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new syllabus > new websitefree13 August 2019

new site coming ... The site for the new Analysis & Approaches course (SL & HL) will soon be available to all current and new subscribers. With regard to the new Analysis course, check out my Analysis... more

sequences & seriesfree2 January 2019

Quick links:► downloadable teaching materials for sequences & series► syllabus content for the Algebra Topic: SL syllabus (see syllabus section 1.1); HL syllabus (see syllabus section 1.1). more

Preparing for HL Paper 3 - Analysis1 August 2019

One of the more significant changes in the new IB maths courses is a completely revamped Paper 3 exam (HL level only). As the Analysis & Approaches Guide puts it, the Paper 3 exam consists of "two compulsory... more

Problem of the Dayfree18 August 2019

There are currently 375 problems (188 SL + 187 HL) with more problems added every week. There are separate pages for the SL Problem of the Day and for the HL Problem of the DayThere are two growing sets... more

Course Planning1 February 2016

Teaching in any curriculum system with external exams that assess a student's knowledge of content contained in a prescribed syllabus demands not only a certain level of mathematical knowledge and effective... more

Prior Learning Topics6 September 2017

Quick links:► downloadable teaching materials for prior learning topics► Prior Learning Topics for HL and Prior Learning Topics for SLThe Subject Guide for both Maths HL and Maths SL include a section... more

Start-of-Course Assessment1 September 2018

In both Maths HL and Maths SL, it is very important to design some lessons at the start of the first year to gather information and insights as to whether the students arriving in your class(es) are sufficiently... more

start of Maths HL yr.1free7 September 2017

Below are some activities, assessments, materials and ideas that I often find useful at the start of teaching the 1st year of Maths Higher Level. I've presented them in a timeline (week 1,2, 3 etc) of... more

SL & HL Core teaching sequencefree16 March 2015

The following is a suggested teaching sequence (plan) for the content in the Maths SL syllabus and the Maths HL Core syllabus. Of course, there is no single teaching sequence which is best for everyone... more

HL Core Syllabus Content2 July 2017

Below is a comprehensive summary of the core syllabus content for Math Higher Level that applies to first examinations in 2014 and final examinations in 2020. The core syllabus content contains six topics... more

Calculus Tests & Review18 June 2019

This page contains several unit tests on calculus - differential calculus and integral calculus for both Sl and HL. Most of the tests below have worked solutions (solution keys) available as a separate... more

Mock Examsfree16 February 2019

There is a strong argument that the most important assessments - other than the official IB exams taken in May or November - are the mock exams (i.e. 'practice' exams) that students take 2 to 4 months... more

exponents & logarithmsfree10 December 2018

Quick links:► downloadable teaching materials for exponents & logarithms► syllabus content for the Algebra Topic: SL syllabus (see syllabus section 1.2); HL syllabus (see syllabus section 1.2). more

basics/composite & inverse functionsfree2 December 2018

Quick links:► downloadable teaching materials for function basics and composite & inverse functions► syllabus content for the Topic: SL syllabus (see syllabus section 2.1); HL syllabus (see syllabus... more

Start Here25 September 2014

The site is organized to complement and coordinate with the content - especially the syllabus content - of the Maths HL and Maths SL courses. Not including the Home page, there are 11 main sections (top-level... more

triangle trigonometry & applications3 February 2018

Quick links:► downloadable teaching materials for triangle trigonometry & applications► syllabus content for the Trigonometry Topic: SL syllabus (see syllabus section 3.6); HL syllabus (see syllabus... more

trig functions, eqns & identities22 June 2018

Quick links:► downloadable teaching materials for trigonometric functions, equations & identities► syllabus content for the Trigonometry Topic: SL syllabus (see syllabus sections 3.2-3.5); HL syllabus... more

angles, circles, arcs & sectorsfree9 November 2016

Quick links:► downloadable teaching materials for angles, circles, arcs & sectors► syllabus content for the Trigonometry Topic: SL syllabus (see syllabus section 3.1); HL syllabus (see syllabus section... more

Teaching Unitsfree2 February 2016

Presented in the table below are suggested teaching units for both Maths SL and Maths HL. These do not correspond exactly with the six topics into which the syllabus is divided (core syllabus for HL)... more

SL Syllabus Content1 July 2015

Below is a comprehensive summary of the syllabus content for Math Standard Level that applies to first examinations in 2014 and final examinations in 2020. The syllabus content contains six topics (numbered... more

Syllabus Content14 July 2013

It is absolutely essential that a teacher of any IB diploma course have a thorough knowledge of the knowledge and skills that are listed in the course's syllabus. Of all the documentation that the IB... more

partial sums race29 September 2017

Use the Geogebra applet below to have a 'race' between the partial sums for two different series. It is initially set up with the geometric series $${\sum\limits_{k = 1}^n {\left( {\frac{4}{5}} \right)} ^{k - 1}}$$ versus the harmonic series $$\sum\limits_{k = 1}^n {\frac{1}{k}}$$. Increase... more

descriptive statisticsfree28 February 2017

Quick links:► downloadable teaching materials for descriptive statistics► syllabus content for the Algebra Topic: SL syllabus (see syllabus section 5.1); HL syllabus (see syllabus section 5.1). more

binomial theorem7 November 2018

Quick links:► downloadable teaching materials for binomial theorem► syllabus content for the Algebra Topic: SL syllabus (see syllabus section 1.3); HL syllabus (see syllabus section 1.3).The first... more

