* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Math 095 – Formulas
Big O notation wikipedia , lookup
Abuse of notation wikipedia , lookup
Positional notation wikipedia , lookup
Location arithmetic wikipedia , lookup
Large numbers wikipedia , lookup
Hyperreal number wikipedia , lookup
Factorization wikipedia , lookup
Line (geometry) wikipedia , lookup
System of polynomial equations wikipedia , lookup
Division by zero wikipedia , lookup
Elementary algebra wikipedia , lookup
Mathematics of radio engineering wikipedia , lookup
Math 095 Reference Sheet Order of Operations: (Please Excuse My Dear Aunt Sally) Parentheses Exponents Multiplication Done at the same time - left to right Division Addition Done at the same time - left to right Subtraction Slope Formulas: 𝑚 = 𝑠𝑙𝑜𝑝𝑒 Q 𝑚= 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 𝑝𝑜𝑖𝑛𝑡𝑠 = (𝑥1 , 𝑦1 ) 𝑎𝑛𝑑 (𝑥2 , 𝑦2 ) or 𝑚 = 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑦 (∆𝑦) 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑥 (∆𝑥) } } 𝑦 −𝑦 or 𝑚 = 𝑥2 −𝑥1 2 1 Horizontal Line: 𝑦 = 𝑚𝑥 + 𝑏 𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1 ) Vertical Line: What Can Slope and Intercepts Tell You About lines? One Line Two Lines Y - Intercept formula: Point – Slope formula: 𝑦=𝑏 𝑥=𝑎 Slope: Positive Negative Zero Undefined Same Same Opposite Reciprocal Different y-Int: Any Any Any None Different Same Same or Different Same or Different Increasing Decreaseing Horizontal Vertical Parrallel Coinciding Perpendicular Intersecting Solving Linear Equations: 1. Deal with any parentheses in the problem. 2. Combine like terms on each side of the equal sign. 3. Move terms with the needed variable on one side of the equal sign everything else to the other side. 4. Isolate the needed variable. Interest: 𝐴=𝑃+𝐼 Simple 𝐼 = 𝑃𝑟𝑡 First, Outside, Inside, Last (𝑎1 𝑥 + 𝑏1 )(𝑎2 𝑥 + 𝑏2 ) = 𝑎1 𝑎2 𝑥 2 + (𝑎1 𝑏2 + 𝑎2 𝑏1 )𝑥 + 𝑏1 𝑏2 Factoring Special Forms 𝐴2 + 2𝐴𝐵 + 𝐵2 = (𝐴 + 𝐵)2 𝐴2 − 2𝐴𝐵 + 𝐵2 = (𝐴 − 𝐵)2 𝐴2 − 𝐵2 = (𝐴 + 𝐵)(𝐴 − 𝐵) 3 𝐴 + 𝐵3 = (𝐴 + 𝐵)(𝐴2 − 𝐴𝐵 + 𝐵2 ) 𝐴3 − 𝐵3 = (𝐴 − 𝐵)(𝐴2 + 𝐴𝐵 + 𝐵2 ) P=Principle r = rate (decimal) A=Future Amount t = time n = # of times compounded per year Continuously Compound Compounded 𝑟 𝑛𝑡 𝐴 = 𝑃 (1 + ) 𝑛 𝐴 = 𝑃𝑒 𝑟𝑡 Step 3: Step 4: Step 5: PT P2 Use with 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 The “AC” Method: Step 1: Step 2: Mixture Problems: A “Visual” Way P1 Binomial Expansion: You may know it as a four letter word starting with “F” Multiply “a” and “c” Find factors of your new number that will add to equal “b”. Rewrite “bx” using your two new numbers. Factor by grouping. Move your “common” binomial out, and make your other two terms a new binomial Quadratic Equation: A1 A2 AT 𝑥= Discriminant: 𝑨𝟏 𝑷𝟏 + 