CM 1 Actuarial Mathematics Actuarial Science Study Material

Cover
Subject CM1 2019 Study Guide
	1.1 Before you start
	1.2 Core study material
		Syllabus
		Core Reading
		ActEd text
	1.3 ActEd study support
		Learning’ products
			Course Notes
			Paper B Online Resources (PBOR)
		‘Learning & revision’ products
			X Assignments
			Combined Materials Pack (CMP)
			X / Y Assignment Marking
			Tutorials
			Online Classroom
		‘Revision’ products
			Flashcards
		‘Revision & rehearsal’ products
			Revision Notes
			ActEd Solutions with Exam Technique (ASET)
		‘Rehearsal’ products
			Mock Exam
			Mock Marking
	1.4 Skills
		Technical skills
		Study skills
			Overall study plan
			Study sessions
			Order of study
			Active study
		Revision and exam skills
			Revision skills
			Exam question skill levels
			Command verbs
	1.5 The examination
		What to take to the exam
		Past exam papers
	1.6 Queries and feedback
		Questions and queries
		Feedback
	2.1 Subject CM1 – background
		History
		Predecessors
		Exemptions
		Links to other subjects
	2.2 Subject CM1 – Syllabus and Core Reading
		Syllabus
			Aim
			Competences
			Syllabus topics
			Detailed syllabus objectives
		Core Reading
			Accreditation
			Further reading
	2.3 Subject CM1 – the course structure
	2.4 Subject CM1 – summary of ActEd products
	2.5 Subject CM1 – skills and assessment
		Technical skills
		Exam skills
			Exam question skill levels
		Assessment
	2.6 Subject CM1 – frequently asked questions
Chapter 1 Data analysis
	0 Introduction
	1 Aims of a data analysis
		1.1 Descriptive analysis
		1.2 Inferential analysis
		1.3 Predictive analysis
	2 The data analysis process
	3 Data sources
		3.1 Big data
		3.2 Data security, privacy and regulation
	4 Reproducible research
		4.1 The meaning of reproducible research
		4.2 Elements required for reproducibility
		4.3 The value of reproducibility
		4.4 References
	Chapter 1 Summary
	Chapter 1 Practice Questions
	Chapter 1 Solutions
Chapter 2 Principles of actuarial modelling
	0 Introduction
	1 Models
		1.1 Why models are used
			Parameters
			Data
			Objectives
		1.2 How models are used
	2 Modelling – the benefits and limitations
		2.1 Advantages of models
		2.2 Disadvantages
	3 Stochastic and deterministic models
	4 Discrete and continuous state spaces and time sets
	5 Scenario-based and proxy models
	6 Suitability of a model
	7 Short-term and long-term properties of a model
	8 Analysing the output of a model
	9 Sensitivity testing
	10 Communication of the results
		Example
	Chapter 2 Summary
	Chapter 2 Practice Questions
	Chapter 2 Solutions
Chapter 3 Cashflow models
	0 Introduction
	1 Cashflow process
	2 Examples of cashflow scenarios
		2.1 A zero-coupon bond
		2.2 A fixed-interest security
		2.3 An index-linked security
		2.4 Cash on deposit
		2.5 An equity
		2.6 An annuity-certain
		2.7 An ‘interest-only’ loan
		2.8 A repayment loan (or mortgage)
	3 Insurance contracts
		3.1 A pure endowment
		3.2 An endowment assurance
		3.3 A term assurance
		3.4 A contingent annuity
		3.5 A car insurance policy
		3.6 A health cash plan
	Chapter 3 Summary
	Chapter 3 Practice Questions
	Chapter 3 Solutions
Chapter 4 The time value of money
	0 Introduction
	1 Interest
		1.1 Simple interest
		1.2 Compound (effective) interest
		1.3 Accumulation factors
		1.4 The principle of consistency
	2 Present values
		Formulae and tables for actuarial examinations
		Note on rounding
	3 Discount rates
		3.1 Simple discount
		3.2 Compound (effective) discount
		3.3 Discount factors
	4 Effective rates of interest and discount
		4.1 Effective rate of interest
		4.2 Effective rate of discount
	5 Equivalent rates
	Chapter 4 Summary
	Chapter 4 Practice Questions
	Chapter 4 Solutions
Chapter 5 Interest rates
	0 Introduction
	1 Nominal rates of interest and discount
		1.1 Nominal rates of interest
		1.2 Accumulating and discounting using nominal interest rates
		1.3 Nominal rates of discount
		1.4 Accumulating and discounting using nominal discount rates
	2 The force of interest
		2.1 Derivation from nominal interest convertible pthly
		2.2 Accumulating and discounting using the force of interest
		2.3 Derivation from nominal discount convertible pthly
	3 Relationships between effective, nominal and force of interest
