https://engineers.academy/product/l3-nd-engineering-principles-exam-preparation/ 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)
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 equations of 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