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IB Maths AI SL · Unit 2: Functions

IB Maths AI SL Solving Equations Questions

Updated October 2026

Exam-style IB Maths AI SL solving equations 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.

12 questions
Paper 1: 6
Paper 2: 6
2 easy
2 medium
4 hard
4 very hard
3 worked examples

Practise Solving Equations questions →

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

Key formulas

Equation of a straight line: $y = m x + c or a x + b y + d = 0$

In the same notation as the IB formula booklet. All AI SL formulas →

Solving Equations worked examples

Worked example 1: Solving a linear equation algebraically · easy

Solve $3 x - 7 = 5 x + 2$ .

Solution

4 steps · 1 to fill in

Examiner tip: Group the

x

-terms on the side that keeps the coefficient positive to avoid a division-by-negative slip in the last step.

Worked example 2: Solving a quadratic by factorisation · medium

Find the exact roots of $x^{2} - 5 x - 14 = 0$ .

Solution

5 steps · 1 to fill in

Examiner tip: If you use the GDC polynomial solver, note the coefficients

(a = 1, b = - 5, c = - 14)

in your working out to show the method.

Worked example 3: Solving a mixed exponential/quadratic equation graphically · hard

Solve $e^{x} = 4 - x^{2}$ using your GDC. Give your answers to 3 s.f.

Solution

5 steps

Examiner tip: Always zoom out initially when finding intersections — a second or third solution can easily hide off-screen if your default window is too narrow.

Try these IB Maths AI SL solving equations 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 · 3 marks · Paper 1

Consider the exponential equation $2 (3)^{x} = 162$ .

By finding a common base, solve for the exact value of $x$ without using a calculator.

Attempt it and see the mark scheme →

Question 2 · medium · 3 marks · Paper 1

Solve the exponential equation $3^{2 x - 1} = 27$ for the exact value of $x$ .

Full worked solution Free, no sign-in

Rewrite 27 as a power of 3: $3^{2 x - 1} = 3^{3}$ M1
Equate the exponents: $2 x - 1 = 3$ A1
Solve for $x$ : $2 x = 4 ⟹ x = 2$ A1

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

Question 3 · very hard · 7 marks · Paper 1

Consider the equation $e^{2 x} - 5 e^{x} + 6 = 0$ .

By using the substitution $u = e^{x}$ , rewrite the equation as a quadratic in terms of $u$ .
Solve the quadratic equation to find the two possible values of $u$ .
Hence, find the exact values of $x$ .

Attempt it and see the mark scheme →

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All 12 solving equations questions with mark schemes →

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Revise solving equations for the exam

FAQ

How many IB Maths AI SL solving equations questions are there?

There are 12 exam-style solving equations questions in the AI SL question bank (Paper 1: 6 · Paper 2: 6), graded 4 very hard, 2 medium, 4 hard, 2 easy. Every question has a full IB-style mark scheme (M, A and R marks).

Is solving equations on Paper 1 or Paper 2?

Both. In the bank, Paper 1: 6 · Paper 2: 6. Practise with your GDC — AI papers expect calculator methods throughout.

Where can I get the mark schemes?

Open the AI 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): Logarithms & exponential equations.

IB Maths AI SL Solving Equations Questions

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Key formulas

Solving Equations worked examples

Worked example 1: Solving a linear equation algebraically · easy

Solution

Worked example 2: Solving a quadratic by factorisation · medium

Solution

Worked example 3: Solving a mixed exponential/quadratic equation graphically · hard

Solution

Try these IB Maths AI SL solving equations questions

Question 1 · easy · 3 marks · Paper 1

Question 2 · medium · 3 marks · Paper 1

Full worked solution Free, no sign-in

Question 3 · very hard · 7 marks · Paper 1

Revise solving equations for the exam

FAQ

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Teaching this topic?

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