		3.1 An alternative way of considering nominal interest convertible pthly
		3.2 An alternative way of considering nominal discount convertible pthly
		3.3 An alternative way of considering force of interest
	4 Force of interest as a function of time
		4.1 Formal definition
		4.2 Relationship to constant force of interest
		4.3 Present values
		4.4 Applications of force of interest
	Chapter 5 Summary
	Chapter 5 Practice Questions
	Chapter 5 Solutions
Chapter 6 Real and money interest rates
	0 Introduction
	1 Definition of real and money interest rates
	2 Deflationary conditions
	3 Usefulness of real and money interest rates
		The purpose to which the rate will be put
		Whether the underlying data have or have not already been adjusted for inflation
	Chapter 6 Summary
	Chapter 6 Practice Questions
	Chapter 6 Solutions
Chapter 7 Discounting and accumulating
	0 Introduction
	1 Present values of cashflows
		1.1 Discrete cashflows
		1.2 Continuously payable cashflows (payment streams)
	2 Valuing cashflows
		2.1 Constant interest rate
		2.2 Payment streams
		2.3 Sudden changes in interest rates
	3 Interest income
	Chapter 7 Summary
	Chapter 7 Practice Questions
	Chapter 7 Solutions
Chapter 8 Level annuities
	0 Introduction
		Terminology
	1 Present values
		1.1 Payments made in arrears
		1.2 Payments made in advance
	2 Accumulations
	3 Continuously payable annuities
	4 Annuities payable pthly
		4.1 Present values
		4.2 Accumulations
		4.3 Annuities payable pthly where p < 1
	5 Non-integer values of n
	6 Perpetuities
	7 Deferred annuities
		7.1 Annual payments
		7.2 Continuously payable annuities
		7.3 Annuities payable pthly
		7.4 Non-integer values of n
		7.5 Sudden changes in interest rates
	Chapter 8 Summary
	Chapter 8 Practice Questions
	Chapter 8 Solutions
Chapter 9 Increasing annuities
	0 Introduction
	1 Varying annuities
		1.1 Annual payments
		1.2 Continuously payable annuities
		1.3 Decreasing payments
	2 Special cases
		2.1 Irregular payments
		2.2 Compound increasing annuities
	Chapter 9 Summary
	Chapter 9 Practice Questions
	Chapter 9 Solutions
	End of Part 1
		What next?
		Time to consider …
		… ‘learning and revision’ products
Chapter 10 Equations of value
	0 Introduction
	1 The equation of value and the yield on a transaction
		1.1 The theory
		1.2 Solving for an unknown quantity
			Security S
			Solving for the timing of a payment (n)
			Solving for the interest rate (i)
			Estimating an unknown interest rate using linear interpolation
		1.3 Example applications
	2 Uncertain payment or receipt
		2.1 Probability of cashflow
		2.2 Higher discount rate
	Chapter 10 Summary
	Chapter 10 Practice Questions
	Chapter 10 Solutions
Chapter 11 Loan schedules
	0 Introduction
	1 An example
	2 Calculating the capital outstanding
		2.1 Introduction
		2.2 The theory
			Prospective loan calculation
			Retrospective loan calculation
	3 Calculating the interest and capital elements
	4 The loan schedule
	5 Instalments payable more frequently than annually
		Capital and interest elements
	6 Consumer credit: APR
	Chapter 11 Summary
	Chapter 11 Practice Questions
	Chapter 11 Solutions
Chapter 12 Project appraisal
	0 Introduction
		Estimating cashflows
	1 Fixed interest rates
		1.1 Accumulated value
		1.2 Net present values
		1.3 Internal rate of return
		1.4 The comparison of two investment projects
			Example
			Solution
	2 Different interest rates for lending and borrowing
		2.1 Payback periods
	3 Other considerations
	Chapter 12 Summary
	Chapter 12 Practice Questions
	Chapter 12 Solutions
Chapter 13 Bonds, equity and property
	0 Introduction
	1 Fixed-interest securities
		1.1 Calculating the price and yield
		1.2 No tax
		1.3 Income tax
		1.4 Capital gains tax
			Capital gains test
			Finding the yield when there is capital gains tax
		1.5 Optional redemption dates
	2 Uncertain income securities
		2.1 Equities
		2.2 Property
	3 Real rates of interest
		3.1 Inflation-adjusted cashflows
		3.2 Calculating real yields using an inflation index
		3.3 Calculating real yields given constant inflation assumptions
		3.4 Payments related to the rate of inflation
		3.5 The effects of inflation
	4 Index-linked bonds
	Chapter 13 Summary
	Chapter 13 Practice Questions
	Chapter 13 Solutions
	End of Part 2
		What next?
