# 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)

**SL (AA)**

deductive proof (1.6)

exponents & logarithms (1.7)

infinite geometric series (1.8)

binomial theorem (1.9)

**HL - Number & Algebra**

**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

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### 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...

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