𝑨𝟐 𝑷𝟐 = 𝑨𝑻 𝑷𝑻 Variation: “k” the constant of variation Varies with the Square Directly 𝑦 =𝑘∙𝑥 𝑦 = 𝑘 ∙ 𝑥2 Inversely Page 1 of 2 𝑦= 𝑘 𝑥 𝑦= 𝑘 𝑥2 + 0 2 real solutions 2 complex solutions 1 real solution −𝑏 ± √𝑏 2 − 4𝑎𝑐 2𝑎 The Vertex of a Quadratic: 𝑓(𝑥) = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 The vertex form: 𝑏 2 − 4𝑎𝑐 A is the amount and P is the percent. One of these will be missing Use with 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0 𝑓(𝑥) = 𝑎(𝑥 − ℎ)2 + 𝑘 The vertex is the point (ℎ, 𝑘) (ℎ, 𝑘) = (− 𝑏 𝑏 , 𝑓 (− )) 2𝑎 2𝑎 Distance, Rate, and Time 𝑑 = 𝑟𝑡 Rev 2.0 4/17/2015 Math 095 Reference Sheet Square Rectangle Triangle Parallogram Trapazoid Circle Perimeter 𝑃 = 4𝑠 𝑃 = 2𝑙 + 2𝑤 𝑃 = 2𝑎 + 2𝑏 𝐴 = 𝑠2 𝐴 = 𝑙𝑤 𝑃 =𝑎+𝑏+𝑐+𝐵 1 𝐴 = ℎ(𝑏 + 𝐵) 2 𝐶 = 2𝜋𝑟 Area Cube Rectangler Solid 𝑃 = 𝑎+𝑏+𝑐 1 𝐴 = 𝑏ℎ 2 Right Circular Cylinder Cone Right Pyramid Sphere Volume 𝑉 = 𝑠3 𝑉 = 𝑙𝑤ℎ 𝑉 = 𝜋𝑟 2 ℎ 1 𝑉 = 𝜋𝑟 2 ℎ 3 1 𝑉 = 𝑙𝑤ℎ 3 4 𝑉 = 𝜋𝑟 2 3 Surface Area 𝑆 = 6𝑠 2 𝑆 = 2𝑙𝑤 + 2𝑙ℎ + 2ℎ𝑤 𝑆 = 2𝜋𝑟ℎ + 2𝜋𝑟 2 𝑆 = 𝜋𝑟√𝑟 2 + ℎ2 + 𝜋𝑟 2 𝑤 2 𝑙 2 𝑆 = 𝑙𝑤 + 𝑙√( ) + ℎ2 + 𝑤 √( ) + ℎ2 2 2 𝑆 = 4𝜋𝑟 2 𝐴 = 𝑏ℎ Pythagorean Theorem: Between Two Points (𝑥1 , 𝑦1 ) and (𝑥2 , 𝑦2 ) The hypotenuse “c” is the longest side and it is opposite the right angle! Distance 𝑑 = √(𝑥2 − 𝑥1 )2 + (𝑦2 − 𝑦1 )2 𝑖 = √−1 Complex Numbers: Midpoint Formula 𝑥2 + 𝑥1 𝑦2 + 𝑦1 ( , ) 2 2 𝑎2 + 𝑏 2 = 𝑐 2 𝐴 = 𝜋𝑟 2 Complex Numbers Have a Real Part and an Imaginary Part Real 𝑎 + Imaginary 𝑏𝑖 Complex numbers have complex conjugates Circles: Center = (𝒉, 𝒌) Radius = 𝒓 Absolute Value: The distance from zero !!! Just think it makes things positive !!! |𝑥 − 𝑎| = 𝑏 (𝑥 − 𝑎) = 𝑏 −(𝑥 − 𝑎) = 𝑏 OR 𝑥−𝑎 =𝑏 −𝑥 + 𝑎 = 𝑏 𝑥 =𝑎+𝑏 𝑥 =𝑎−𝑏 2 (𝑥 − ℎ) + (𝑦 − 𝑘) = 𝑟 Interval Set Builder 𝑥<𝑎 (−∞, 𝑎) {𝑥| 𝑥 < 𝑎 } 𝑥≥𝑏 [𝑏, ∞) {𝑥| 𝑥 ≥ 𝑏 } 𝑎<𝑥<𝑏 (𝑎, 𝑏) {𝑥| 𝑎 < 𝑥 < 𝑏 } 𝑎<𝑥≤𝑏 (𝑎, 𝑏] {𝑥| 𝑎 < 𝑥 ≤ 𝑏 } 𝑎≤𝑥<𝑏 [𝑎, 𝑏) {𝑥| 𝑎 ≤ 𝑥 < 𝑏 } 𝑎≤𝑥≤𝑏 [𝑎, 𝑏] {𝑥| 𝑎 ≤ 𝑥 ≤ 𝑏 } Page 2 of 2 2 𝑎 + 𝑏𝑖 𝑎 − 𝑏𝑖 When you multiply remember to treat 𝒊 like 𝒙 Inequalities: Remember to change the direction of the inequality when multiplying or dividing by a negative. Solution Center: “How to answer the question” A number that makes the equation true Solve for “x” An ordered pair that makes the equation true Find a point The point(s) where a graph crosses the X Axis X -Intercept The point(s) where a graph crosses the Y Axis Y-Intercept Notation 2 𝑎≥𝑏 −1 ∙ 𝑎 ≤ −1 ∙ 𝑏 −𝑎 ≤ −𝑏 until you get 𝒊𝟐 which is – 𝟏. 𝑖= 𝑖 𝑖5 = 𝑖 2 𝑖 = −1 𝑖 6 = −1 3 𝑖 = −𝑖 𝑖 7 = −𝑖 4 𝑖 = 1 𝑖8 = 1 𝑥= (𝑥, 𝑦) ( ,0) (0, ) Graph Meter Conversions Gram kilo hecto deca UNIT deci 1000 100 10 1 0.1 1 𝑚𝑖 = 5280 𝑓𝑡 1 𝑙𝑏 = 16 𝑜𝑧 1 𝑔𝑎𝑙 = 4 𝑞𝑡 = 16 𝑐 9 𝐹 = 𝐶 + 32 5 Rev 2.0 Liter centi 0.01 milli 0.001 1 𝑚𝑖 = 1.61 𝑘𝑚 1 𝑙𝑏 = 0.45 𝑘𝑔 1 𝑔𝑎𝑙 = 3.79 𝐿 1 𝑠𝑞𝑓𝑡 = 0.09 𝑚2 4/17/2015