• IB
  • IB Docs (2) Team
    Logout
  • Maths
  • Biology
  • Chemistry
  • Physics
  • Combined Science
  • English Language
  • Geography
  • Other Subjects
GCSE Maths
Edexcel Topic QuestionsRevision NotesPast PapersPast Papers Questions
AQA Topic QuestionsRevision NotesPast Papers
OCR Topic QuestionsRevision NotesPast Papers
GCSE Biology
Edexcel Topic QuestionsRevision NotesPast Papers
AQA Topic QuestionsRevision NotesPast Papers
OCR Gateway Topic QuestionsRevision NotesPast Papers
GCSE Chemistry
Edexcel Topic QuestionsRevision NotesPast Papers
AQA Topic QuestionsRevision NotesPast Papers
OCR Gateway Topic QuestionsRevision NotesPast Papers
GCSE Physics
Edexcel Topic QuestionsRevision NotesPast Papers
AQA Topic QuestionsRevision NotesPast Papers
OCR Gateway Topic QuestionsRevision NotesPast Papers
GCSE Combined Science
Edexcel Combined: Biology Topic QuestionsRevision NotesPast Papers
Edexcel Combined: Chemistry Topic QuestionsRevision NotesPast Papers
Edexcel Combined: Physics Revision NotesPast Papers
AQA Combined: Biology Topic QuestionsRevision NotesPast Papers
AQA Combined: Chemistry Topic QuestionsRevision NotesPast Papers
AQA Combined: Physics Topic QuestionsRevision NotesPast Papers
OCR Gateway Combined: Biology Topic QuestionsRevision Notes
OCR Gateway Combined: Chemistry Revision Notes
OCR Gateway Combined: Physics Revision Notes
GCSE English Language
AQA Revision NotesPractice PapersPast Papers
Edexcel Past Papers
OCR Past Papers
GCSE Geography
AQA Topic QuestionsRevision Notes
Edexcel Topic Questions
GCSE Other Subjects
AQA English LiteratureBusinessComputer ScienceEconomicsFurther MathsGeographyHistoryPsychologySociologyStatistics
Edexcel English LiteratureBusinessComputer ScienceGeographyHistoryPsychologyStatistics
OCR English LiteratureBusinessComputer ScienceEconomicsPsychology
OCR Gateway GeographyHistory
  • Maths
  • Biology
  • Chemistry
  • Physics
  • Double Science
  • Economics
  • English Language
  • Geography
  • Other Subjects
IGCSE Maths
Edexcel Topic QuestionsRevision NotesPast PapersBronze-Silver-Gold Questions
CIE (Extended) Topic QuestionsRevision NotesPast Papers
CIE (Core) Topic QuestionsPast Papers
IGCSE Biology
Edexcel Topic QuestionsRevision NotesPast Papers
CIE 2020-2022 Topic QuestionsRevision NotesPast Papers
CIE 2023-2025 Topic QuestionsRevision NotesPast Papers
IGCSE Chemistry
Edexcel Topic QuestionsRevision NotesPast Papers
CIE 2020-2022 Topic QuestionsRevision NotesPast Papers
CIE 2023-2025 Topic QuestionsRevision NotesPast Papers
IGCSE Physics
Edexcel Topic QuestionsRevision NotesPast Papers
CIE 2020-2022 Topic QuestionsRevision NotesPast Papers
CIE 2023-2025 Topic QuestionsRevision NotesPast Papers
IGCSE Double Science
Edexcel Double: Biology Topic QuestionsRevision NotesPast Papers
Edexcel Double: Chemistry Topic QuestionsRevision NotesPast Papers
Edexcel Double: Physics Topic QuestionsRevision NotesPast Papers
IGCSE Economics
CIE Topic QuestionsRevision NotesPast Papers
IGCSE English Language
CIE Revision NotesPractice PapersPast Papers
Edexcel Past Papers
IGCSE Geography
CIE Revision NotesTopic QuestionsPast Papers
Edexcel Topic QuestionsRevision NotesPast Papers
IGCSE Other Subjects
CIE Additional MathsEnglish LiteratureBusinessComputer ScienceHistorySociology
Edexcel English LiteratureBusinessComputer ScienceHistoryFurther Maths
  • Maths
  • Biology
  • Chemistry
  • Physics
  • English Language
  • Other Subjects
AS Maths
Edexcel Pure MathsMechanicsStatistics
AQA Pure MathsMechanicsStatistics
OCR Pure MathsMechanicsStatistics
CIE Pure 1Pure 2MechanicsProbability & Statistics 1
Edexcel IAS Pure 1Pure 2MechanicsStatistics
AS Biology
AQA Topic QuestionsRevision NotesPast Papers
OCR Topic QuestionsRevision NotesPast Papers
CIE 2019-2021 Topic QuestionsRevision NotesPast Papers
CIE 2022-2024 Topic QuestionsRevision NotesPast Papers
Edexcel IAL Revision Notes
AS Chemistry
Edexcel Revision Notes
AQA Topic QuestionsRevision NotesPast Papers
OCR Revision Notes
CIE 2019-2021 Topic QuestionsRevision NotesPast Papers
CIE 2022-2024 Topic QuestionsRevision NotesPast Papers
Edexcel IAL Revision Notes
AS Physics
Edexcel Revision Notes
