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. 2. 3. 4. 5. 6.

Exponents Practice Practice: Simplify these two expressions. Answers will still have exponents in them. 1) 550 x 512 = ? 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 1. 2. 3. 4.

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 ab = ba Associative Property: a+(b+c) = (a+b)+c a(bc) = (ab)c Distributive Property: a(b+c) = ab+ac Additive Identity: 0+a = a Multiplicative Identity: 1a = a Additive Inverse: a-a = a+(-a) = 0 Multiplicative Inverse:

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 Division Addition Subtraction These are done together at the same time, LEFT to RIGHT. These are done after × and ÷, LEFT to RIGHT.

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 -1 -2 _ | | | | | | | | | | -5 -4 -3 -2 -1 1 2 3 4 5 x

Formulas For Lines Slope-Intercept Form: y=mx+b Slope: or m = slope b = y-intercept Slope: or y 2 1 -1 -2 run rise _ | | | | | | | | | | -5 -4 -3 -2 -1 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 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 Trigonometry will deal only with Right Triangles, and deals with their angles (θ). Include the following diagram on your note sheet: Hypotenuse (h) Opposite Side (o) θ Adjacent Side (a)

Trigonometry The following are the equations used in trigonometry: 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 5 meters θ