		Time to consider …
		… ‘learning and revision’ products
Chapter 14 Term structure of interest rates
	0 Introduction
	1 Discrete-time rates
		1.1 Discrete-time spot rates
		1.2 Discrete-time forward rates
	2 Continuous-time rates
		2.1 Continuous-time spot rates
		2.2 Continuous-time forward rates
		2.3 Instantaneous forward rates
			Note
	3 Theories of the term structure of interest rates
		3.1 Why interest rates vary over time
			Supply and demand
			Base rates
			Interest rates in other countries
			Expected future inflation
			Tax rates
			Risk associated with changes in interest rates
		3.2 The theories
			Expectations theory
			Liquidity preference
			Market segmentation
		3.3 Yields to maturity
		3.4 Par yields
	4 Duration, convexity and immunisation
		4.1 Interest rate risk
		4.2 Effective duration
		4.3 Duration
		4.4 Convexity
			Why is it called ‘convexity’?
		4.5 Immunisation
			Redington’s conditions
	Chapter 14 Summary
	Chapter 14 Practice Questions
	Chapter 14 Solutions
Chapter 15 The life table
	0 Introduction
	1 Present values of payments under life insurance and annuity contracts
		1.1 Equations of value
		1.2 Allowance for investment income
		1.3 Other assumptions
	2 The life table
		2.1 Introduction
		2.2 Constructing a life table
		2.3 The force of mortality
		2.4 Interpretation
		2.5 Using the life table
		2.6 Lifetime random variables
		2.7 The pattern of human mortality
		2.8 More notation
	3 Life table functions at non-integer ages
		3.1 Introduction
		3.2 Method 1 – uniform distribution of deaths (UDD)
		3.3 Method 2 – constant force of mortality (CFM)
	4 Evaluating probabilities without use of the life table
	5 Select mortality
		5.1 Introduction
		5.2 Mortality rates that depend on both age and duration
		5.3 Displaying select rates
		5.4 Constructing select and ultimate life tables
		5.5 Using tabulated select life table functions
	Chapter 15 Summary
		Modelling mortality
		Definitions of probabilities of death and survival
		Force of mortality
		Using a life table
		Dealing with non-integer ages
		Uniform distribution of deaths
		Constant force of mortality
		Select mortality
	Chapter 15 Practice Questions
	Chapter 15 Solutions
Chapter 16 Life assurance contracts
	0 Introduction
	1 Whole life assurance contracts
		1.1 Present value random variable
		1.2 The expected present value
			Actuarial notation for the expected present value
		1.3 Variance of the present value random variable
	2 Term assurance contracts
		2.1 Present value random variable
		2.2 Expected present value
			Actuarial notation for the expected present value
		2.3 Variance of the present value random variable
	3 Pure endowment contracts
		3.1 Present value random variable
		3.2 Expected present value
			Actuarial notation for the expected present value
		3.3 Variance of the present value random variable
	4 Endowment assurance contracts
		4.1 Present value random variable
		4.2 Expected present value
			Actuarial notation for the expected present value
		4.3 Variance of the present value random variable
	5 Deferred assurance benefits
		5.1 Present value random variable
		5.2 Expected present value
		5.3 Variance of the present value random variable
		5.4 Deferred term assurance
			Present value random variable
			Expected present value
			Variance of the present value random variable
	6 Benefits payable immediately on death
		6.1 Whole life assurance
			Present value random variable
			Expected present value
		6.2 Term assurance
			Present value random variable
			Expected present value
			Actuarial notation for the expected present value
			Variance of the present value random variable
		6.3 Endowment assurance
			Present value random variable
			Expected present value
		6.4 Other relationships
		6.5 Claims acceleration approximation
		6.6 Further approximation
	7 Evaluating means and variances using select mortality
	Chapter 16 Summary
