All Formulas

• What is the formula for percentage change?

  Percentage Change = (Change / Original) × 100
• How do you calculate the original value from a new value and percentage?

  Original Value = New Value / (1 ± (Percentage / 100))
• What is the formula for calculating lower and upper bounds?

  Lower Bound = Rounded Value − (Unit of Rounding / 2)
• What is the upper bound formula?

  Upper Bound = Rounded Value + (Unit of Rounding / 2)
• What is the law of indices for multiplying powers with the same base?

  $a^m \cdot a^n =$$a^{m+n}$
• What is the law of indices for dividing powers with the same base?

  $\frac{a^m}{a^n} =$$a^{m-n}$
• What is the law of indices for raising a power to another power?

  $(a^m)^n =$$a^{mn}$
• What is the value of any number raised to the power of zero?

  $a^0 =$$1$
• What is the law of indices for negative powers?

  $a^{-n} =$$\frac{1}{a^{n}}$
• What is the formula for the equation of a straight line?

  y = mx + c
• What does 'm' represent in the equation of a straight line?

  'm' is the gradient of the line
• What does 'c' represent in the equation of a straight line?

  'c' is the y-intercept of the line
• What is the condition for the gradients of parallel lines?

  Gradient of parallel lines: m1 = m2
• What is the condition for the gradients of perpendicular lines?

  Product of gradients: m1 × m2 = -1
• What is the quadratic formula?

  $x =$$\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
• How do you calculate the gradient of a line from two points?

  m = $\frac{change\ in\ y}{change\ in\ x}$
• What is the formula for inverse proportion?

  y = k divided by x
• What is the formula for direct proportion?

  y = kx
• What is the formula for speed?

  Speed = Distance / Time
• What is the formula for distance?

  Distance = Speed × Time
• What is the formula for time?

  Time = Distance / Speed
• What is the formula for density?

  Density = Mass / Volume
• What is the formula for pressure?

  Pressure = Force / Area
• What is the formula for the circumference of a circle?

  Circumference = 2πr or πd
• What is the formula for the area of a circle?

  Area = πr²
• What is the formula for the area of a trapezium?

  Area = (1/2) × (a + b) × h
• What is the formula for the volume of a prism?

  Volume = Area of Cross-Section × Length
• What is the formula for the surface area of a cylinder?

  Surface area = 2πrh + 2πr²
• What is the formula for the volume of a sphere?

  Volume = (4/3)πr³
• What is the formula for the surface area of a sphere?

  Surface Area = 4πr²
• What is the formula for the volume of a cone?

  Volume = (1/3)πr²h
• What is the formula for the surface area of a cone?

  Surface Area = πr² + πrl
• What is the formula for the area of a sector?

  Area = (θ / 360) × πr²
• What is the formula for arc length?

  Arc Length = (θ / 360) × 2πr
• What is Pythagoras’ Theorem?

  $a^2 +$$b^2 =$$c^2$
• What are the trigonometric ratios for sine, cosine, and tangent?

  sin(A) = Opposite / Hypotenuse
• What is the cosine ratio?

  cos(A) = Adjacent / Hypotenuse
• What is the tangent ratio?

  tan(A) = Opposite / Adjacent
• What is the sine rule?

  $\frac{a}{\sin(A)} =$$\frac{b}{\sin(B)} =$$\frac{c}{\sin(C)}$
• What is the cosine rule?

  $a^2 =$$b^2 +$$c^2 - 2bc \cdot \cos(A)$