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2
P2 · Pure Mathematics 2
- 2.5.2 Pure Mathematics 2: building on the P1 toolkit
- 2.1.1 2.1.2 2.1.3 Proof
- 2.2.1 Algebra: the factor and remainder theorems
- 2.3.1 Coordinate geometry of the circle
- 2.4.1 2.4.2 2.4.3 2.4.4 2.4.5 Sequences and series
- 2.5.1 2.5.2 2.5.3 Exponentials and logarithms
- 2.6.1 2.6.2 Trigonometric identities and equations
- 2.7.1 Differentiation: stationary points
- 2.8.1 2.8.2 2.8.3 Integration: areas and the trapezium rule
- 2.8.1 2.8.2 2.8.3 Checklist before you call this unit done
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3
P3 · Pure Mathematics 3
- 3.2.3 순수 수학 3: 속도로 배우는 함수, 항등식 및 미적분학
- 3.1.1 3.1.2 Algebra: rational expressions and functions
- 3.1.3 3.1.4 절댓값 함수와 합성 변환
- 3.2.1 3.2.2 3.2.3 추가 삼각함수: sec, cosec, cot 및 조화형
- 3.3.1 3.3.2 3.3.3 지수함수, 로그 및 로그-그래프 모델
- 3.4.1 3.4.2 3.4.3 3.4.4 미분: 규칙, 암미분 및 모델
- 3.5.1 3.5.2 적분: 표준 형태 및 식별
- 3.6.1 3.6.2 수치 해석법: 부호 변화와 반복법
- 3.6.1 3.6.2 이 단원을 완료하기 전 체크리스트
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4
P4 · Pure Mathematics 4
- 4.4.1 Pure Mathematics 4: proof, parametrics and the full calculus
- 4.1.1 Proof by contradiction
- 4.2.1 Partial fractions
- 4.3.1 Parametric equations
- 4.4.1 The binomial series for any rational n
- 4.5.1 Implicit and parametric differentiation
- 4.5.2 4.6.4 Differential equations and connected rates
- 4.6.2 4.6.3 Integration: substitution, parts and partial fractions
- 4.6.1 4.6.5 Volumes of revolution and parametric areas
- 4.7.1 4.7.2 4.7.3 4.7.4 4.7.5 4.7.6 4.7.7 Vectors
- 4.7.1 4.7.2 4.7.3 4.7.4 4.7.5 4.7.6 4.7.7 Checklist before you call this unit done
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5
FP1 · Further Pure Mathematics 1
- 1.4.1 Further Pure Mathematics 1: complex numbers, matrices and proof
- 1.1.1 1.1.2 1.1.3 1.1.4 Complex numbers
- 1.1.5 1.1.6 Complex roots of polynomials
- 1.2.1 1.2.2 1.2.3 Roots of quadratic equations
- 1.3.1 Numerical solution of equations
- 1.4.1 1.4.2 1.4.3 1.4.4 Parabola and rectangular hyperbola
- 1.5.1 1.5.2 1.5.3 1.5.4 1.5.5 Matrix algebra
- 1.6.1 1.6.2 1.6.3 1.6.4 Transformations using matrices
- 1.7.1 Series
- 1.8.1 Proof by mathematical induction
- 1.8.1 Checklist before you call this unit done
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FP2 · Further Pure Mathematics 2
- 2.1.1 Further Pure Mathematics 2: inequalities, further complex numbers and differential equations
- 2.1.1 Inequalities involving the modulus sign
- 2.2.1 The method of differences
- 2.3.1 2.3.2 Euler's relation and de Moivre's theorem
- 2.3.3 2.3.4 Loci, regions and z→w transformations
- 2.4.1 2.4.2 2.4.3 First order differential equations
- 2.5.1 2.5.2 Second order differential equations
- 2.6.1 2.6.2 2.6.3 2.6.4 Maclaurin and Taylor series
- 2.7.1 2.7.1#occurrence2 Polar coordinates and areas
- 2.7.1 2.7.1#occurrence2 Checklist before you call this unit done
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7
FP3 · Further Pure Mathematics 3
- 3.1.1 Further Pure Mathematics 3: hyperbolic functions, conics, vectors and matrices
- 3.1.1 Hyperbolic functions
- 3.1.2 Inverse hyperbolic functions
- 3.2.1 3.2.2 The ellipse and the hyperbola
- 3.2.3 3.2.4 Tangents, normals and loci
- 3.3.1 3.3.2 Differentiating hyperbolic and inverse functions
- 3.4.1 3.4.2 Integrating hyperbolic and inverse functions
- 3.4.3 3.4.4 3.4.5 3.4.6 Substitutions, reduction formulae and surfaces of revolution
- 3.5.1 3.5.2 3.5.3 Vectors: products, lines and planes
- 3.6.1 3.6.2 3.6.3 3.6.4 3.6.5 3.6.6 3.6.7 3.6.8 Further matrix algebra
- 3.6.1 3.6.2 3.6.3 3.6.4 3.6.5 3.6.6 3.6.7 3.6.8 Checklist before you call this unit done
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