		Types of contracts
		Whole life assurance with benefit payable at the end of the year of death
		Whole life assurance with benefit payable immediately on death
		Term assurance (n-year term) with benefit payable at the end of the year of death
		Term assurance (n-year term) with benefit payable immediately on death
		Pure endowment (n-year term
		Endowment assurance (n-year term) with benefit payable on survival to the maturity date or at the end of the year of earlier death
		Endowment assurance (n-year term) with benefit payable on survival to the maturity date or immediately on earlier death
		Deferred whole life assurance with benefit paid at end of year of death
	Chapter 16 Practice Questions
	Chapter 16 Solutions
Chapter 17 Life annuity contracts
	1 Life annuity contracts
	2 Whole life annuities payable annually in arrears
		2.1 Present value random variable
		2.2 Expected present value
			Actuarial notation for the expected present value
		2.3 Variance of the present value random variable
	3 Whole life annuities payable annually in advance
		3.1 Present value random variable
		3.2 Variance of the present value random variable
	4 Temporary annuities payable annually in arrears
		4.1 Present value random variable
		4.2 Expected present value
			Actuarial notation for the expected present value
		4.3 Variance of the present value random variable
	5 Temporary annuities payable annually in advance
		5.1 Present value random variable
		5.2 Expected present value
		5.3 Variance of the present value random variable
	6 Deferred annuities
		6.1 Present value random variable
		6.2 Expected present value
			Actuarial notation for the expected present value
	7 Deferred annuities-due
	8 Guaranteed annuities payable annually in advance
		8.1 Present value random variable
		8.2 Expected present value
		8.3 Variance of the present value random variable
	9 Guaranteed annuities payable annually in arrears
		9.1 Present value random variable
		9.2 Expected present value
		9.3 Variance of the present value random variable
	10 Continuous annuities
		10.1 Immediate annuity
			Present value random variable
			Expected present value
			Variance of the present value random variable
		10.2 Other annuities
		10.3 Approximations
	11 Evaluating means and variances using select mortality
	Chapter 17 Summary
		Annuities
		Whole life immediate annuity in arrears
		Whole life immediate annuity-due
		Continuously payable whole life annuity
		Temporary immediate annuity in arrears
		Temporary immediate annuity-due
		Deferred annuity-due
		Guaranteed annuity-due
	Chapter 17 Practice Questions
	Chapter 17 Solutions
Chapter 18 Evaluation of assurances and annuities
	0 Introduction
	1 Evaluating assurance benefits
	2 Evaluating annuity benefits
	3 Premium conversion formulae
		3.1 Discrete version
		3.2 Continuous version
		3.3 Variance of benefits
	4 Expected present values of annuities payable m times each year
	5 Expected present values under a constant force of mortality
	Chapter 18 Summary
	Chapter 18 Practice Questions
	Chapter 18 Solutions
Chapter 19 Variable benefits and conventional with-profits policies
	0 Introduction
	1 Variable payments
	2 Payments varying at a constant compound rate
	3 Payments varying by a constant monetary amount
		3.1 Whole life assurance
		3.2 Term assurance
		3.3 Endowment assurance
		3.4 Decreasing term assurance
		3.5 Increasing assurances payable immediately on death
		3.6 Whole life annuity payable annually in arrears
		3.7 Whole life annuity payable annually in advance
		3.8 Temporary annuities
		3.9 Annuities payable continuously
	4 Conventional with-profits contracts
		4.1 Types of bonus
	Chapter 19 Summary
		Variable benefits
		Payments varying at a constant compound rate
		Payments changing by a constant monetary amount
		Conventional with-profits contracts
	Chapter 19 Practice Questions
	Chapter 19 Solutions
	End of Part 3
		What next?
