Syllabus breakdown

AI SL Number and Algebra syllabus points

The checklist below details the official syllabus points required for Paper 1 and Paper 2 in Topic 1.

  1. 1.1Scientific notation / standard form $a \times 10^k$, rounding, estimation, and percentage error $\varepsilon = \left|\frac{v_A - v_E}{v_E}\right| \times 100\%$
  2. 1.2Arithmetic sequences and series: general term $u_n = u_1 + (n-1)d$, sum $S_n = \frac{n}{2}(2u_1 + (n-1)d)$
  3. 1.3Geometric sequences and series: general term $u_n = u_1 r^{n-1}$, sum $S_n = \frac{u_1(r^n - 1)}{r - 1}$
  4. 1.4Financial mathematics: compound interest, nominal vs effective annual rates, depreciation, loans, and amortization schedules using GDC TVM Solver
  5. 1.5Solving systems of linear equations in up to 3 variables using technology and algebraic methods

Interactive guides

Topic 1 Interactive Study Guides

Each guide features full study notes, 10 progressive practice exercises with complete markschemes, formula sheets with common pitfalls, and an exam mini test.

Lesson 1.1

Scientific Notation & Percentage Error

Operations with $a \times 10^k$, significant figures, bounds, and calculating percentage error in real measurements.

Start Guide
Lesson 1.2 & 1.3

Arithmetic & Geometric Sequences

Recursive patterns, $n$-th terms, sigma notation, partial sums, and real-world linear and exponential growth modeling.

Start Guide
Lesson 1.4

Financial Math: Compound Interest & Loans

Future value compounding, annual depreciation, mortgages, annuity investments, and GDC TVM Solver workflows.

Start Guide
Lesson 1.5

Systems of Linear Equations

Formulating equations from context, solving $2 \times 2$ and $3 \times 3$ systems algebraically and with GDC matrix polynomial solvers.

Start Guide

Exam insights

Key ideas & Common GDC Pitfalls

  • Compounding Periods: When interest compounds quarterly ($k=4$) or monthly ($k=12$), remember that the nominal annual rate must be divided by $k$, and the total periods $n$ is multiplied by $k$.
  • Percentage Error Denominator: The official IB formula is $\varepsilon = \left|\frac{v_A - v_E}{v_E}\right| \times 100\%$. Always divide by the exact value ($v_E$), never the approximation.
  • TVM Sign Convention on GDC: Money leaving your pocket (investment, down payment) is negative; money received (loan principal, withdrawal) is positive.

Next topic

Continue to Topic 2

Once you have consolidated sequences and financial models, proceed to Topic 2: Functions & Modelling.