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Level 3 engineering principles algebra info and equations sheet
- 1. LEVEL 3 ENGINEERINGPRINCIPLES - ALGEBRA INFORMATION & EQUATIONS Laws of Indices a × a = a( ) a a = a( ) (a ) = a Laws of Logarithms log A + log B = log (AB) log A − log B = log A B log A = n(log A) Exponential Growth and Decay Exponential Growth a(t) = a(0)𝑒 a(t) = value after t time periods a(0) = value at time zero (initial value) k = rate of growth / decay, per time period t = number of time periods Exponential Decay a(t) = a(0)𝑒
- 2. Quadratic Formula For equationsof the form: 𝑎𝑥 + 𝑏𝑥 + 𝑐 = 0 Find both values of x using: 𝑥 = −𝑏 ± √(𝑏 − 4𝑎𝑐) 2𝑎 Simultaneous Equations Procedure for Solving by Substitution 1. Choose either equation 1 or equation 2 and rearrange to make x or y the subject. Label this as equation 3 2. Substitute equation 3 into the equation that WAS NOT used in the previous step, replacing either x or y. Label this as equation 4 3. Simplify equation 4 and solve for the only remaining variable (this will be x or y depending on the outcome of the previous steps) 4. Now you have a value for either x or y, you can find the remaining variable by inputting this into either equation 1 or 2 and solving Procedure for Solving by Elimination 1. To solve by elimination, the coefficient of x or y must be the same in both equations. To achieve this, multiply equation 1 or equation 2 by an appropriate number. Label this as equation 3 5. Subtract equation 3 from the equation that WAS NOT used in the previous step, eliminating either x or y. Label this as equation 4 2. Simplify equation 4 and solve for the only remaining variable (this will be x or y depending on the outcome of the previous steps) 3. Now you have a value for either x or y, you can find the remaining variable by inputting this into either equation 1 or 2 and solving