜𝑙𝑒 For tax, tip, or discount problems, Remember that the original price goes in the whole position!! Example: The original price of a T-shirt is $19.50. The discount is 20%. What is the sale price ? 20 100 = 𝑥 19.50 Step One: Find discount. 100𝑥 100 = 390 100 x = $3.90 Step Two: Subtract discount. $19.50 - $3.90 = $15.60

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= Commutative Property + + 2x + (½ · 4) = xyz = yzx (½ · 4) + 2x ORDER Notice that the ________ switches, but the answer stays the same!

Who do you Associate with? ASSOCIATIVE PROPERTY + + = (x + 4) + 2y = x + (4 + 2y) GROUPING Notice that the _____________ changes, but answer stays the same! Who do you Associate with?

Distributive Property + = + 7(x + y) = ___________ 7x + 7y

Identity Property ½ 1 ½ ½ + ____ = ____ OR ½ ● ____ =____ Nobody wants to lose their identity! Just remember you can secure your identity if you: ½ + ____ = ____ OR ½ ● ____ =____ ½ 1 ½ Notice that the “1/2” keeps its identity (stays the same)!

Inverse Property 4x + ___ = 0 -4x 1/4 4 ● ___ = 1 “Zero Pair” Property!! Inverse Property of Addition: 4x + ___ = 0 -4x Inverse Property of Multiplication: 1/4 4 ● ___ = 1 INVERSE means OPPOSITE!

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