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Math Review Gallery Walk Laws of Exponents • These rules deal with simplifying numbers when there is more than one exponent in an equation. The letters a, b, m and n represent whatever number happens to show up in a particular problem (2, 5, 2000, 1.4, …). The Laws of Exponents Are: 1. (a )( a ) a 2. (ab) a b 3. (a m ) n a mn 4. a 1 5. 6. m n m m 0 m a mn a n a 1 m a m a mn m Exponents Practice • Practice: Simplify these two expressions. Answers will still have exponents in them. • 1) 550 x 512 = ? • 2) 25 ? 3 2 Rules of Zero • These are rules showing how to simplify when there are zeros in an expression, and when you cannot simplify ( A number is undefined) Rules of Zero 2. 0 0 a 0 a 1 3. 0 0 4. a0 0 1. a Rules of Zero • Practice: Simplify the following two expressions: • 1. 19500 = ? • 2. 01,000,000 = ? Algebraic Simplification • Basic rules that can be used to simplify or rearrange formulas. • These are most useful when using variables in equations, but can also be useful with numbers too. Algebraic Simplification • • • • • • • • • • • • • Commutative Property: a+b = b+a Associative Property: a+(b+c) = (a+b)+c Distributive Property: ab = ba a(bc) = (ab)c a(b+c) = ab+ac Additive Identity: 0+a = a Multiplicative Identity: 1a = a Additive Inverse: a-a = a+(-a) = 0 Multiplicative Inverse: a 1 a 1 a a Algebraic Simplification • Practice: Rewrite the following two expressions using the rules of simplification: • 1. a(b+c) = ? • 2. a(bc) = ? Order of Operations • In order to correctly simplify a formula, you have to do the math in a certain order. Use the Pneumonic PEMDAS to help you remember that order. Order of Operations • • • • • • Parenthesis- do all math inside () first. Exponents- group or simplify any exponents Multiplication These are done together at the Division same time, LEFT to RIGHT. Addition These are done after × and ÷, LEFT to RIGHT. Subtraction Order of Opperations • Simplify the following into a single numerical answer: • 1. (3+2)2 = ? • 2. 5+3*4-2 = ? Lines • With lines, you need to be able to calculate slope and recognize Slope-Intercept Form for the equation of a line. Copy the following diagram onto your review sheet: y 2 _ 1 _ | -5 | -4 | -3 | -2 | -1 -1 _ -2 _ | 1 | 2 | 3 | 4 | 5 x Formulas For Lines • Slope-Intercept Form: y=mx+b m = slope b = y-intercept y 2 y1 x2 x1 or m rise run run y 2 _ rise • Slope: m 1 _ | -5 | -4 | -3 | -2 | -1 -1 _ -2 _ | 1 | 2 | 3 | 4 | 5 x b: y-intercept Practice with Lines • Complete the following two problems: • 1.) Write the equation for the line shown in the diagram using slope-intercept form. • 2.) What is the slope of a line with equation: y = 12x - 4 Geometry • In Geometry, we will be using formulas dealing with circles, squares, and triangles. • Include the following diagram on your handout: r: radius Circle Formulas • The following formulas will be useful for circles and spheres: • Perimeter: 2πr • Area: πr2 • Surface Area of a Sphere: 4πr2 • Volume of a Sphere: 4/3πr3 Note: π is just a number that never changes (π=3.14 always) Geometry • Include the following two diagrams on your note sheet: X a X c b Geometry • The following formulas will be useful for squares and triangles. Squares Perimeter: P = (x+x+x+x) = 4x Area: A = x2 Volume of a cube: V = x3 Triangle Pythagorean Theorem: a2 + b2 = c2 Area: 1/2ba Geometry Practice • Solve for the following: • 1.) What is the Volume of a cube that measures 2cm to a side? • 2) What is the length of side c of this traingle? 3 c 4 Trigonometry Opposite Side (o) • Trigonometry will deal only with Right Triangles, and deals with their angles (θ). • Include the following diagram on your note sheet: θ Adjacent Side (a) Trigonometry • The following are the equations used in trigonometry: sin opposite hypotenuse adjacent cos hypotenuse opposite tan adjacent • Pneumonic: • An easy way to remember this is “soh cah toa” or Some Old Hippie Caught Another Hippie Trippin on Acid Trigonometry Practice • Solve the Following problem: • What would tanθ be for the following triangle? 10 meters 11 meters θ 5 meters