maths unit2 HIGHER

• Curved Sketching:

  • find y intercepts (x=0)
  • find roots by synthetic division
  • find SP's by calculus, set =0 for x
  • use brackets and sub into equation
  • draw nature table ad find maximum
• Finding Coefficients of Polynomial:

  • use synthetic division and insert factors
  • use remainder and find subject of formula

  Multiple Factors

  • use synthetic division and insert factors
  • use simultaneous equation of remainders
  • find each value by subbing in
• Functions from Graphs:

  • note down roots
  • f(x)=k(roots)(roots) -> f(x)=y
  • sub in other given coordinate for k
  • sub in k for final equation
• Solving Polynomials:

  • use final numbers factors for potential function
  • use synthetic division, find factor
  • use factor and new bracket
  • factorise for x
• Factor Theorem:

  • use factor in synthetic division
  • if =0, its a factor

  Factorise fully

  • use factor and brackets to factorise fully

  No factorising

  • if you can't factorise use discriminant and explain why, since b^2 -4ac <0 it has no real roots
• Synthetic Division:

  • when told to evaluate an equation use synthetic table
  • f(x) is a factor
• Optimisation:

  • write general formula
  • sub in what we know
  • create an equation of what we want
  • find the subject of formula of unwanted
  • insert into equation and solve for final equation

  Minimum/Maximum

  • use final equation solved before
  • make sure no fractions
  • differentiate
  • =0 for SP's
  • solve for x by subject of formula
  • make nature table for min/max
  • work out missing components
• Trigonometry - Radians/Degrees:

  • pi radians= 180 degrees
  • a/b radians means divide 180 by b and multiply by a

  Degrees

  • subject of formula
  • divide by 180, multiply by degree
  • simplify
• Using Exact Values:

  • use CAST diagram
  • positive or negative
  • what quadrants
  • add or subtract

  With Radians

  • convert to degrees
  • use CAST diagram
• Trig Equations:

  • make sin(a)x subject of formula
  • period check (360/a)
  • this is the limit
  • use CAST diagram to find coordinates
  • divide by a
  • keep adding period until limit has been reached
• periods:

  • sin: 360
  • cos: 360
  • tan: 180
• Trig Equations - Radians:

  • subject of formula to sin/cos/tan
  • use exact value table and CAST diagram
  • after finding degrees, convert into radians
  • use exact value table for help
• Trig equations - Compound Angles:

  • divide by number before sin/cos/tan
  • use CAST diagram
  • add or subtract last number for x
  • period check (number before x)
  • add period until limit has been reached
  • convert into units
• Factorising to Solve:

  • convert to factorisation without sin/cos/tan
  • factorise normally
  • switch x with sin/cos/tan
  • solve for x
  • use CAST diagrams
• Trig Graphs:

  • y=(a)sin(b)x+(c)
  • a= add a to y from 0 (horisontal)
  • b= divide 360 by b
  • c= add c to y (verticle)
  • a being -ve flips graph
• Double Agent:

  • use formula sheet (sin2A=2sinAcosA ...)
  • sun in formula
  • factorise
  • solve for x, use CAST diagram
  • stay within limit

  Radians

  after solving for x. convert into radians, use exact value table for help