Maths

• Gradient


  The slope of a line, calculated as the change in y over the change in x
• Finding the gradient


  1. Given two points (x1, y1) and (x2, y2)

  2. Calculate m = (y2 - y1) / (x2 - x1)
• General straight line equation

  y - b = m(x - a)
• m is the gradient of the line
• b is the coordinate of a point on the line
• a is the coordinate of the same point
• Expanding the equation


  1. y - 6 = 5(x - 7)

  2. y = 5x - 35 + 6

  3. y = 5x - 29
• Simplifying the equation


  1. y - 2 = 3(x - 3)

  2. y - 2 = 3x - 9

  3. y = 3x - 7
• Interquartile Range (IQR)


  The difference between the third quartile (Q3) and the first quartile (Q1)
• Q3 - Q1 = IQR
• Q1 = 8
• Q3 = 16
• IQR = 16 - 8 = 8
• Median (Q2) = 12
• Equation of a straight line

  • y=-2x-1
  • y=-3x+2
  • y=4-3x
  • y=2x-4
  • y=3-15
• Finding the equation of a straight line


  1. Identify gradient

  2. Identify y-intercept

  3. Use point-slope form

  4. Rearrange to slope-intercept form
• Slope-intercept form


  • y=mx+c
  • m is the gradient
  • c is the y-intercept
• Lines with the same gradient are parallel
• Gradient (m) is calculated as m=(y2-y1)/(x2-x1)
• Volume of a cone is calculated using the formula V=(1/3)πr²h
• Evaluate expressions by substituting values into the equation
• To solve equations, isolate the variable on one side
• Evaluate expressions like -4m² + 26 by substituting the value of m
• Evaluate expressions like 36m + 6 when m is substituted
• Equation of a straight line can be found using two points
• Example of rearranging straight line equations is y=mx+c
• Example of evaluating an expression is 2 + b when b=7
• Example of evaluating an expression is 3a + 2 = 5
• Example of evaluating an expression is 3x7x(-2) - 72
• Example of evaluating an expression is -4x(-3) + 2x7
• Example of evaluating an expression is 9 - 4x
• Example of evaluating an expression is 5y
• Example of evaluating an expression is 2x4 + 7
• Example of evaluating an expression is 8 + 7
• Example of evaluating an expression is -16 + 14
• Example of evaluating an expression is -42 + 49
• Example of evaluating an expression is 6.28 nm³
• Solving inequalities is done the same way as equations
• When dividing by a negative

  You must flip the sign
• Changing the subject of a formula

  Isolate the variable on its own