What function topics should I revise for IB Maths AA?

Revise function notation, domain and range, graphs, composites, inverses, transformations, equations, intersections, and mathematical models. You should also be confident with the major function families taught at your level, including linear, quadratic, polynomial, reciprocal, exponential, logarithmic, and trigonometric functions where relevant. HL students face additional depth and may need to connect function behaviour with polynomial structure, rational functions, inequalities, and calculus. Do not study these ideas as completely separate chapters because examination questions often combine them. Use the official syllabus guide supplied through your school to distinguish SL content from HL-only extensions.

How do I find the domain of a composite function?

For $f\circ g$, begin by finding all inputs allowed by the inner function $g$. Then require the output $g(x)$ to belong to the domain of the outer function $f$. For example, if $f(x)=\sqrt{x}$ and $g(x)=x-4$, then $f(g(x))=\sqrt{x-4}$ requires $x\geq4$. Restrictions from denominators, logarithms, and even roots must all be preserved. Simply intersecting the original domains of $f$ and $g$ is not always valid because the output of $g$, rather than the original input, enters $f$.

When does an inverse function exist?

A function has an inverse function on a stated domain when it is one-to-one there, meaning that different permitted inputs do not produce the same output. Graphically, this is checked using the horizontal line test. A quadratic over all real numbers is not one-to-one, but it can become one-to-one after restricting its domain to one side of the vertex. After finding the inverse, exchange the original domain and range. You can verify the result by checking that the appropriate compositions simplify to the identity function.

Should I use a calculator for IB Maths AA functions questions?

Paper 1 does not permit technology, so you must be able to manipulate functions, solve suitable equations, and sketch key features by hand. Technology is allowed on Paper 2 and on the HL Paper 3, where it may be appropriate for graphing, finding intersections, or solving equations numerically. Even on a technology paper, write the equation or mathematical setup that produced the calculator result. Check the viewing window and ensure that you have found every solution in the stated domain. Unless a question gives different instructions, preserve exact values where appropriate or give numerical answers to the required accuracy.

Why do I lose marks even when my final answer is correct?

IB mathematics markschemes may award marks for method, accuracy, reasoning, answers, and interpretation, depending on the question. The official guide explains that full marks are not necessarily awarded for an unsupported correct answer on Papers 1 and 2. A calculator result without an equation, a graph without labelled features, or an inverse without a domain may therefore be incomplete. Command terms also control the expected evidence, so show, justify, and find require more than state or write down. Make your setup visible and include restrictions, units, coordinates, or contextual interpretation whenever they are relevant.

What is the best way to practise IB Maths AA functions questions?

Attempt a small set before consulting notes or solutions so that the practice tests method recognition rather than copying. After each attempt, watch a complete worked video solution and identify the first point where your reasoning diverged. Reproduce the solution from memory, then solve a similar question without support. Keep a categorized error log covering domain restrictions, inverse branches, composition order, transformations, calculator use, and presentation. Finish each revision cycle with mixed timed questions because the examination will not identify the method for you in advance.

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IB Maths AA Functions Questions: Exam Methods

• 5 Aug 2026•13

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IB Maths AA Functions Questions: Exam Methods | RevisionDojo

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IB Maths AA Functions Questions: Exam Methods

• 5 Aug 2026•13

IB Maths AA functions questions become much more manageable when you identify the question type before calculating. Most test one or more recurring methods: interpreting notation, finding a domain or range, composing functions, constructing an inverse, transforming a graph, solving an equation, or interpreting a model.

The most effective preparation is an active cycle: attempt a question, compare your method with a complete worked video solution, record the specific error, and then solve a similar question without help. This builds recognition and mathematical method faster than repeatedly reading notes because it forces you to make the decisions required in an examination.

How functions are examined in IB Maths AA

Functions is one of the five syllabus topics in Mathematics: Analysis and Approaches. It is not confined to isolated function questions. Function notation and graph reasoning also appear in calculus, sequences, trigonometry, probability models, and optimization.