AQA Topic QuestionsRevision NotesPast Papers
OCR Revision NotesPast Papers
CIE 2019-2021 Topic QuestionsRevision NotesPast Papers
CIE 2022-2024 Topic QuestionsRevision NotesPast Papers
Edexcel IAL Revision Notes
AS English Language
AQA Past Papers
Edexcel Past Papers
OCR Past Papers
AS Other Subjects
AQA BusinessComputer ScienceEconomicsEnglish LiteratureFurther MathsGeographyHistoryPsychologySociology
Edexcel BusinessEconomicsEnglish LiteratureFurther MathsGeographyHistoryPsychology
OCR BusinessComputer ScienceEconomicsEnglish LiteratureFurther Maths AGeographyHistoryPsychologySociology
CIE Further Maths
  • Maths
  • Biology
  • Chemistry
  • Physics
  • English Language
  • Economics
  • Further Maths
  • Psychology
  • Other Subjects
A Level Maths
Edexcel Pure MathsMechanicsStatistics
AQA Pure MathsMechanicsStatistics
OCR Pure MathsMechanicsStatistics
CIE Pure 1Pure 3MechanicsProbability & Statistics 1Probability & Statistics 2
Edexcel IAL Pure 1Pure 2Pure 3Pure 4Mechanics 1Mechanics 2Statistics 1Statistics 2Decision 1
A Level Biology
Edexcel Topic QuestionsPast Papers
Edexcel A (SNAB) Revision Notes
AQA Topic QuestionsRevision NotesPast Papers
OCR Topic QuestionsRevision NotesPast PapersGold Questions
CIE 2019-2021 Topic QuestionsRevision NotesPast Papers
CIE 2022-2024 Topic QuestionsRevision NotesPast Papers
Edexcel IAL Topic QuestionsRevision NotesPast Papers
A Level Chemistry
Edexcel Topic QuestionsRevision NotesPast Papers
AQA Topic QuestionsRevision NotesPast Papers
OCR Topic QuestionsRevision NotesPast PapersGold Questions
CIE 2019-2021 Topic QuestionsRevision NotesPast Papers
CIE 2022-2024 Topic QuestionsRevision NotesPast Papers
Edexcel IAL Topic QuestionsRevision NotesPast Papers
A Level Physics
Edexcel Topic QuestionsRevision NotesPast Papers
AQA Topic QuestionsRevision NotesPast Papers
OCR Topic QuestionsRevision NotesPast Papers
CIE 2019-2021 Topic QuestionsRevision NotesPast Papers
CIE 2022-2024 Topic QuestionsRevision NotesPast Papers
Edexcel IAL Topic QuestionsRevision NotesPast Papers
A Level English Language
AQA Past Papers
CIE Past Papers
Edexcel Past Papers
OCR Past Papers
Edexcel IAL Past Papers
A Level Economics
Edexcel Topic QuestionsRevision NotesPast Papers
AQA Topic QuestionsPast Papers
OCR Past Papers
CIE Past Papers
A Level Further Maths
Edexcel Topic QuestionsRevision NotesPast Papers
AQA Past Papers
OCR Past Papers
CIE Past Papers
Edexcel IAL Past Papers
A Level Psychology
AQA Topic QuestionsRevision NotesPast Papers
CIE Past Papers
Edexcel Past Papers
OCR Past Papers
Edexcel IAL Past Papers
A Level Other Subjects
AQA BusinessComputer ScienceEconomicsEnglish LiteratureGeographyHistorySociology
CIE BusinessComputer ScienceEconomicsEnglish LiteratureGeographySociology
Edexcel BusinessEconomics AEnglish LiteratureGeographyHistory
OCR BusinessComputer ScienceEconomicsEnglish LiteratureGeographyHistorySociology
Edexcel IAL English LiteratureGeography
CIE IAL History
  • Biology
  • Chemistry
  • Physics
  • Other Subjects
O Level Biology
CIE Topic QuestionsPast Papers
O Level Chemistry
CIE Topic QuestionsPast Papers
O Level Physics
CIE Topic QuestionsPast Papers
O Level Other Subjects
CIE Additional MathsMaths D
  • Maths
  • Biology
  • Chemistry
  • Physics
Pre U Maths
CIE Topic QuestionsPast Papers
Pre U Biology
CIE Topic QuestionsPast Papers
Pre U Chemistry
CIE Topic QuestionsPast Papers
Pre U Physics
CIE Topic QuestionsPast Papers
  • Maths
  • Biology
  • Chemistry
  • Physics
  • Economics
IB Maths
Maths: AA HL Topic QuestionsRevision NotesPractice Papers
Maths: AI HL Topic QuestionsRevision NotesPractice Papers
Maths: AA SL Topic QuestionsRevision NotesPractice Papers
Maths: AI SL Topic QuestionsRevision NotesPractice Papers
IB Biology
Biology: SL Topic QuestionsRevision NotesPractice Papers
Biology: HL Topic QuestionsRevision NotesPractice Papers
IB Chemistry
Chemistry: SL Topic QuestionsRevision NotesPractice Papers
Chemistry: HL Topic QuestionsRevision NotesPractice Papers
IB Physics
Physics: SL Topic QuestionsRevision NotesPractice Papers
Physics: HL Topic QuestionsRevision NotesPractice Papers
IB Economics
Economics: SL Revision Notes

