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.
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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)
SL (AA)
deductive proof (1.6)
exponents & logarithms (1.7)
infinite geometric series (1.8)
binomial theorem (1.9)
HL - Number & Algebra
HL (AA)
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
AA_SLC_1.2_arith_seq_series1_v2
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.
AA_Quiz1_seq_series_v1
Quiz on arithmetic and geometric sequences and series. Six questions with GDC allowed on all. Worked solutions below..
AA_Quiz1_seq_series_v1_SOL_KEY
Solution key (worked solutions) for Quiz1 on sequences and series above.
Test-seq_series_binomial_thm
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.
Test-seq_series_binomial_thm_SOL_KEY
Worked solutions for above test on sequences & series, binomial expansions, sigma notation and binomial theorem.
AA_HL_Test1_seq_series_bin_thm_v1
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.
AA_HL_Test1_seq_series_bin_thm_v1_SOL_KEY
Worked solutions for above HL test on sequences & series, binomial expansions, sigma notation and binomial theorem.
Selected Pages
1. Number & Algebra
Complex numbers HL Free
go to teaching materials ↴The fact that the HL syllabus content for complex numbers is in the first syllabus topic (Number...
1. Number & Algebra
Deductive proof
teaching materials ↴All students, SL and HL, need to be familiar with the concept of a deductive proof. According to the...
1. Number & Algebra
Binomial theorem
syllabus contentSL 1.9: The binomial theorem: expansion of \({\left( {a + b} \right)^n},\;n \in \mathbb{N}\); use of Pascal's...
1. Number & Algebra
Counting principles
go to teaching materials ↴Syllabus contentAHL 1.10: Counting principles, including permutations and combinations.Not required:...
1. Number & Algebra
Sequences & series
teaching materialsAlthough it's interesting (and I would say worthwhile) to discuss sequences that are defined by recursive...
1. Number & Algebra
Proof by induction HL
Proof by mathematical induction - and proof by contradiction - are the two formal proof methods included at HL level. Generally...