Let $f(x) = x e^{-x}$ and $g(x) = 0.2x$, for $0 \le x \le 5$. On the same axes, sketch the graphs of $f$ and $g$. [2] Find the coordinates of the maximum point of $f$. [2] Find the $x$-coordinate of the point of intersection of the graphs where $x > 0$. [2] Hence write down the set of values of $x$, $0 g(x)$. [1]

$f$: rises from the origin to a maximum near $x = 1$, then decays towards $0$ A1 $g$: straight line through the origin with gradient $0.2$ A1 $(1,\ 0.368)$ A1A1 $xe^{-x} = 0.2x \implies e^{-x} = 0.2$ (M1) $x = \ln 5 = 1.61$ A1 $0 < x < 1.61$ A1

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IB Maths AA SL · Unit 2: Functions

IB Maths AA SL Graphing Functions Questions

Q: How many IB Maths AA SL graphing functions questions are there?

There are 34 exam-style graphing functions questions in the AA SL question bank (Paper 1: 2 · Paper 2: 32), graded 9 easy, 13 medium, 9 hard, 3 very hard. Every question has a full IB-style mark scheme (M, A and R marks).

Q: Is graphing functions on Paper 1 or Paper 2?

Both. In the bank, Paper 1: 2 · Paper 2: 32. Paper 1 is non-calculator, so practise the exact-value algebra as well as the GDC methods.

Q: Where can I get the mark schemes?

Open the AA SL Unit 2 practice page: every question has a step-by-step IB-style mark scheme, and you can photograph your working for instant AI marking. The worked examples on this page are free.

Updated October 2026

Exam-style IB Maths AA SL graphing functions questions with worked solutions. Start with the 3 fully worked examples below — each is solved step by step, showing the working that earns the marks — then try the practice questions and check your working against the mark scheme.

34 questions
Paper 1: 2
Paper 2: 32
9 easy
13 medium
9 hard
3 very hard
3 worked examples

Practise Graphing Functions questions →

🖩 How do I do this on my calculator? Keystrokes for the Casio fx-CG50, TI-84 Plus CE and TI-Nspire.

What's examined in AA SL graphing functions

The question bank covers these graphing functions question types (number of questions in brackets):

Graph Properties (20)
Sketching and Displaying Graphs (7)
Solving Graphical Intersections (7)

Graphing Functions worked examples

Worked example 1: Finding intercepts and asymptotes algebraically · easy

Let $g (x) = \frac{4 x - 5}{2 x + 3}$ for $x \neq - 1.5$ . Find the exact equations of the vertical and horizontal asymptotes, and the exact coordinates of the $x$ and $y$ -intercepts.

Solution

4 steps · 1 to fill in

Examiner tip: For any rational function

y = \frac{a x + b}{c x + d}

, the horizontal asymptote is simply

y = \frac{a}{c}

Worked example 2: Solving intersections graphically · medium

Consider $f (x) = 5 - x^{2}$ and $g (x) = e^{0.5 x}$ . Use your GDC to find the $x$ -coordinates of their intersections to 3 s.f.

Solution

4 steps

Examiner tip: Always check your V-Window if intersections are not visible. Never try to solve mixed exponential-polynomial equations algebraically.

Worked example 3: Intersecting a function with its inverse · hard

Consider $f (x) = \ln (x + 2)$ for $x > - 2$ . The graph of $y = f (x)$ intersects $y = f^{- 1} (x)$ exactly twice. Find both intersection coordinates to 3 s.f.

Solution

5 steps

Examiner tip: Never find the algebraic inverse first if you only need intersection points — solving

f (x) = x

is much faster and bypasses complex algebraic manipulation.

Try these IB Maths AA SL graphing functions questions

Three questions from the bank, easiest first. Mark schemes and AI marking of your written working are in the practice area. One of them has its full worked solution here, open to everyone.

Question 1 · easy · 4 marks · Paper 2

Consider the quadratic function $f (x) = 2 x^{2} - 5 x - 12$ .

Use your graphic display calculator to find the coordinates of the $x$ -intercepts.
Find the coordinates of the vertex of the graph of $f$ .

Attempt it and see the mark scheme →

Question 2 · medium · 7 marks · Paper 2

Let $f (x) = x e^{- x}$ and $g (x) = 0.2 x$ , for $0 \leq x \leq 5$ .

On the same axes, sketch the graphs of $f$ and $g$ . [2]
Find the coordinates of the maximum point of $f$ . [2]
Find the $x$ -coordinate of the point of intersection of the graphs where $x > 0$ . [2]
Hence write down the set of values of $x$ , $0 < x \leq 5$ , for which $f (x) > g (x)$ . [1]

Full worked solution Free, no sign-in

$f$ : rises from the origin to a maximum near $x = 1$ , then decays towards $0$ A1
$g$ : straight line through the origin with gradient $0.2$ A1
$(1, 0.368)$ A1A1
$x e^{- x} = 0.2 x ⟹ e^{- x} = 0.2$ (M1)
$x = \ln 5 = 1.61$ A1
$0 < x < 1.61$ A1

Every question here has a full worked solution. See them all →

Question 3 · hard · 5 marks · Paper 2

Let $f (x) = \sin (e^{x})$ for $0 \leq x \leq 1.5$ . The angle $x$ is measured in radians.

Sketch the graph of $f$ on the given domain.
Find the exact $x$ -intercept of the graph of $f$ .

Attempt it and see the mark scheme →

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Revise graphing functions for the exam

FAQ

How many IB Maths AA SL graphing functions questions are there?

There are 34 exam-style graphing functions questions in the AA SL question bank (Paper 1: 2 · Paper 2: 32), graded 9 easy, 13 medium, 9 hard, 3 very hard. Every question has a full IB-style mark scheme (M, A and R marks).

Is graphing functions on Paper 1 or Paper 2?

Both. In the bank, Paper 1: 2 · Paper 2: 32. Paper 1 is non-calculator, so practise the exact-value algebra as well as the GDC methods.

Where can I get the mark schemes?

Open the AA SL Unit 2 practice page: every question has a step-by-step IB-style mark scheme, and you can photograph your working for instant AI marking. The worked examples on this page are free.

What else is free here

Save your answers and track your progressA free account remembers the questions you have done on every topic and brings you back to this page.

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Free ready-to-teach lesson (slides and teacher notes): Key features of graphs & intersections with technology.

IB Maths AA SL Graphing Functions Questions

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What's examined in AA SL graphing functions

Graphing Functions worked examples

Worked example 1: Finding intercepts and asymptotes algebraically · easy

Solution

Worked example 2: Solving intersections graphically · medium

Solution

Worked example 3: Intersecting a function with its inverse · hard

Solution

Try these IB Maths AA SL graphing functions questions

Question 1 · easy · 4 marks · Paper 2

Question 2 · medium · 7 marks · Paper 2

Full worked solution Free, no sign-in

Question 3 · hard · 5 marks · Paper 2

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