Build cards for the answer you need to give

Actuaries Institute pathways combine university-accredited subjects with Institute-set assessments. Later-stage assessments commonly involve written problem-solving and applied communication tasks. The exact content depends on your subject and stage, so check the current Institute and university materials for the syllabus and assessment requirements. Don’t treat a general deck as a substitute for those sources.

Flashcards are useful for retrieving a definition, formula, or decision rule quickly. They are less useful if they train you to recite a formula without recognising its assumptions or explaining what a result means. For each card, practise saying the fact, naming any condition that matters, and giving a short interpretation where relevant.

The 18-card deck below is a general quantitative-methods set, not a claim about a particular paper. Match it to your own notes: remove material outside your course, and add the notation or methods your subject uses. Study one card at a time. Read the question, answer aloud or on scrap paper, reveal the answer, then grade your recall honestly. Use Again if you could not retrieve it, Hard if you needed substantial effort, Good if it was clear, and Easy only if it came promptly and accurately. Review the answer before moving on when you missed a condition or sign.

A MySummaries deck on quantitative methods can be worked through like this:

Cards — Quantitative methods — general revision18 due

For discrete cash flows Cₜ at times t = 0,…,n, what is their present value at effective rate i per period?

PV = Σₜ₌₀ⁿ Cₜ(1+i)⁻ᵗ, with the cash-flow timing and compounding period stated consistently.

All 18 cards
For discrete cash flows Cₜ at times t = 0,…,n, what is their present value at effective rate i per period?PV = Σₜ₌₀ⁿ Cₜ(1+i)⁻ᵗ, with the cash-flow timing and compounding period stated consistently.
What is the present value of an n-payment annuity-immediate paying 1 each period at effective rate i, for i ≠ 0?a-angle-n = [1 − (1+i)⁻ⁿ] / i.
How do you convert nominal annual rate j^(m), convertible m times yearly, to an effective annual rate?i_eff = (1 + j^(m)/m)^m − 1.
For effective annual rate i, what is the equivalent force of interest δ?δ = ln(1+i), so i = e^δ − 1.
For a discrete random variable X with values x and probabilities p(x), how is E[X] calculated?E[X] = Σₓ x p(x), provided the expectation exists.
What is the variance of X in terms of its first and second moments?Var(X) = E[X²] − [E(X)]², when the second moment is finite.
State the law of total expectation for a partition into events Aᵢ.E[X] = Σᵢ E[X | Aᵢ] P(Aᵢ), for a countable partition with probabilities summing to 1.
State Bayes’ theorem for events A and B, where P(B) > 0.P(A | B) = P(B | A)P(A) / P(B).
If X has a Binomial(n,p) distribution, what are its mean and variance?E[X] = np and Var(X) = np(1−p).
How do you standardise an observation x from a normal distribution with mean μ and standard deviation σ > 0?z = (x−μ)/σ; the standardised variable has a standard normal distribution if X is normal.
For n independent, identically distributed observations with finite variance σ², what is the standard error of the sample mean?SE(X-bar) = σ/√n; if σ is unknown, estimate it with the sample standard deviation s to obtain s/√n.
Under normality, or an adequate large-sample approximation, what is a common approximate 95% interval for an estimate θ-hat?θ-hat ± 1.96 × SE(θ-hat), when the normal approximation and standard-error estimate are appropriate.
What does maximum likelihood estimation do?It chooses parameter value(s) that maximise the likelihood of the observed data under the specified model.
For independent observations with densities or probability functions f(xᵢ; θ), how is the log-likelihood formed?ℓ(θ) = Σᵢ log f(xᵢ; θ), because the joint likelihood is the product of the individual contributions.
How is Macaulay duration defined for dated cash flows under a flat effective yield per period?D = Σₜ t·PV(Cₜ) / P, where P = Σₜ PV(Cₜ); it is the present-value-weighted average payment time.
For a small parallel yield change, what is the first-order modified-duration approximation to a bond’s price change?ΔP/P ≈ −D_mod·Δy. It is a local approximation; it omits convexity and assumes the yield change is small.
If claim count N is Poisson with mean λ and severities are independent of N with finite mean E[S], what is expected aggregate claims?For aggregate claims S₁+…+S_N, E[aggregate] = λE[S], under the stated frequency-severity assumptions.
In a simple credibility blend, how is a subject estimate combined with a collective estimate?Estimate = Z·subject estimate + (1−Z)·collective estimate, with 0 ≤ Z ≤ 1; the credibility model determines Z.

