IB Mathematics Applications & Interpretation HL Flashcards

Say the prompt out loud, then reveal the answer. Edit any pair in wp-admin if your class uses different wording.

• What should a mathematical model include besides a formula?The meaning of the variables, the units, and the assumptions you are making.
• What is an exponential growth factor?The multiplier applied to the quantity in each equal time step.
• What is a residual?The gap between an observed value and the value the chosen model predicts.
• What does a definite integral often measure in context?A total accumulated quantity, such as distance or total change, over an interval.
• When is a linear model a poor first choice?When a scatter plot or residuals show a clear curve or changing spread.
• What is a sample space?The set of outcomes you are treating as possible for the chance experiment.
• What does “interpret” require beyond a number?A sentence in the context, with units, that a non-specialist could use.

These are recall prompts, not a substitute for the official formula booklet your cohort is allowed to use in examinations.

• Percentage change from old value A to new value B((B − A) / A) × 100%
• Mean of a list of n numbersSum of the values divided by n
• Equation of a regression line you would write after technologyŷ = a + bx, with a and b stated to a sensible accuracy
• Area of a triangle given two sides a, b and included angle C(1/2) ab sin C
• Compound interest idea (growth factor form)New = start × (growth factor)^(number of periods)
• z-score idea for a value x(x − mean) / standard deviation
• Expected value of a discrete random variable, in wordsEach outcome times its probability, then add.

Use this deck after a mock. Add a card whenever the same mistake appears twice.

• Why can a calculator answer still score zero?If you never show the method or the equation you solved, a marker cannot award method marks.
• What goes wrong if you mix degrees and radians?Trig derivatives and many exact values assume radians; a degree mode silently wrecks the calculus line.
• Why is rounding in part (a) dangerous?Later parts often need the exact expression. Round only when a part asks for a decimal.
• What is a domain trap after solving an equation?Extra roots that fail a restriction (length, probability, or given interval) must be discarded in writing.
• How do students lose an “explain” mark?They restate a number instead of connecting it to the context or the graph feature.
• What is the independence trap in probability?Multiplying probabilities that are not independent, or treating mutually exclusive as independent.
• Why does a sketch lose marks even when the shape is right?Missing intercepts, asymptotes, or a labelled scale — the features the question asked you to show.

If two students disagree on a command term, write your class rule under the answer and keep it.

• What does f′(x) denote?The derivative of f with respect to x.
• What does P(A | B) denote?The probability of A given that B has occurred.
• What does a bold or underlined final answer signal to a marker?The value or expression you want credited; box or underline it once.
• What does “show that” allow that “find” does not?You may use the given result as a target; you still need a complete method toward it.
• What does Σ (sigma) ask you to do?Add a sequence of terms that follow the stated index.
• What is the difference between a parameter and a variable in a model?A parameter is treated as a fixed number for that situation; a variable is the changing input or output.
• What should “sketch” include that “plot” might not?The key features and shape, not a table of many plotted points.

Say the prompt, then reveal. These are habits for graphs and models, not a catalogue of every possible composition.

• In a model h(t) = f(t) + k, what does k change?The baseline or intercept; every output is shifted by k.
• What does replacing t by (t − 3) do in a time model?Delays the same pattern by 3 time units.
• What does a negative coefficient in front of a whole model do?Reflects outputs through the input axis; peaks become troughs.
• What does y = 2 f(x) do to every output?Doubles it. Units stay the same if f was already in those units.
• Why do inside changes often look reversed?You are changing the input that produces a given output, so the graph moves opposite to the substitution.
• How do you describe y = f(2x) in words?The same outputs happen twice as fast (compressed in the input direction).
• Point (4, 10) under y = 0.5 f(x) + 1?(4, 6): x unchanged, y halved then plus 1.
• What should you state after transforming a model?New intercepts, new practical domain, and whether units changed.
• Periodic model f(x − 2): what happens to the period?The period stays the same; the phase shifts by 2.
• Vertical translation vs vertical stretch in data?Translation adds a constant; stretch multiplies deviations from the x-axis.
• Inverse of a conversion model?Swap input and output meanings and reflect through y = x; check the new domain.
• Piecewise tariff after a time shift?Shift each breakpoint, then rewrite the intervals.

If your class uses a slightly different rule for a verb, edit the answer in wp-admin and keep it.

• What does “state” usually require?A short fact, name, or value with little or no working.
• What does “calculate” require?A numerical answer with working shown.
• What does “find” require?An answer with working; it may be exact or rounded as asked.
• What does “show that” allow?You may aim at a given result, but the method must still be complete.
• What does “hence” forbid?Starting a new method that ignores the previous part.
• What does “explain” need beyond a number?A reason tied to the context, graph, or definition.
• What should a “sketch” show?Shape and key features (intercepts, turning points, asymptotes), not a table of plotted points.
• How is “draw” or “plot” stricter than “sketch”?Use a sensible scale and plot accurately enough to read values.
• What does “write down” signal?Little working is expected; the result should be immediate from a previous line or a diagram.
• What does “determine” often mean?Obtain a value with reasoning, frequently from a graph, table, or model.
• What does “justify” ask for?A valid reason for a choice, not a restatement of the choice.
• What does “comment” or “suggest” allow?A short, plausible remark in context; “suggest” need not be the only possible reason.

Use this deck the week before a timed paper. Add a card whenever a GDC habit cost you a mark.

• What do you record from a regression besides a and b?The variables, units, and the window or lists you used.
• Why turn diagnostics on for a linear fit?So you can quote r or r² if the question asks, and judge whether linear is plausible.
• pdf vs cdf for a continuous distribution?pdf is a density; probabilities for intervals come from a cdf or an area.
• What is a list-length trap?Frequency and data lists of different lengths, or a leftover extra value from a previous question.
• How should you report a GDC integral in context?Write the integral, the limits, and the interpreted quantity with units.
• Default window problem in modelling?A practical domain (time ≥ 0) may need a window that matches the situation, not −10 to 10.
• When is a numerical solver risky?It can miss extra roots or depend on the guess; sketch first.
• Chi-squared expected counts: what do you check?That expected frequencies are large enough for the test you chose, and that you used counts not percentages.
• Rounding money or people?Do not leave a fractional person; say how you rounded and whether the model still makes sense.
• What should you clear between questions?Lists, stored regressions, and plot stats that would contaminate the next fit.
• Residual plot: what are you looking for?Random scatter. A curve or fan shape says the model is a poor fit.
• Why write the calculator command for a normal probability?To show whether you used a cdf, a tail, or a continuity decision.