HL Maths Homepage
Series and Counting
Algebra and Functions
This unit should be taught over a period of about 2-3 weeks. It will build on the work from pre-IB. The focus should be on solving and graphing quadratics, and especially using the GDC for solving and graphing. You should be able to complete the square, know its uses as well as use the quadratic discriminant. You should also understand using the roots of quadratics, their sum and product.
HL Functions and Algebra
This unit should take 3-4 weeks depending on prior knowledge of functions. It is important for the remainder of the course to understand the function notation, especially the domain, range and inverse as this will be used throughout the entire course. You will also cover the transformations of curves, reciprocal curves, absolute and inequalities with reference to functions and graphs.
Logarithms are actually only a small part of the course, but again they will be used in other units, including calculus and especially series. This should take about 2 weeks to teach, but may need to be revisited from time to time.
HL Series, Expansions, and Counting
This unit is one of the longer units, about 4 weeks. It will build on previous work using quadratics, functions and logarithms. You should be able to find term and sums of series, as well as use binomial expansions by the end of this unit. It will also move into counting problems using the factorial (!) and combinations.
HL Proof by Induction
This unit is marked here as a quick couple of lessons on the concept of induction. You will find induction questions occurring throughout all subsequent units.
This is an important unit as you will need the key skills for both calculus and vectors in later units. Spend some time on this unit (4-5 weeks), and in particular master the radian formulae as well the exact non-GDC trigonometric ratios you will need. E.g. sin 30, cos 60, etc. Further, ensure that you can use the GDC to graph trig functions and solve function from graphs. You will also need to understand double, compound, and Pythagorean formulae.
HL Complex Numbers
It is important to have covered trigonometry prior to this unit as you will need some exact trigonometric ratios when doing this unit. The unit takes 3-4 weeks and should go through the concept of the number i, operations with complex numbers, and then representing complex numbers on the Argand diagrams. The final part will be De. Moivre’s theorem.
This unit could be seen as a stand alone unit, although it build on some trigonometry formulae. This usually takes about 3-4 weeks to cover. Particular points to ensure you have learnt will be 3d vectors, vector line equations and magnitudes of vectors. The HL course moves into equations of planes, cross product and angles and intersection points between lines and planes.
This is a short unit (2 weeks), and one of the easier units on the course. Make sure that you can use the GDC proficiently to find averages, standard deviation, and regression lines with correlation coefficients. You should also ensure that you understand the equations used to find the mean and standard deviation.
The first calculus unit, and differentiation may be new to some SL students. Take at least 4 weeks on this unit, going over techniques for differentiation (chain, product, quotient). It always helps to understand why you are differentiating (to find the gradient or the rate of change). The top end of this unit will focus on turning points and points of inflexion.
Integration is the opposite of differentiation. Again, it is a large unit (about 4 weeks), and you will find a large proportion of examination questions on this subject. Use integration to find areas under curves and volumes of revolution. Ensure that you can find areas and volumes with your GDC directly. At HL you will need to understand the different techniques, such as substitution and parts to integrate functions.
This is quite a long unit (at least 4-5 weeks). It should focus on solving simple probability using Venn diagrams and tree diagrams, and move on to using the GDC to solve probabilities for distributions such as binomial, poisson and normal. Also ensure that you fully understand the concept of conditional probability (given that) questions. Continuous distributions are covered and this will require a good understanding of integration.
Leave plenty of time at the end of the course to revise and recap the main units. Each of the revision topics has a Google Form and in addition graded questions (green, orange, red) on each topic.
Use the reviews at the end of each unit, or at the end of the course.