DP IB Maths: AI HL

Revision Notes

Home / IB / Maths: AI HL / DP / Revision Notes / 1. Number & Algebra / 1.4 Financial Applications / 1.4.2 Amortisation & Annuities


1.4.2 Amortisation & Annuities


Amortisation

What is amortisation?

  • Amortisation is the process of repaying a loan over a fixed period of time
    • Most commonly questions will be about mortgages (loans taken out to buy a home) or loans taken out for a large purchase
  • Interest will be paid on the original amount
    • Each repayment that is made will partly repay the original loan and partly pay the interest on the loan
    • As payments are made the amount owed will decrease and so the interest paid will decrease
      • As you continue to repay a loan more of the repayment goes on the loan and less on the interest

How can the GDC be used to make calculations involving loans?

  • Your GDC should be used to solve questions involving loans
    • Use the finance solver mode (sometimes called the TVM (time value of money) solver)
      • N will be the number of repayment periods (remember to include months and years if necessary)
      • I (%) is the interest rate
      • PV is the amount that was borrowed at the start – as this has been received it will be entered as a positive number
      • PMT is the payments made per period – this is repaying the loan so will be a negative number
      • FV is the future value (this will be zero as the loan will be paid off at the end of the period)
      • P/Y is the number of payments per year, usually 12 as payments are made monthly
      • C/Y is the compounding periods per year
      • PMT@ is the time of the year or month the payment is made (assume this is the end unless told otherwise)
    • Leave the section that you need to find out blank and fill in all other sections
    • Your GDC will fill in the last part for you
  • It is sensible to check your final answer, you can do this by finding the total amount paid back overall and comparing it to the original loan
    • The total amount repaid will be a little more than the original loan plus I % of the original loan

Exam Tip

  • Be sure to write down the values that you put into the financial solver on your GDC, don't just write down the final answer as if it is incorrect you won't get any marks if there is no working shown!
  • Make sure that you are clear on what the signage of any monetary value is, if it's positive then money is coming in to you, if it's negative then you are paying money out