The official course structure creates different demands across the examination papers:

Paper	Level	Technology	What functions questions commonly demand
Paper 1	SL and HL	No technology	Exact algebra, graph sketches, transformations, inverses, composites, and equation solving
Paper 2	SL and HL	Technology allowed	Graphical intersections, numerical solutions, regression or modelling, and interpretation
Paper 3	HL only	Technology allowed	Extended problem solving that may connect functions with calculus, proof, or unfamiliar patterns

Paper 1 and Paper 2 contain compulsory short-response and extended-response questions. The IB also states that a correct unsupported answer does not necessarily receive full marks: working, graphs, calculations, or explanations may be required. Consequently, calculator output should support a mathematical method rather than replace it.

The official command terms matter. State normally calls for a brief answer, whereas find and calculate require relevant working. Show that means constructing a valid argument that reaches the given result, not treating that result as an assumption.

Students can review the whole topic through the RevisionDojo Maths AA Functions hub before moving into targeted questions.

The recurring functions question types

Function notation, domain, and range

For an expression such as $f(x)=\sqrt{5-2x}$ , the domain is controlled by the square root:

$5-2x\geq 0$ , so $x\leq \frac{5}{2}$ .

The range is $f(x)\geq 0$ . A common mistake is to give the unrestricted domain $x\in\mathbb R$ simply because no domain was printed beside the function.

Use these checks whenever a domain is requested:

A denominator cannot equal zero.
A square-root expression must be non-negative over the real numbers.
A logarithm's argument must be positive.
A composite function must satisfy the restrictions of both functions.
A contextual variable may have practical restrictions, such as time being non-negative.

Write restrictions precisely. For example, $x\in(-\infty,5)\cup(5,\infty)$ communicates more than saying only that the domain is all real numbers except 5.

Composite functions

For $(f\circ g)(x)$ , apply $g$ first and then $f$ . If $f(x)=2x+1$ and , then

$(f\circ g)(x)=f(g(x))=2(x^2-3)+1=2x^2-5$ .

By contrast,

$(g\circ f)(x)=g(2x+1)=(2x+1)^2-3$ .

Composition is generally not commutative, so these answers should not be expected to match. The domain of $f\circ g$ consists of inputs permitted by $g$ for which the resulting value $g(x)$ is also permitted as an input to $f$ .

Inverse functions

An inverse function reverses the original mapping. The original function must be one-to-one on its stated domain; otherwise, a restricted domain may be needed.

Consider $f(x)=(x-2)^2+1$ with domain $x\geq2$ . To find the inverse:

Write $y=(x-2)^2+1$ .
Rearrange: $y-1=(x-2)^2$ .

The domain of the inverse is $x\geq1$ , which is the range of the original function. The negative square-root branch is not included because it conflicts with the original restriction $x\geq2$ .

Remember that $f^{-1}(x)$ means an inverse, not $1/f(x)$ . A strong check is to verify that $f(f^{-1}(x))=x$ over the appropriate domain. Graphically, a function and its inverse are reflections in the line .

Graph transformations

Transformation questions frequently test signs and order. A reliable reference is:

Expression	Effect on $y=f(x)$
$f(x)+a$	Translation upward by $a$
$f(x-a)$

The recurring trap is that changes inside the function act horizontally and appear reversed. Thus $f(x+3)$ translates the graph three units left, not right.

When sketching, transform identifiable points and features rather than trying to redraw the entire curve by intuition. Track intercepts, turning points, endpoints, asymptotes, and excluded values. Label the axes and all features the question asks you to show.

Intersections and equations

An equation such as $f(x)=g(x)$ asks for the $x$ -coordinates where the two graphs intersect. On a technology paper, graph both functions, locate each intersection, and report the requested coordinate or solution to the required accuracy.

