Algebra, Module 1, Certify66

Simulation

Straight-Line Graphs & Simultaneous EquationsFull screen ↗

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Simulation

Quadratic Equations & the ParabolaFull screen ↗

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Simulation

Logarithms & Log ScalesFull screen ↗

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Notes

Main ideas

Transposing (rearranging) a formula isolates the quantity you need. Whatever operation you apply to one side, apply to the other, that is the whole rule.
Laws of indices let you combine powers without expanding them. A negative index means a reciprocal; a fractional index means a root.
Simultaneous equations solve for two unknowns from two equations, by substitution or by elimination.
A quadratic equation contains a squared term and generally has two solutions; the quadratic formula solves any of them.
Logarithms convert multiplication into addition and are the basis of decibel and other logarithmic scales used in avionics.
Binary and hexadecimal are the number systems behind digital aircraft systems, see Module 5 for their full treatment.

Key formulas

Laws of indices: aᵐ × aⁿ = aᵐ⁺ⁿ, aᵐ ÷ aⁿ = aᵐ⁻ⁿ, (aᵐ)ⁿ = aᵐⁿ
Negative & fractional index: a⁻ⁿ = 1 / aⁿ, a^(1/2) = √a, a⁰ = 1
Quadratic formula: x = [−b ± √(b² − 4ac)] / 2a
Log laws: log(ab) = log a + log b, log(a/b) = log a − log b, log(aⁿ) = n log a

Solved examples

Transpose V = IR to make R the subject.
Divide both sides by I: R = V / I. This is the form used whenever a resistance is calculated from a measured voltage and current.
Simplify (2x³)(3x⁴).
Multiply the coefficients and add the indices: 2 × 3 = 6 and x³⁺⁴ = x⁷, giving 6x⁷.
Solve x² − 5x + 6 = 0.
Factorising: (x − 2)(x − 3) = 0, so x = 2 or x = 3. Check with the formula: b² − 4ac = 25 − 24 = 1, x = (5 ± 1)/2 = 3 or 2. ✓

Algebra