		Time to consider …
		… ‘revision’ products
Chapter 20 Gross premiums
	0 Introduction
	1 The gross premium
	2 Gross future loss random variable
		2.1 Calculating premiums that satisfy probabilities, using the gross future loss random variable
			Example
			Solution
	3 Principle of equivalence
		3.1 Definition
		3.2 Determining gross premiums using the equivalence principle
		3.3 The basis
		3.4 Premium payment structures
		3.5 Annual premium contracts
		3.6 Conventional with-profits contracts
		3.7 Premiums payable m times per year
	4 Calculating gross premiums using simple criteria other than the equivalence principle
	Chapter 20 Summary
		Future loss random variable
		Principle of equivalence
		Gross premiums
		Premiums that satisfy probabilities
	Chapter 20 Practice Questions
	Chapter 20 Solutions
Chapter 21 Gross premium reserves
	0 Introduction
	1 Why hold reserves?
	2 Prospective reserves
		2.1 Calculating gross premium prospective reserves
		2.2 Calculating prospective reserves that satisfy probabilities
		2.3 Gross premium prospective reserves for conventional with-profits policies
		2.4 Reserve conventions
	3 Retrospective reserves
		3.1 Retrospective accumulations
			Example 1: pure endowment
			Example 2: term assurance
			Notation
		3.2 Gross premium retrospective reserve
			Example: Whole life assurance
	4 Equality of prospective and retrospective reserves
		4.1 Conditions for equality
		4.2 Demonstrating the equality of prospective and retrospective reserves
			Example: Whole life assurance
	5 Recursive relationship between reserves for annual premium contracts
		Example: Whole life assurance
		(1) Actual profit over the year
		(2) Expected profit over the year
	6 Net premium reserves for conventional without profit contracts
		6.1 Difference from gross premium reserve
			Example: whole life assurance
		6.2 A special result for the net premium reserve for some endowment and whole life assurance contracts
			Example: Whole life assurance
	Chapter 21 Summary
		Reserves
		Gross premium prospective reserves
		Retrospective accumulations
		Gross premium retrospective reserves
		Calculating reserves that satisfy probabilities
		Equality of reserves
		Recursive formula for reserves
		Profit
		Net premium reserves for without-profit contracts
	Chapter 21 Practice Questions
	Chapter 21 Solutions
Chapter 22 Joint life and last survivor functions
	0 Introduction
	1 Random variables to describe joint life functions
		1.1 Single life functions
		1.2 Joint life functions
		1.3 Joint lifetime random variables and joint life table functions
		1.4 Last survivor lifetime random variables
	2 Simple probabilities involving two lives
		2.1 Evaluating probabilities of death or survival of either or both of two lives
		2.2 Evaluating last survivor functions
	3 Present values involving two lives
		3.1 Present values of joint life and last survivor assurances
			Joint life
			Last survivor
		3.2 Present values of joint life and last survivor annuities
	4 Calculations, premiums, reserves
		4.1 Evaluating premiums
		4.2 Calculating reserves
		4.3 Future loss random variable
	Chapter 22 Summary
	Chapter 22 Practice Questions
	Chapter 22 Solutions
Chapter 23 Contingent and reversionary benefits
	0 Introduction
	1 Contingent probabilities of death
	2 Contingent assurances
	3 Reversionary annuities
	4 Joint life functions dependent on term
		4.1 Expected present values of joint life assurances and annuities which also depend upon term
		4.2 Expected present values of last survivor assurances and annuities that also depend upon term
		4.3 More complex conditions
		4.4 Expected present values of reversionary annuities that depend upon term
			Type 1 – an annuity payable after a fixed term has elapsed
			Type 2 – an annuity payable to (y) on the death of (x), but ceasing at time n
			Type 3 – an annuity payable to (y) on the death of (x) provided that (x) die swithin n years
			Type 4 – an annuity payable to (y) on the death of (x) for a maximum of n years
			Type 5 – an annuity payable to (y) on the death of (x) and guaranteed for n years
			Type 6 – an annuity payable to (y) on the death of (x) and continuing for n years after (y)’s death
		4.5 Expected present values of contingent assurances that depend upon term
	5 Expected present value of annuities payable m times a year
	6 Further aspects
		6.1 Premium conversion relationships
		6.2 Premium payment term
	Chapter 23 Summary
		Contingent probabilities
		Contingent assurances
		Reversionary annuities
		Functions with specified terms
		Premium conversion formulae
	Chapter 23 Practice Questions
	Chapter 23 Solutions
	End of Part 4
		What next?
