1. Number & Algebra

The Number & Algebra topic has the lowest number of suggested teaching hours of the five syllabus topics at SL level: 19 hours for SL. However, the number of suggested teaching hours at HL level is significantly higher (39 hours for HL) because of the inclusion of partial fractions, complex numbers, proof and solutions of systems of linear equations.

∼ quick link ∼
exercise sets, quizzes & tests for teaching units in Number & Algebra

Changes compared to previous Maths HL-SL syllabusses:
The following syllabus items have been added:
SL 1.2 arithmetic sequences and series: interpretation and prediction where a model is not perfectly arithmetic in real life; students will need to approximate common differences
SL 1.4 financial applications of geometric sequences & series: annual depreciation, calculate value of an investment with interest rate and inflation rate (exam Qs may require technology, including use of GDC financial package)
SL 1.6 simple deductive proof, numerical and algebraic; how to lay out a left-hand side to right-hand side proof; the symbols and notation for equality and identity
HL 1.10 extension of the binomial theorem to fractional and negative indices
HL 1.11 partial fractions; maximum of two distinct linear terms in the denominator, with degree of numerator less than the degree of the denominator
HL 1.15 proof by contradiction; use of a counterexample to show that a statement is not always true

Number & Algebra - syllabus overview 
Syllabus item numbers are in brackets.

SL - Number & Algebra

SL core (AA & AI)

arithmetic sequences & series (1.2)

geometric sequences & series (1.3, 1.4)

exponents & intro logarithms (1.1, 1.5)


deductive proof (1.6)

exponents & logarithms (1.7)

infinite geometric series (1.8)

binomial theorem (1.9)

HL - Number & Algebra


counting principles (1.10)

binomial theorem (1.10)

partial fractions (1.11)

complex numbers (1.12, 1.13, 1.14)

proofs & mathematical induction (1.15)

systems of linear equations (1.16)

  Exercise Sets, Quizzes & Tests

Set of 10 exercises on arithmetic sequences and series (Qs 1-4 no GDC; and Qs 5-10 GDC allowed). Answers included. Corrected version 2.

Quiz on arithmetic and geometric sequences and series. Six questions with GDC allowed on all.  Worked solutions below..

Solution key (worked solutions) for Quiz1 on sequences and series above.

Test covering sequences & series, binomial expansions, sigma notation and binomial theorem. Test has 9 questions (total of 50 mrks) with no GDC on first 4 questions and GDC allowed on last 5 questions. Suitable for SL and HL. Worked solutions available below.

Worked solutions for above test on sequences & series, binomial expansions, sigma notation and binomial theorem.

Test covering sequences & series, binomial expansions, sigma notation and binomial theorem. Test has 9 questions (total of 50 mrks) with GDC allowed on all questions. More suitable for HL. Worked solutions available below.

Worked solutions for above HL test on sequences & series, binomial expansions, sigma notation and binomial theorem.

Selected Pages

1A. Sequences & series intro (SN) 13 July 2021

Sub-sections on this page:1A.1 Basics1A.2 Finding the \(n\)th term1A.3 Using technology1A.4 Summary1A.5 Challenge...

Proof by induction HL 27 December 2020

Proof by mathematical induction - and proof by contradiction - are the two formal proof methods included at HL level. Generally...

Complex numbers HL 10 November 2020

teaching materialsThe fact that the HL syllabus content for complex numbers is in the first syllabus topic (Number & Algebra)...

Permutations & Combinations (SN) 10 November 2020

Andrea, Beatrice, Celia, Dinah and Eva are competing in an 800-metre run. Medals will be awarded for 1st place, 2nd place...

Euler's identity 9 November 2020

Although time for teaching Maths HL is very precious and a teacher should endeavour to not use up valuable class time for...

1C. Geometric sequences & series (SN) 25 August 2020

Sub-sections:1C.1 General term of a geometric sequence1C.2 Graph of a geometric sequence1C.3 Geometric series1C.4 Summary...

All materials on this website are for the exclusive use of teachers and students at subscribing schools for the period of their subscription. Any unauthorised copying or posting of materials on other websites is an infringement of our copyright and could result in your account being blocked and legal action being taken against you.