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Mock Examsfree1 April 2021

* Recent updates *25 March 2021: A second HL Paper 3 mock exam (MockB) with worked solutions has been posted on the Sample Mock Exams page.21 March 2021: A table with suggested grade boundaries for the... more

Paper 3 HL11 October 2020

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

Review Examsfree11 June 2020

review examsIn my opinion, one of the important objectives of any set of review questions should be giving students the experience of answering a wide variety of questions - variety in both syllabus material... more

Trig functions, equations & identities20 January 2021

The trigonometry syllabus content can essentially be split into two parts (with some overlap) of triangle trigonometry and trigonometric functions, equations & identities. Triangle trigonometry involves... more

5. Calculus18 March 2021

The Calculus topic has the largest number of suggested teaching hours of the five syllabus topics: 28 hours for SL (just one more hour than the Statistics & Probability topic at SL) and 55 hours for HL... more

Exams26 October 2017

DetailsExternal assessment (written exams) contributes 80% to the final grade that a student earns for either Maths HL or SL. The Internal assessment component, the Exploration, contributes the other... more

Differentiation basics8 June 2020

The introductory content for differential calculus is not too different between SL and HL; however, SL students do not need to learn the limit definition of the derivative (first principles) and to be... more

Triangle trig & applications23 March 2021

A large portion of the Geometry & Trigonometry syllabus topic (especially SL) focuse on trigonometry - and a large portion of the trigonometry content involves what I would refer to as "triangle" trigonometry.... more

4. Statistics & Probability2 March 2020

The Statistics & Probability topic is the syllabus topic (out of 5) that has the least amount of HL content. The suggested teaching hours for SL is 27 hours and it's only a few hours more for HL at 33... more

Probability distributions (TN)10 February 2021

go to teaching materialsSyllabus content (* SL content shared with Applications & Interpretation course)SL 4.7* Concept of discrete random variables and their probability distributions; expected value... more

2. Functions19 January 2021

The Functions topic includes several concepts and skills that play an important role in other parts of the course, such as: domain & range, inverse function, composite function, nature of the roots of... more

Problem of the Weekfree8 April 2021

skip to the Problem of the Week list belowTo me, a 'problem' is a question for which it is not clear how to begin a solution. The vast majority of questions that students are asked to answer during a... more

Managing the Exploration11 March 2021

I have written a Student Guide for the Exploration (v9) which can be viewed on the Exploration Student Guide page. The page has been marked as 'student accessible' so the Exploration Guide can be shared... more

3. Geometry & Trigonometry11 February 2021

The Geometry & Trigonometry topic has twice as much content at the HL level (51 suggested teaching hrs) than the SL level (25 suggested teaching hrs) because there is no vectors content at the SL level. more

Vectors HL18 November 2020

go to unit tests on vectors below ↴Comparing the syllabus content on vectors for the 'new' Analysis & Approaches course to the previous Maths HL and Maths SL courses is simple.Analysis & Approaches▪... more

IA - Exploration24 December 2019

The Internal Assessment (IA) requirement for both Maths-Analysis & Approaches (SL & HL) is for students to write a paper (recommended 12-20 pages) that explores a mathematical topic of their choice (with... 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

Exponential & logarithmic functions8 February 2021

go to teaching materialsSyllabus content:SL 1.7 Laws of exponents with rational exponents; laws of logarithms; change of base of a logarithm; solving exponential equations, including using logarithms.SL... more

Start-of-Course Assessment23 August 2020

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 prepared so that they... more

Complex numbers HL10 November 2020

teaching materialsThe fact that the HL syllabus content for complex numbers is in the first syllabus topic (Number & Algebra) is a perfect illustration of why the order in which content is listed in the... more

1. Number & Algebra5 February 2020

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... more

Units & Teaching Plan13 September 2020

skip down to Analysis & Approaches teaching plan v5Presented in the table below are suggested SL teaching units and HL teaching units for the Analysis & Approaches course. These do not correspond exactly... more

Sample Explorations21 July 2020

Included on this page are five samples of student Explorations (two SL students and three HL students) that are not part of the 29 Exploration examples (exemplars) provided by the IB in the 'Assessed... more

Exam Tips for Studentsfree24 April 2017

→ download a copy of these exam tips: 33 Exam Tips more

Basics/composite & inverse functions29 September 2020

go to teaching materials below ↴Function basics include items such as:▪ using appropriate notation for functions, composite functions & inverse functions▪ determining whether a relation is a function... more

Exploration Overview24 December 2019

"Education, then, must provide the opportunities for self-fulfillment; it can at best provide a rich and challenging environment for the individual to explore, in his own way."Noam Chomsky (excerpt from... more

Integration basics30 April 2020

When first teaching integration, I think it is helpful to look back at differentiation and try to impress upon students that differentiation is basically about finding rates of change, and that integration... more