Worked Example

Olivia takes a mortgage of EUR €280 000 to purchase a house at a nominal annual interest rate of 3.2%, compounded monthly. She agrees to pay the bank EUR €1500 at the end of every month to amortise the loan. Find

i)
the number of years and months it will take Olivia to pay back the loan,
ai-sl-1-3-2-annuities-we1

 

ii)
the total amount Olivia will pay to purchase the house.

ai-sl-1-3-2-amortisation-we-ii

Annuities

What is an annuity?

  • An annuity is a fixed sum of money paid to someone at specified intervals over a fixed period of time
    • Most commonly this will be because of an initial lump sum investment which will be returned at fixed intervals of time with a fixed interest rate
    • Either from personal savings or from receiving an inheritance

How are annuities calculated?

  • Your GDC should be used to solve questions involving annuities
    • Use the finance solver mode (sometimes called the TVM (time value of money) solver)
      • N will be the number of payment periods (remember to include months and years if necessary)
      • I (%) is the interest rate
      • PV is the amount that was invested – as this has been invested it will be entered as a negative number
      • PMT is the amount paid per period – as this is being received it will be a positive number
      • FV is the future value (for an annuity this will be zero as the balance at the end of the payment period will be zero)
      • P/Y is the number of payments per year
      • C/Y is the compounding periods per year
      • PMT@ is the time of the year or month the payment is made (usually the start)
    • Leave the section that you need to find out blank and fill in all other sections
    • Your GDC will fill in the last part for you
  • Although you are unlikely to need to use it, the formula for calculating an annuity is:

F V equals A fraction numerator left parenthesis 1 plus r to the power of n right parenthesis minus 1 over denominator r end fraction

    • Where
      • FV is the future value
      • A is the amount invested
      • n is the number of years
      • r% is the interest rate
    • This formula is not given in the formula booklet, however your GDC will work out annuities for you so you do not need to remember it

Exam Tip

  • Be sure to write down the values that you put into the financial solver on your GDC, don't just write down the final answer as if it is incorrect you won't get any marks if there is no working shown!
  • Try to remember the difference between amortization and annuities:
    • with amortization you are paying money out
    • with annuities you are receiving money

Worked Example

Janni invests 2 million DKK (Danish krone) into an annuity for her retirement. The annuity returns 3% compounded annually. Find the monthly payments Janni will receive if she wants the annuity to last for 25 years.

