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Summary Flashcards of Key Equations for Pure Mathematics A-Level (year 2) $8.41   Add to cart
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Summary Flashcards of Key Equations for Pure Mathematics A-Level (year 2)
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  • Course
  • A-Level
  • Institution
  • PEARSON (PEARSON)
  • Book
  • Edexcel A level Mathematics Pure Mathematics Year 2 Textbook e-book

This document outlines the key equations necessary for the Pure Mathematics (year 2 only) (Pearson Edexcel) course. Note that the specification may be subject to change in the future, meaning these notes may or may not have all the required information.

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  • No
  • Key equations
  • September 4, 2024
  • 1
  • 2021/2022
  • Summary

Subjects

  • edexcel
  • maths
  • mathematics
  • year 2
  • a level
  • as level
  • key equations
  • flashcards
  • pearson

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  • Brief Overview / Summary Sheets for part of Year 2 Pire (NOT YET COMPLETED)
  • Edexcel a Level Pure Mathematics 2024 Paper 2
  • Edexcel A level Pure Mathematics 2023 Pure Paper 2
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  • PEARSON (PEARSON)
  • Pure Mathematics
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TRIG DIFFERENTIATION DIFFERENTIATION DIFFERENTIATION DIFFERENTIATION
𝑎 sin 𝑥 ± 𝑏 cos 𝑥 →
𝑅 sin(𝑥 ± 𝑎) 𝑦 = ln 𝑥 𝑦 = 𝑎𝑘𝑥 𝑦 = 𝑎𝑥 Chain
𝑎 cos 𝑥 ± 𝑏 sin 𝑥 → 𝑑𝑦 1 𝑑𝑦 𝑑𝑦 𝑑𝑦 𝑑𝑦 𝑑𝑣
= ×1 = 𝑎𝑘𝑥 𝑘𝑙𝑛 𝑎 = 𝑎 𝑥 ln 𝑎 = ×
𝑅 cos (𝑥 ∓ 𝑎) 𝑑𝑥 𝑥 𝑑𝑥 𝑑𝑥 𝑑𝑥 𝑑𝑢 𝑑𝑥


DIFFERENTIATION DIFFERENTIATION DIFFERENTIATION DIFFERENTIATION DIFFERENTIATION
S
Product Quotient: 𝑓 (𝑥) = cos 𝑘𝑥 𝑓 (𝑥) = sin 𝑘𝑥
𝑑𝑦 𝑑𝑣 𝑑𝑢 𝑑𝑢 𝑑𝑣 -C C
=𝑢 + 𝑣 𝑑𝑦 𝑣 −𝑢 𝑓 ′(𝑥) = −𝑘𝑠𝑖𝑛 𝑘𝑥 𝑓 ′(𝑥) = 𝑘𝑐𝑜𝑠 𝑘𝑥
𝑑𝑥 𝑑𝑥 𝑑𝑥 = 𝑑𝑥 2 𝑑𝑥
𝑑𝑥 𝑣 -S

DIFFERENTIATION INTEGRATION INTEGRATION INTEGRATION VECTORS

Concave: 𝑓 ′′(𝑥) ≤ 0 Distance from origin to
Convex: 𝑓 ′′ (𝑥) ≥ 0 (𝑥, 𝑦, 𝑧) is
Point of inflection: 𝑓 ′′ (𝑥)
√𝑥 2 + 𝑦 2 + 𝑧 2
changes sign


VECTORS VECTORS

𝑝 𝑎 = 𝑥𝑖 + 𝑦𝑗 + 𝑧𝑘 makes
𝑝𝑖 + 𝑞𝑗 + 𝑟𝑘 = 𝑞 an angle with the positive
𝑥
𝑟 x-axis then 𝑐𝑜𝑠𝜃𝑥 = |𝑎|
Same for y and z

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