Do not copy an unrounded calculator display without checking the instruction. The official specimen-paper convention says that, unless stated otherwise, numerical answers should be given exactly or correct to three significant figures. Keep extra digits during intermediate work and round only the final value.

On Paper 1, look for factorization, substitution, logarithm laws, or a known graph relationship. If the question says hence, use the preceding result where possible because the structure is directing you toward an efficient method.

Function models

A modelling question may provide a function for population, cost, height, temperature, or another quantity. The algebra is only part of the answer; you must interpret the output in context.

Suppose $P(t)=1200(1.04)^t$ models a population $t$ years after measurement began. Solving $P(t)=1800$ gives a time, but the final statement should include units and contextual meaning. You should also respect the model's stated domain and avoid claiming that its behaviour remains realistic indefinitely.

A reliable method for answering any functions question

Use this sequence under examination conditions:

Identify the representation. Decide whether the function is given algebraically, graphically, numerically, or in context.
Translate the command. Determine whether you must state, find, sketch, solve, show, justify, or interpret.
Write restrictions first. Check denominators, roots, logarithms, inverse branches, and contextual limits.
Choose the method. Decide between exact algebra, graph technology, substitution, or a combination.
Show the mathematical setup. Write the composition, equation, transformation, or rearrangement before calculating.
Check the result. Substitute back, inspect the graph, test the domain, and verify whether the answer is reasonable.
Present the requested form. Include exact values or appropriate rounding, coordinates, interval notation, and units as needed.

This process prevents many errors that appear to be algebra mistakes but are actually interpretation mistakes.

Common traps that cost marks

The most frequent problems are predictable:

Applying $f$ before $g$ in $(f\circ g)(x)$ .
Confusing $f^{-1}(x)$ with .

Create an error log organized by these categories. Writing only careless mistake is not useful; recording forgot that the inverse domain equals the original range gives you a specific behaviour to correct.

Why worked video solutions accelerate improvement

Notes explain concepts, but examination questions test method selection. A worked video solution reveals the decisions between the lines: why a domain restriction is written first, why one inverse branch is rejected, where calculator technology is appropriate, and how the final answer is presented.

Use the following practice cycle:

Attempt one question without notes.
Mark the point at which you became uncertain.
Watch the complete worked solution, not only the final calculation.
Compare each line with your own working.
Close the solution and reproduce the method from memory.
Attempt a parallel question one or two days later.

The Functions Questionbank with worked solutions supports targeted practice, while the Functions video library lets you watch methods being worked through. Students using school-provided or licensed past questions can apply the same attempt, watch, reproduce, and retest sequence with RevisionDojo's per-question and topic video support.

Once individual methods are secure, use the broader IB Maths AA resource hub and Maths AA predicted papers for mixed practice. Jojo AI can help diagnose why a response lost marks, but you should still write and check the mathematics yourself.

A practical revision plan

Begin with a short diagnostic set from the RevisionDojo Questionbank. Sort every missed question into notation, domain and range, composition, inverse, transformation, equation, graph, or model.

During the next week, complete short clusters from one weak category at a time. Finish with a mixed, timed block so that you must recognize the method without being told the subtopic. The guide to targeted Maths Questionbank revision provides a useful structure for this process.

Do some work without a calculator and some with permitted technology. Fluency on Paper 1 and efficient graph use on Paper 2 are separate skills, and both must be practised deliberately.

Conclusion

IB Maths AA functions questions use recurring structures, but success depends on more than memorizing formulas. You must recognize the function type, preserve domain restrictions, choose an appropriate algebraic or graphical method, show enough working, and present the result in the requested form.

The fastest improvement usually comes from attempting questions before studying their worked video solutions, then reproducing the method and testing it on a similar problem. RevisionDojo's Functions Questionbank, video solutions, Jojo AI feedback, and mixed Maths AA papers can support that cycle from targeted practice to timed exam preparation.

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