Syllabus content (TN)23 July 2020

In the red box below are a set of notes on how the new syllabus for Analysis & Approaches compares to the current (or 'old') syllabuses for Maths HL and Maths SL.Below the box is a condensed list of the... more

Proof by induction HL27 December 2020

Proof by mathematical induction - and proof by contradiction - are the two formal proof methods included at HL level. Generally speaking, students do not have much experience (often none at all) in writing... more

Challenge Problems10 April 2016

Here you will find a miscellaneous collection of problems that require some amount of insight and problem solving skills. The difficulty level varies quite a bit - and not all of them are at the level... more

Probability of events (TN)10 February 2021

■ downloadable teaching materials for probabilities of eventsThe syllabus content on the probabilities of events overlaps a little with the other probability part of the syllabus: probability distributions... more

Related rates12 April 2020

Calculus gives us the tools and tecniques to precisely analyze situations where different quantities are changing in relation to each other. In other words, we can use calculus to solve problems involving... more

Exploration (IA) Ideas16 November 2019

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

Differential equations HL (TN)28 February 2021

HL syllabus content: first order differential equations; numerical solution of \(\frac{{{\rm{d}}y}}{{{\rm{d}}x}} = f\left( {x,y} \right)\) using Euler’s method; by separation of variables; homogeneous differential equations; solutions using the integrating... more

Linear regression (TN)10 February 2021

A more precise title for this syllabus content would be linear correlation of bivariate data - or, alternatively, simply bivariate statistics. It is worth emphasizing the word bivariate since it is critical... more

Distance Learning & Student Exploration (IA)24 April 2020

During this unsettling time when normal face-to-face teaching has been replaced with remote, or distance, learning there is the natural question about what kind of ‘lessons’ would be most suitable... more

4E. Probability introduction (SN)13 July 2020

… It is remarkable that this science, which originated in the consideration of games of chance, should become the most important object of human knowledge … The most important questions in life are,... more

Start Here20 November 2019

This site is organized to complement and coordinate with the content - especially the syllabus content - of the new IBDP maths course: Analysis & Approaches. Not including the Home page, there are 9 main... more

Integration by substitution (tutorial)27 April 2020

Throughout this tutorial you will often see the Leibniz notation for derivatives and differentials, named after the German mathematician Gottfried Wilhelm Leibniz (1646-1716). The beauty of this notation... more

Sketch the derivativefree5 January 2021

In the Geogebra applet below, you are presented with the graph of a function (blue) with a point P on it.The challenge is to sketch the graph of the derivative of the given function. Create the sketch... more

1A. Sequences & series intro (SN)6 October 2020

Sub-sections on this page:1A.1 Basics1A.2 Finding the \(n\)th term1A.3 Using technology1A.4 Summary1A.5 Challenge questionA numerical sequence is a set of numbers that are listed in a specific... more

Transformations of graphs29 April 2020

Use the two Geogebra applet below to test your knowledge of transformations of graphs that may include a translation, reflection or dilation (stretch or shrink). more

P.o.t.W. #116 November 2019

■ GDC is allowed ■SL: parts (a) & (b) HL: all parts(a) Determine the exact area bounded by the graph of \(f\left( x \right) = \sqrt {4 - {x^2}} \) and the x-axis.(b) Consider the function \(g\left( x \right) = \sqrt {\frac{{x + 2}}{p}} \) where \(p > \frac{1}{2}\). more

IBDP Maths Overview20 November 2019

The figure below shows the overall structure of IBDP mathematics (first exams May 2021) consisting of two courses: Analysis & Approaches and Applications & Interpretation. This depiction is constructed... more

Syllabus content (SN)23 July 2020

click on topic to skip down to that section of the syllabusTopic 1: Number and AlgebraTopic 2: FunctionsTopic 3: Geometry and trigonometryTopic 4: Probability and statistics more

Course Planning31 December 2019

Teaching in any curriculum system with external exams demands not only a certain level of mathematical knowledge and effective teaching methods, but also requires the teacher to make a significant effort... more

Inverse functions30 April 2020

Only a one-to-one function can have an inverse function. Any one-to-one relationship (e.g. \(y = {x^3}\) or \(y = \ln x\)) or many-to-one relationship (e.g. \(y = {x^2}\) or \(y = \sin x\)) is a function. However, if we tried... more

Math Articles for Students30 March 2020

Below is a list of 33 short thought-provoking articles on mathematics. Clicking on an article will open a downloadable PDF in a new window. Many of the articles are written by university professors and... more

Quadratic functions & equations17 September 2020

There is virtually no difference between SL and HL for the syllabus content on quadratic functions & equations. All of the content is at SL level and includes:SL 2.7 Solving quadratic equations and inequalities;... more

Start of Analysis course (year 1)23 August 2020

Below are some activities, assessments, materials and ideas that I often find useful at the start of teaching the 1st year of IB Maths-Analysis & Approaches. They are most suitable for HL students but... more