IB Maths AI SL · Unit 2: Functions
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 the way an IB examiner expects — then try the practice questions and check your working against the mark scheme.
Solve $3x - 7 = 5x + 2$.
1. Subtract $3x$ from both sides: $-7 = 2x + 2$.
2. Subtract $2$: $-9 = 2x$.
3. Divide by $2$: $x = \frac{-9}{2}$.
4. State: $\mathbf{x = -4.5}$.
Find the exact roots of $x^2 - 5x - 14 = 0$.
1. Identify two numbers that multiply to $-14$ and add to $-5$.
2. Determine: $-7$ and $+2$.
3. Factorise: $(x - 7)(x + 2) = 0$.
4. Solve: $x = 7$ or $x = -2$.
5. State: $\mathbf{x = 7 \text{ and } x = -2}$.
Solve $e^x = 4 - x^2$ using your GDC. Give your answers to 3 s.f.
1. Recognise: mixed exponential and quadratic — must be solved graphically.
2. Enter $Y_1 = e^x$ and $Y_2 = 4 - x^2$ on the GDC.
3. Use the intersection tool.
4. Read the intersections: $x = -1.964\ldots$ and $x = 1.058\ldots$
5. Round: $\mathbf{x = -1.96 \text{ and } x = 1.06}$.
Three questions from the bank, easiest first. Mark schemes and AI marking of your written working are in the practice area.
Consider the exponential equation \(2(3)^x = 162\).
By finding a common base, solve for the exact value of \(x\) without using a calculator.
Solve the exponential equation \(3^{2x-1} = 27\) for the exact value of \(x\).
Consider the equation \(e^{2x} - 5e^x + 6 = 0\).
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).
Both. In the bank, Paper 1: 6 · Paper 2: 6. Practise with your GDC — AI papers expect calculator methods throughout.
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.