ai-sl-1-3-2-amortisation-we-i



  • 1. Number & Algebra
    • 1.1 Number Toolkit
      • 1.1.1 Standard Form
        • 1.1.2 Approximation & Estimation
          • 1.1.3 GDC: Solving Equations
          • 1.2 Exponentials & Logs
            • 1.2.1 Exponents
              • 1.2.2 Logarithms
              • 1.3 Sequences & Series
                • 1.3.1 Language of Sequences & Series
                  • 1.3.2 Arithmetic Sequences & Series
                    • 1.3.3 Geometric Sequences & Series
                      • 1.3.4 Applications of Sequences & Series
                      • 1.4 Financial Applications
                        • 1.4.1 Compound Interest & Depreciation
                          • 1.4.2 Amortisation & Annuities
                          • 1.5 Complex Numbers
                            • 1.5.1 Intro to Complex Numbers
                              • 1.5.2 Modulus & Argument
                                • 1.5.3 Introduction to Argand Diagrams
                                • 1.6 Further Complex Numbers
                                  • 1.6.1 Geometry of Complex Numbers
                                    • 1.6.2 Forms of Complex Numbers
                                      • 1.6.3 Applications of Complex Numbers
                                      • 1.7 Matrices
                                        • 1.7.1 Introduction to Matrices
                                          • 1.7.2 Operations with Matrices
                                            • 1.7.3 Determinants & Inverses
                                              • 1.7.4 Solving Systems of Linear Equations with Matrices
                                              • 1.8 Eigenvalues & Eigenvectors
                                                • 1.8.1 Eigenvalues & Eigenvectors
                                                  • 1.8.2 Applications of Matrices
                                                • 2. Functions
                                                  • 2.1 Linear Functions & Graphs
                                                    • 2.1.1 Equations of a Straight Line
                                                    • 2.2 Further Functions & Graphs
                                                      • 2.2.1 Functions
                                                        • 2.2.2 Graphing Functions
                                                          • 2.2.3 Properties of Graphs
                                                          • 2.3 Modelling with Functions
                                                            • 2.3.1 Linear Models
                                                              • 2.3.2 Quadratic & Cubic Models
                                                                • 2.3.3 Exponential Models
                                                                  • 2.3.4 Direct & Inverse Variation
                                                                    • 2.3.5 Sinusoidal Models
                                                                      • 2.3.6 Strategy for Modelling Functions
                                                                      • 2.4 Functions Toolkit
                                                                        • 2.4.1 Composite & Inverse Functions
                                                                        • 2.5 Transformations of Graphs
                                                                          • 2.5.1 Translations of Graphs
                                                                            • 2.5.2 Reflections of Graphs
                                                                              • 2.5.3 Stretches of Graphs
                                                                                • 2.5.4 Composite Transformations of Graphs
                                                                                • 2.6 Further Modelling with Functions
                                                                                  • 2.6.1 Properties of Further Graphs
                                                                                    • 2.6.2 Natural Logarithmic Models
                                                                                      • 2.6.3 Logistic Models
                                                                                        • 2.6.4 Piecewise Models
                                                                                      • 3. Geometry & Trigonometry
                                                                                        • 3.1 Geometry Toolkit
                                                                                          • 3.1.1 Coordinate Geometry
                                                                                            • 3.1.2 Radian Measure
                                                                                              • 3.1.3 Arcs & Sectors
                                                                                              • 3.2 Geometry of 3D Shapes
                                                                                                • 3.2.1 3D Coordinate Geometry
                                                                                                  • 3.2.2 Volume & Surface Area
                                                                                                  • 3.3 Trigonometry
                                                                                                    • 3.3.1 Pythagoras & Right-Angled Triganometry
                                                                                                      • 3.3.2 Non Right-Angled Trigonometry
                                                                                                        • 3.3.3 Applications of Trigonometry & Pythagoras
                                                                                                        • 3.4 Further Trigonometry
                                                                                                          • 3.4.1 The Unit Circle
                                                                                                            • 3.4.2 Simple Identities
                                                                                                              • 3.4.3 Solving Trigonometric Equations
                                                                                                              • 3.5 Voronoi Diagrams
                                                                                                                • 3.5.1 Voronoi Diagrams
                                                                                                                  • 3.5.2 Toxic Waste Dump Problem
                                                                                                                  • 3.6 Matrix Transformations
                                                                                                                    • 3.6.1 Matrix Transformations
                                                                                                                      • 3.6.2 Determinant of a Transformation Matrix
                                                                                                                      • 3.7 Vector Properties
                                                                                                                        • 3.7.1 Introduction to Vectors
                                                                                                                          • 3.7.2 Position & Displacement Vectors
                                                                                                                            • 3.7.3 Magnitude of a Vector
                                                                                                                              • 3.7.4 The Scalar Product
                                                                                                                                • 3.7.5 The Vector Product
                                                                                                                                  • 3.7.6 Components of Vectors
                                                                                                                                    • 3.7.7 Geometric Proof with Vectors
                                                                                                                                    • 3.8 Vector Equations of Lines
                                                                                                                                      • 3.8.1 Vector Equations of Lines
                                                                                                                                        • 3.8.2 Shortest Distances with Lines
                                                                                                                                        • 3.9 Modelling with Vectors
                                                                                                                                          • 3.9.1 Kinematics with Vectors
                                                                                                                                            • 3.9.2 Constant & Variable Velocity
                                                                                                                                            • 3.10 Graph Theory
                                                                                                                                              • 3.10.1 Introduction to Graph Theory
                                                                                                                                                • 3.10.2 Walks & Adjacency Matrices
                                                                                                                                                  • 3.10.3 Minimum Spanning Trees
                                                                                                                                                    • 3.10.4 Chinese Postman Problem
                                                                                                                                                      • 3.10.5 Travelling Salesman Problem
                                                                                                                                                        • 3.10.6 Bounds for Travelling Salesman Problem
                                                                                                                                                      • 4. Statistics & Probability
                                                                                                                                                        • 4.1 Statistics Toolkit
                                                                                                                                                          • 4.1.1 Sampling
                                                                                                                                                            • 4.1.2 Data Collection
                                                                                                                                                              • 4.1.3 Statistical Measures
                                                                                                                                                                • 4.1.4 Frequency Tables
                                                                                                                                                                  • 4.1.5 Linear Transformations of Data
                                                                                                                                                                    • 4.1.6 Outliers
                                                                                                                                                                      • 4.1.7 Univariate Data
                                                                                                                                                                        • 4.1.8 Interpreting Data
                                                                                                                                                                        • 4.2 Correlation & Regression
                                                                                                                                                                          • 4.2.1 Bivariate Data
                                                                                                                                                                            • 4.2.2 Correlation Coefficients
                                                                                                                                                                              • 4.2.3 Linear Regression
                                                                                                                                                                              • 4.3 Further Correlation & Regression
                                                                                                                                                                                • 4.3.1 Non-linear Regression
                                                                                                                                                                                  • 4.3.2 Logarithmic Scales
                                                                                                                                                                                    • 4.3.3 Linearising using Logarithms
                                                                                                                                                                                    • 4.4 Probability
                                                                                                                                                                                      • 4.4.1 Probability & Types of Events
                                                                                                                                                                                        • 4.4.2 Conditional Probability
                                                                                                                                                                                          • 4.4.3 Sample Space Diagrams
                                                                                                                                                                                          • 4.5 Probability Distributions
                                                                                                                                                                                            • 4.5.1 Discrete Probability Distributions
                                                                                                                                                                                              • 4.5.2 Expected Values
                                                                                                                                                                                              • 4.6 Random Variables
                                                                                                                                                                                                • 4.6.1 Linear Combinations of Random Variables
