LEVEL 3 ENGINEERING PRINCIPLES - ALGEBRA INFORMATION & EQUATIONS Laws of Indices
a Ă— 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
Exponential Decay
a(t) = value after t time periods
a(t) = a(0)đ?‘’
a(0) = value at time zero (initial value) k = rate of growth / decay, per time period
a(t) = a(0)đ?‘’
t = number of time periods
Quadratic Formula For equations of the form:
đ?‘Žđ?‘Ľ + đ?‘?đ?‘Ľ + đ?‘? = 0 Find both values of x using:
đ?‘Ľ=
−đ?‘? Âą √(đ?‘? − 4đ?‘Žđ?‘?) 2đ?‘Ž
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