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Summary Grade 12 CAPS Mathematics Paper 2 Notes
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  • Course
  • Mathematics
  • Institution
  • 12

A summary of everything you need to know to ace the CAPS Grade 12 Maths Paper 2! The summary includes notes on trigonometry, statistics, analytical geometry and euclidean geometry.

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Document information

  • June 29, 2021
  • 5
  • 2020/2021
  • Summary

Subjects

  • maths
  • mathematics
  • math
  • pure maths
  • grade 12
  • matric
  • paper 2
  • geometry
  • analytical geometry
  • euclidean geometry
  • statistics
  • trigonometry
  • trig
  • trig graphs
  • trigonometric
  • caps
  • nsc
  • exams
  • south africa
  • exam
  • notes

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  • 12
  • Mathematics
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GRADE 12 MATHS PAPER 2

TRIGONOMETRY

Compound Angles: Double Angles:
sin(𝛼 + 𝛽) = sin 𝛼 cos 𝛽 + cos 𝛼 sin 𝛽 sin 2𝛼 = 2 sin 𝛼 cos 𝛼
sin(𝛼 − 𝛽) = sin 𝛼 cos 𝛽 − cos 𝛼 sin 𝛽 cos 2𝛼 = 1 − 2𝑠𝑖𝑛 2 𝛼
cos(𝛼 + 𝛽) = cos 𝛼 cos 𝛽 − sin 𝛼 sin 𝛽 cos 2𝛼 = 2𝑐𝑜𝑠 2 𝛼 − 1
cos(𝛼 − 𝛽) = cos 𝛼 cos 𝛽 + sin 𝛼 sin 𝛽

𝑂 𝐴 𝑂
𝑆=𝐻 𝐶=𝐻 𝑇=𝐴

Special Angles: Trig Rules:

𝑎 𝑏 𝑐
Sine rule: 𝑠𝑖𝑛𝐴 = 𝑠𝑖𝑛𝐵 = 𝑠𝑖𝑛𝐶

Cosine rule: 𝑎2 = 𝑏2 + 𝑐 2 − 2𝑏𝑐 ∙ 𝑐𝑜𝑠𝐴

1
Area rule: 𝐴𝑟𝑒𝑎∆𝐴𝐵𝐶 = 2 ∙ 𝑎𝑏 ∙ 𝑠𝑖𝑛𝐶



Reduction Formulae: Identities:

𝑠𝑖𝑛𝜃
𝑡𝑎𝑛𝜃 = 𝑐𝑜𝑠𝜃
𝑠𝑖𝑛 2 𝜃 + 𝑐𝑜𝑠 2 𝜃 = 1



Trig Graphs:

Move left/right:
sin(𝑥 ± 1) ; cos(𝑥 ± 1) ; tan (𝑥 ± 1)

Vertical stretch:
𝑎 ∙ 𝑠𝑖𝑛𝑥; 𝑎 ∙ 𝑐𝑜𝑠𝑥; 𝑎 ∙ 𝑡𝑎𝑛𝑥

Move up/down:
𝑠𝑖𝑛𝑥 ± 1; 𝑐𝑜𝑠𝑥 ± 1; 𝑡𝑎𝑛𝑥 ± 1

Change period:
𝑠𝑖𝑛𝑎(𝑥); 𝑐𝑜𝑠𝑎(𝑥); 𝑡𝑎𝑛𝑎(𝑥)

General Solutions:

𝑠𝑖𝑛: 𝑥 = ∠ + 𝑘. 360°
𝑜𝑟
𝑠𝑖𝑛: 𝑥 = 180° + ∠ + 𝑘. 360°; 𝑘 ∈ 𝑍

𝑐𝑜𝑠: 𝑥 = ±∠ + 𝑘. 360°; 𝑘 ∈ 𝑍

𝑡𝑎𝑛: 𝑥 = ∠ + 𝑘. 180°; 𝑘 ∈ 𝑍

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