		Time to consider …
		… ‘revision and rehearsal’ products
Chapter 24 Mortality profit
	0 Introduction
	1 Mortality profit on a single policy
		1.1 Death strain at risk (DSAR)
		1.2 Expected death strain (EDS)
		1.3 Actual death strain (ADS)
		1.4 Mortality profit
	2 Mortality profit on a portfolio of policies
	3 Allowing for death benefits payable immediately
	4 Allowing for survival benefits
		4.1 Annuities
	5 Allowing for different premium or annuity payment frequencies
	6 Calculation of mortality profit for policies involving two lives
	Chapter 24 Summary
		Single life and joint life (first death) policies
		Last survivor policies
	Chapter 24 Practice Questions
	Chapter 24 Solutions
Chapter 25 Competing risks
	0 Introduction
	1 Health insurance contracts
	2 Multiple state models
		2.1 Notation
		2.2 Valuing continuous cashflows using multiple state models
		2.3 Designing the multiple state model
			Defining the model
			How to design a model
	3 Multiple decrement models
		3.1 A simple example
		3.2 Multiple decrement probabilities
		3.3 Deriving probabilities from transition intensities
	4 Multiple decrement tables
		4.1 Associated single decrement tables
		4.2 Relationships between single and multiple decrement tables
		4.3 Constructing a multiple decrement table
		4.4 Obtaining dependent probabilities
			From the forces of decrement
			From an existing multiple decrement table
			From existing single decrement tables
		4.5 Integral formulae for multiple decrement probabilities
	5 Using multiple decrement tables to evaluate expected present values of cashflows
		5.1 Continuous approach
		5.2 Discrete approach
	Chapter 25 Summary
		Multiple state models
		Multiple decrement models
		Multiple decrement tables
	Chapter 25 Practice Questions
	Chapter 25 Solutions
Chapter 26 Unit-linked and accumulating with-profits contracts
	0 Introduction
	1 Unit-linked contracts
		1.1 Unit funds and non-unit funds
	2 Accumulating with-profits contracts
		2.1 Definition
		2.2 Unitised (accumulating) with-profits contracts
		2.3 Charges and benefits under UWP
		2.4 Comparison between UWP and the simple AWP designs
	Chapter 26 Summary
		Unit-linked contracts
		Accumulating with-profits (AWP)
	Chapter 26 Practice Questions
	Chapter 26 Solutions
Chapter 27 Profit testing
	0 Introduction
	1 Evaluating expected cashflows for various contract types
		1.1 Example 1: Conventional whole life assurance
		1.2 Example 2: Conventional endowment assurance
		1.3 Example 3: Unit-linked endowment assurance
		1.4 Example 4: Single premium unitised with-profits contract
			The reason for profit-testing unitised with-profits contracts
	2 Profit tests for annual premium contracts
		2.1 Summary measures of profit
			Profit margin
			The internal rate of return (IRR)
	3 Profit testing using the present value random variable
		3.1 Introduction
		3.2 Example
	4 Pricing using a profit test
		4.1 Profit criterion
	Chapter 27 Summary
		Projecting profit flows – conventional products
		Projecting cashflows – unit-linked and unitised with-profits
		Summary measures of profit
		Profit testing
	Chapter 27 Practice Questions
	Chapter 27 Solutions
Chapter 28 Reserving aspects of profit testing
	0 Introduction
	1 Pricing and reserving bases
	2 Calculating reserves for unit-linked contracts
		2.1 Reserves revisited
		2.2 Calculating reserves for unit-linked contracts
			General approach
			Summary of the method
			Incorporating non-unit reserves into the profit test
	3 Calculating reserves for conventional contracts using a profit test
	4 Effect of pricing and reserving bases on a profit test
	5 Setting out the calculations
	Chapter 28 Summary
		Calculating reserves using cashflow projections
		Different bases
	Chapter 28 Practice Questions
	Chapter 28 Solutions
	End of Part 5
		What next?
		Time to consider …
		… ‘rehearsal’ products
Subject CM1: Assignment X1 2019 Examinations
Subject CM1: Assignment X1 2019 Examinations
Subject CM1: Assignment X2 2019 Examinations
Subject CM1: Assignment X2 2019 Examinations
Subject CM1: Assignment X3 2019 Examinations
Subject CM1: Assignment X3 2019 Examinations
Subject CM1: Assignment X4 2019 Examinations
Subject CM1: Assignment X4 2019 Examinations
Subject CM1: Assignment X5 2019 Examinations
Subject CM1: Assignment X5 2019 Examinations
Assignment X1 – Solutions
Assignment X2 – Solutions
Assignment X3 – Solutions
Assignment X4 – Solutions
Assignment X5 – Solutions