Useful Equations

Perimeter, Area, and Volume

  • \( \text{Area of a rectangle} = b \times h \)
  • \( \text{Area of a triangle} = \frac{1}{2} × b × h \)
  • \( \text{Area of a trapezium} = \frac{1}{2}(a + b)h \)
  • \( \text{Volume of a prism = A × L} \)
  • \( \text{Volume of a pyramid} = \frac{1}{3} × b × h \)
  • \( \text{Circumference of a circle} = 2\pi r = \pi d \)
  • \( \text{Area of a circle} = \pi r^2 \)
  • \( \text{Volume of a cylinder} = \pi r^2 × h \)

Quadratic formula

The solution of ax² + bx + c = 0 where a ≠ 0:

\( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \)

Proportion, Percentages

  • \( \text{Direct proportion} = x = k × y \)
  • \( \text{Inverse proportion} = x = \frac{k}{y} \)
  • \( \text{Compund Interest} = P(1 + \frac{r}{100})^n \)

Pythagoras and Trigonometry

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  • \( \text{Pythagoras Theorem} = a^2 + b^2 = c^2 \)
  • \( \text{Trigonometry} = S\frac{o}{h} C\frac{a}{h} T\frac{o}{a} \)
  • \( \text{Sine Rule} = \frac{a}{sinA} = \frac{b}{sinB} = \frac{c}{sinC} \)
  • \( \text{Cosine Rule} = a^2 = b^2 + c^2 - 2(b)(c)cosA \)
  • \( \text{Area of a triangle} = \frac{1}{2} a × b × sinC \)

Compund Measures

  • \( \text{speed} = \frac{distance}{time} \)
  • \( \text{density} = \frac{mass}{volume} \)
  • \( \text{pressure} = \frac{force}{area} \)

Angles

  • \( \text{Interior angle} = \frac{(n-2)×180}{n} \)
  • \( \text{Exterior angle} = \frac{360}{n} \)