                                                                                                                                                                                                  • 4.6.2 Unbiased Estimates
                                                                                                                                                                                                  • 4.7 Binomial Distribution
                                                                                                                                                                                                    • 4.7.1 The Binomial Distribution
                                                                                                                                                                                                      • 4.7.2 Calculating Binomial Probabilities
                                                                                                                                                                                                      • 4.8 Normal Distribution
                                                                                                                                                                                                        • 4.8.1 The Normal Distribution
                                                                                                                                                                                                          • 4.8.2 Calculations with Normal Distribution
                                                                                                                                                                                                          • 4.9 Further Normal Distribution (inc Central Limit Theorem)
                                                                                                                                                                                                            • 4.9.1 Sample Mean Distribution
                                                                                                                                                                                                              • 4.9.2 Confidence Interval for the Mean
                                                                                                                                                                                                              • 4.10 Poisson Distribution
                                                                                                                                                                                                                • 4.10.1 Poisson Distribution
                                                                                                                                                                                                                  • 4.10.2 Calculating Poisson Probabilities
                                                                                                                                                                                                                  • 4.11 Hypothesis Testing
                                                                                                                                                                                                                    • 4.11.1 Hypothesis Testing
                                                                                                                                                                                                                      • 4.11.2 Chi-squared Test for Independence
                                                                                                                                                                                                                        • 4.11.3 Goodness of Fit Test
                                                                                                                                                                                                                        • 4.12 Further Hypothesis Testing
                                                                                                                                                                                                                          • 4.12.1 Hypothesis Testing for Mean (One Sample)
                                                                                                                                                                                                                            • 4.12.2 Hypothesis Testing for Mean (Two Sample)
                                                                                                                                                                                                                              • 4.12.3 Binomial Hypothesis Testing
                                                                                                                                                                                                                                • 4.12.4 Poisson Hypothesis Testing
                                                                                                                                                                                                                                  • 4.12.5 Hypothesis Testing for Correlation
                                                                                                                                                                                                                                    • 4.12.6 Type I & Type II Errors
                                                                                                                                                                                                                                    • 4.13 Transition Matrices & Markov Chains
                                                                                                                                                                                                                                      • 4.13.1 Markov Chains
                                                                                                                                                                                                                                        • 4.13.2 Transition Matrices
                                                                                                                                                                                                                                      • 5. Calculus
                                                                                                                                                                                                                                        • 5.1 Differentiation
                                                                                                                                                                                                                                          • 5.1.1 Introduction to Differentiation
                                                                                                                                                                                                                                            • 5.1.2 Applications of Differentiation
                                                                                                                                                                                                                                              • 5.1.3 Modelling with Differentiation
                                                                                                                                                                                                                                              • 5.2 Further Differentiation
                                                                                                                                                                                                                                                • 5.2.1 Differentiating Special Functions
                                                                                                                                                                                                                                                  • 5.2.2 Techniques of Differentiation
                                                                                                                                                                                                                                                    • 5.2.3 Related Rates of Change
                                                                                                                                                                                                                                                      • 5.2.4 Second Order Derivatives
                                                                                                                                                                                                                                                        • 5.2.5 Further Applications of Differentiation
                                                                                                                                                                                                                                                          • 5.2.6 Concavity & Points of Inflection
                                                                                                                                                                                                                                                          • 5.3 Integration
                                                                                                                                                                                                                                                            • 5.3.1 Trapezoid Rule: Numerical Integration
                                                                                                                                                                                                                                                              • 5.3.2 Introduction to Integration
                                                                                                                                                                                                                                                                • 5.3.3 Applications of Integration
                                                                                                                                                                                                                                                                • 5.4 Further Integration
                                                                                                                                                                                                                                                                  • 5.4.1 Integrating Special Functions
                                                                                                                                                                                                                                                                    • 5.4.2 Techniques of Integration
                                                                                                                                                                                                                                                                      • 5.4.3 Further Applications of Integration
                                                                                                                                                                                                                                                                        • 5.4.4 Volumes of Revolution
                                                                                                                                                                                                                                                                        • 5.5 Kinematics
                                                                                                                                                                                                                                                                          • 5.5.1 Kinematics Toolkit
                                                                                                                                                                                                                                                                            • 5.5.2 Calculus for Kinematics
                                                                                                                                                                                                                                                                            • 5.6 Differential Equations
                                                                                                                                                                                                                                                                              • 5.6.1 Modelling with Differential Equations
                                                                                                                                                                                                                                                                                • 5.6.2 Separation of Variables
                                                                                                                                                                                                                                                                                  • 5.6.3 Slope Fields
                                                                                                                                                                                                                                                                                    • 5.6.4 Approximate Solutions to Differential Equations
                                                                                                                                                                                                                                                                                    • 5.7 Further Differential Equations
                                                                                                                                                                                                                                                                                      • 5.7.1 Coupled Differential Equations
                                                                                                                                                                                                                                                                                        • 5.7.2 Second Order Differential Equations
                                                                                                                                                                                                                                                                                      Amber Perry