That is a MySummaries deck, filled with Actuaries Institute material. Yours is written from your own notes. Start free

The caption describes a general-purpose deck; select and adapt cards to the material in your own course. The numerical relationships are only useful when you can also say when they apply. For example, the normal interval card is not permission to use 1.96 in every setting: check the distributional approximation, standard error, and interval method required by your subject.

A repeatable card routine

Use this routine whenever you study a card:

  1. Retrieve before revealing. Say the answer and its conditions, rather than recognising it after reading.
  2. Check the notation and units. Confirm that the time period in a rate matches the cash-flow period, and that a result has the units expected for the quantity.
  3. Check signs and direction. For example, the duration approximation says a small rise in yield corresponds to a fall in price, all else equal.
  4. Grade the recall, not your confidence. If you recalled the equation but missed a necessary assumption, grade it as a miss or a difficult recall.
  5. Apply it to a small example. After reviewing a formula, use a value from your notes and explain what the result means in that example.

When a card repeatedly causes trouble, don’t merely repeat the same wording. Check whether the issue is notation, an assumption, a calculation step, or interpretation. Make a separate card only if it tests a distinct fact. For a calculation that needs several steps, keep the flashcard on the key relationship and practise the full working as a written question.

The core the deck was cut from

A compact core checklist helps you decide whether a deck is supporting a complete answer rather than isolated recall. Keep it next to your course notes, and use the notation your lecturer or subject materials use.

A MySummaries core checklist for this general deck would read:

Must not miss coreQuantitative methods — general revision
Discount dated cash flows consistently: PV = Σₜ Cₜ(1+i)⁻ᵗ; state the timing and effective rate period.
For a random variable with finite second moment: E[X] = Σₓ xp(x) and Var(X) = E[X²] − [E(X)]².
Use model assumptions explicitly: for example, aggregate expected claims λE[S] requires Poisson frequency with mean λ and severity independent of frequency, with finite mean.
Interpret approximations with their limits: ΔP/P ≈ −D_mod·Δy is first-order for a small parallel yield change and excludes convexity.

The caption identifies this as an illustrative checklist, not an official syllabus. To make the core relevant, compare it against the learning outcomes and worked examples for your particular subject. Add any prescribed method or convention from those materials, and remove anything not in scope.

Turn repeated misses into practice

A recurring error is useful information. If you confuse effective and nominal rates, make a short conversion example and check the compounding basis. If you use a formula but cannot state its assumptions, practise adding an assumptions line before the calculation. If your calculation is sound but your answer stops at a number, add one sentence about its meaning for the question’s decision-maker.

That is also how you should review written problem-solving work. A strong response usually makes assumptions visible, shows a suitable method and clear workings, checks units and signs, and interprets the result. Where relevant, it also notes sensitivities, limitations, and model risk. These are useful practice habits, not a claim about a particular official marking scheme. Follow the requirements stated in your own assessment materials.

A remediation card can target a specific gap rather than asking you to reread a whole topic:

Remediation tray

You lost this mark twice: expected aggregate claims were written as λE[S]. State the assumptions that make this formula valid, then explain what you would check if frequency and severity were dependent.

Add cardDismiss

The caption describes an illustrative review prompt based on a repeated omission. After answering it, check your notes and revise the card if the course uses a more specific model or convention. A flashcard should bring a fact back to mind; a timed written response is where you practise selecting methods, justifying assumptions, and communicating a conclusion under pressure.

How MySummaries helps

MySummaries builds revision boards from your own PDFs, slides, and photographed notes, then generates flashcards from those materials. For this task, start with a quantitative-methods board drawn from the content and notation you are assessed on, review the resulting cards with spaced repetition, and use written mock exams to practise showing method and interpreting results. Open MySummaries.