Level 3 Engineering Principles - Algebra Info and Equations Sheet

1. LEVEL 3 ENGINEERING PRINCIPLES - ALGEBRA INFORMATION & EQUATIONS Laws of Indices a?× a?= a(???) a? a?= a(???) (a?)?= a?? Laws of Logarithms log A + log B = log (AB) logA − logB = log?A B? log A?= n(log A) Exponential Growth and Decay 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 Growth a(t) = a(0)??? Exponential Decay a(t) = a(0)????

2. Quadratic Formula For equations of the form: ???+ ?? + ? = 0 Find both values of x using: ? =−? ± √(??− 4??) 2? Simultaneous Equations 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 Substitution 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 Procedure for Solving by Elimination