                                                                                                                                                                                                                                                                                      Author: Amber

                                                                                                                                                                                                                                                                                      Amber gained a first class degree in Mathematics & Meteorology from the University of Reading before training to become a teacher. She is passionate about teaching, having spent 8 years teaching GCSE and A Level Mathematics both in the UK and internationally. Amber loves creating bright and informative resources to help students reach their potential.


                                                                                                                                                                                                                                                                                      Save My Exams Logo
                                                                                                                                                                                                                                                                                      Resources
                                                                                                                                                                                                                                                                                      Home Join Support

                                                                                                                                                                                                                                                                                      Members
                                                                                                                                                                                                                                                                                      Members Home Account Logout

                                                                                                                                                                                                                                                                                      Company
                                                                                                                                                                                                                                                                                      About Us Contact Us Jobs Terms Privacy Facebook Twitter

                                                                                                                                                                                                                                                                                      Quick Links
                                                                                                                                                                                                                                                                                      GCSE Revision Notes IGCSE Revision Notes A Level Revision Notes Biology Chemistry Physics Maths 2022 Advance Information

                                                                                                                                                                                                                                                                                       
                                                                                                                                                                                                                                                                                      © IB Documents (2) Team & u/aimlesskr
                                                                                                                                                                                                                                                                                      IBO was not involved in the production of, and does not endorse, the resources created by Save My Exams.