CIE – P3(1) June 2014

The worked solutions to this paper are given as written solutions (not as videos). I have generally put in more steps and stages than may be necessary on purpose so that you have some help and support through the solution.

I would encourage you try the question first and if stuck look at the tutorials and then try again and then if still stuck look at the worked solution.

• 1)

  
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  • Identities for sin2A, cos2A and tan2A
  1(i) 1(ii)

• 2)

  
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  • Integration by substitution
  • Integration of trigonometric functions by substitution
  

• 3)

  
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  • Differentiation: Parametric functions
  • Chain rule: Natural log types
  • The quotient rule
  

• 4)

  
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  • Differential Equations - Finding a general and a particular solution
  • Working with constants in log types
  • Integrating exponential functions e^x, e^ax and e^(ax+b)
  • Exponential and log equations
  

• 5)

  
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  • Division of a complex number by a complex number
  • Argand diagrams
  • Exponential Form (Euler's relation)
  (i) (ii)

• 6)

  
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  • Exponential and log equations
  • The factor theorem
  • Algebraic long division
  • How to solve a cubic equation
  (i) (ii) (iii)

• 7)

  
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  • Cartesian form of a plane
  • Shortest distance from a point to a plane
  (i) (ii) (iii)

• 8)

  
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  • Graphs of sec θ, cosec θ and cot θ
  • Iteration
  (i) (ii) (iii)(a) (iii)(b)

• 9)

  
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  • Partial fractions
  • Denominator contains 2 or 3 linear factors
  • Denominator contains repeated factors
  • Using partial fractions with the binomial expansion
  (i) (ii)

• 10)

  
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  • The product rule
  • Chain rule: Exponential types
  • Quadrant rule to solve trig equations
  (i) (ii)