Edvora/Mathematics

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Mathematics

Algebra, geometry, functions, statistics, and the habits that make multi-step problems manageable.

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CORE TOPICS

Build the foundation.

These are concise review notes—not a replacement for your course textbook or teacher’s instructions.

01

Linear equations

Isolate a variable by doing the same operation to both sides. For a line, slope is the rate of change and y = mx + b is slope-intercept form.

  • Slope: m = (y₂ − y₁) / (x₂ − x₁)
  • Slope-intercept form: y = mx + b
  • Check a solution by substituting it into the original equation.
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02

Systems of equations

A system asks for values that make every equation true at once. Use graphing, substitution, or elimination depending on the structure.

  • Graphing: the solution is an intersection point.
  • Substitution works well when one variable is already isolated.
  • Elimination works well when coefficients can cancel.
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03

Quadratics

Quadratic functions produce parabolas. Connect standard form, factoring, zeros, the vertex, and the quadratic formula.

  • Standard form: ax² + bx + c
  • Quadratic formula: x = (−b ± √(b² − 4ac)) / 2a
  • The discriminant b² − 4ac helps describe the real roots.
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04

Geometry essentials

Use definitions, diagrams, and relationships rather than memorizing isolated formulas.

  • Triangle angle sum: 180°
  • Pythagorean theorem: a² + b² = c² for right triangles
  • Circle area: A = πr²; circumference: C = 2πr
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05

Functions

A function maps each input to exactly one output. Read functions from equations, tables, graphs, and words.

  • Function notation: f(x)
  • Domain describes allowed inputs; range describes resulting outputs.
  • Transformations explain shifts, stretches, and reflections.
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06

Statistics & probability

Describe data before making claims from it. Separate center, spread, association, and chance.

  • Mean is sensitive to extreme values; median is more resistant.
  • Range and interquartile range describe spread.
  • Correlation alone does not prove causation.
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07

Right-triangle trigonometry

Sine, cosine, and tangent connect angles to side ratios in right triangles.

  • sin θ = opposite / hypotenuse
  • cos θ = adjacent / hypotenuse
  • tan θ = opposite / adjacent
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08

Problem-solving workflow

Translate the question, label what is known, choose a relationship, solve, then check whether the answer makes sense.

  • Write units during the calculation.
  • Estimate size or sign before finalizing.
  • If stuck, solve a simpler version first.
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