Teaching Units - content detailsfree2 February 2016

Content Details for Maths HL and Maths SL Teaching Unitsgo to SL teaching units 0. Fundamentals HLthe real numbers (and subsets); set notation; sets relations & operations; inequalities & inequality... more

Site Guide24 September 2014

If this is your first visit to the InThinking Maths HL & SL subject site, then you've come to the right place to start a look around the site ... and if it's a repeat visit then this is a good page to... more

probability distributions17 October 2018

Quick links:► downloadable teaching materials for probability distributions► syllabus content for Statistics & Probability Topic: SL syllabus (see syllabus sections 5.7, 5.8 & 5.9); HL syllabus (see... more

counting principles (HL)16 November 2017

Quick links:► downloadable teaching materials for counting principles► syllabus content for the Algebra Topic: HL syllabus (see syllabus item 1.3).Counting principles is specifically listed in the... more

Review Materials30 June 2019

This section contains collections of exam review questions for both HL and SL. There are three sub-pages included under this page:1. Sets of SL(HL) Review Exercises2. Sets of HL(SL) Review Exercises3.... more

integration by substitution / by parts12 March 2019

Quick links:► downloadable teaching materials for integration by substitution► syllabus content for the Calculus Topic: SL syllabus (see syllabus section 6.4); HL syllabus (see syllabus section 6.7). more

differentiation basics25 April 2019

Quick links:► downloadable teaching materials for differentiation basics► syllabus content for the Calculus Topic: SL syllabus (see syllabus section 6.1 ); HL syllabus (see syllabus section 6.1). more

Calculus10 November 2018

Quick links:► downloadable teaching materials for calculus (calculus tests & review quizzes)The Calculus Topic is the largest syllabus topic in terms of the recommended teaching hours for both SL and... more

probability of events12 September 2018

Quick links:► downloadable teaching materials for probabilities of events► syllabus content for the Statistics & Probability Topic: SL syllabus (see syllabus sections 5.5 & 5.6 ); HL syllabus (see... more

maxima & minima3 March 2019

Quick links:► downloadable teaching materials for maxima & minima► syllabus content for the Algebra Topic: SL syllabus (see syllabus section 6.3); HL syllabus (see syllabus section 6.3).The overall... more

rational functions14 November 2016

Quick links:► downloadable teaching materials for rational functions► syllabus content for the Topic: SL syllabus (see syllabus section 2.5); HL syllabus (see syllabus section 2.4)Information on rational... more

Trigonometry15 May 2018

Although trigonometry historically developed from the use of triangles in applications such as navigation, surveying, map-making and architecture, it is important for students to be aware that there are... more

vector basics & operations28 February 2018

Quick links:► downloadable teaching materials for vector basics & operations► syllabus content for the Vectors Topic: SL syllabus (see syllabus section 4.1); HL syllabus (see syllabus section 4.1). more

differentiation basics - Notes1 February 2015

A very important early concept in the study of differential calculus is the rate of change of a function. Students are very familiar with this idea in the context of a linear function - that is, the slope... more

Assessment13 December 2014

Assessments for Maths HL & Maths SL consist of written exams (external assessment) and a single internal assessment (IA) task. Maths HL has three written exams and SL has two written exams. The IA task... more

Algebra6 November 2014

There is a significant difference in syllabus content between the Algebra topic in Maths HL and the Algebra topic in SL. The number of recommended teaching hours for the Algebra topic in HL is 30 hours... more

exp & log functions & eqns21 November 2018

Quick links:► downloadable teaching materials for exponential & logarithmic functions and equations► syllabus content for the Topic: SL syllabus (see syllabus section 2.6); HL syllabus (see syllabus... more

complex numbers (HL)16 November 2018

Quick links:► downloadable teaching materials for complex numbers► syllabus content for the Algebra Topic: HL syllabus (see syllabus items 1.5, 1.6 & 1.7).complex number vs imaginary number more

Calculus HL option4 October 2018

► downloadable teaching materials for Calculus HL optionIn the previous Maths HL syllabus this HL option topic was entitled Infinite Series and Differential Calculus - and this title is still a reasonable... more

proof by induction (HL)free28 March 2016

Proof by mathematical induction is only in the HL course (not in SL) - and is the only formal proof method in the HL syllabus. Generally speaking, students do not have much experience (often none at... more

Resources26 January 2014

The resources included in this sub-section cover a wide range of items - websites, books, calculators, software, etc. Not included in this sub-section are downloadable teaching materials (tests, worksheets,... more

transformations of graphs28 May 2018

Quick links:► downloadable teaching materials for transformations of graphs► syllabus content for the Topic: SL syllabus (see syllabus section 2.3); HL syllabus (see syllabus section 2.3) more

Exploration (IA) Ideasfree9 September 2015

Most secondary students have very little or no experience in formal writing tasks in which they discuss and analyze mathematical ideas. They have completed countless hours of doing mathematics - e.g.... more

tangents & normalsfree8 March 2018

Quick links:► downloadable teaching materials for tangents & normals► syllabus content for the Calculus Topic: SL syllabus (see syllabus section 6.1); HL syllabus (see syllabus sections 6.1). more

Managing the Explorationfree17 February 2016

I have written a 10-page Student Guide for the Exploration - one for HL, and one for SL. Each Student Guide is available as a PDF such that the dates for the different steps can be filled in by you, the... more

Sample Explorations19 November 2014

The main purpose of this section of the IA (Exploration) part of the site is to provide a range of Exploration ideas that have been 'worked out' to some extent - somewhere from full 'original' (i.e. non-IB)... more