IB Mathematics Analysis & Approaches HL Flashcards

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

• What must you state when you define a function f?A rule that assigns each valid input exactly one output, plus the intended domain if it is restricted.
• What is an arithmetic sequence?A sequence with a constant difference between consecutive terms.
• What does a definite integral represent on a graph?The signed area between the curve and the x-axis from the lower to the upper limit.
• When is a function invertible on a domain?When it is one-to-one on that domain, so each output comes from exactly one input.
• What is the derivative at a point, in words?The instantaneous rate of change, or the slope of the tangent, at that input.
• What is a residual in a simple model fit?Observed value minus the value the model predicts at the same input.
• What does “hence” ask you to do?Use the previous result directly rather than starting a new method from scratch.

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

• nth term of an arithmetic sequence with first term u1 and common difference du_n = u_1 + (n − 1)d
• Sum of n terms of a geometric sequence with first term u1 and ratio r ≠ 1S_n = u_1 (r^n − 1) / (r − 1)
• Derivative of sin(x) with x in radianscos(x)
• Product rule for y = uvy' = u'v + uv'
• Equation of a line through (x1, y1) with slope my − y1 = m(x − x1)
• Quadratic formula for ax^2 + bx + c = 0x = (−b ± √(b^2 − 4ac)) / (2a)
• Chain rule in wordsDifferentiate the outside, then multiply by the derivative of the inside.

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.

• What does y = f(x) + k do to the graph of y = f(x)?Translates it vertically by k (up if k > 0).
• What does y = f(x − h) do?Translates it horizontally by h (to the right if h > 0).
• What does y = −f(x) do?Reflects the graph in the x-axis.
• What does y = f(−x) do?Reflects the graph in the y-axis.
• What does y = a f(x) do when |a| > 1?Vertical stretch from the x-axis by factor |a|.
• What does y = f(bx) do when |b| > 1?Horizontal compression towards the y-axis by factor 1/|b|.
• Which part of a formula is the “inside” transformation?Operations on x. They affect the graph horizontally, often opposite to the sign you first expect.
• Image of the point (2, 5) under y = f(x − 3) + 1?(5, 6): x increases by 3, y increases by 1.
• What stays fixed in a vertical stretch y = a f(x)?Points on the x-axis (x-intercepts).
• How does the asymptote y = 2 move under y = f(x) − 4?It becomes y = −2.
• How is an inverse related to a reflection?The graph of y = f⁻¹(x) is the reflection of y = f(x) in the line y = x.
• After translating a piecewise function, what else must you update?The domain inequalities for each piece.

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.

• When must the calculator be in radian mode?For calculus with trigonometric functions, and whenever the question uses radians.
• What should you store instead of a rounded intermediate?The exact expression or a high-precision value. Round only in the final part that asks for a decimal.
• What must you write when a GDC solves an equation?The equation you solved, not only the output.
• Why check the graph window?Roots or intercepts can sit outside a default view and look as if they do not exist.
• How do you confirm a factorisation?Expand it, or plot both expressions and check they overlay.
• What is a degree-mode trap on a derivative of sin?The derivative rules assume radians; degree mode silently gives the wrong slope.
• When is a numerical solve not enough?When the question wants exact form, or when extra roots in an interval must be listed.
• What should you reset or check at the start of a paper?Angle mode, and that you are not in a leftover stat or graphing setup from revision.
• How do you avoid losing an exact log or radical?Keep it until a part asks for 3 s.f. or similar.
• What does a table of values help you catch?Discontinuities, extra roots, or a sign change you missed on a sketch.
• Why write the window or list you used?So a marker can follow the technology step and award method marks.
• What is a “trace” trap?Reading a pixel approximation as an exact intercept; zoom or solve to the accuracy required.