HL Math

Higher Level Mathematics Resources

I use this curriculum: IB HL Curriculum
We use this textbook: Higher Level Mathematics - Wazir & Garry
These are the worked out solutions: Solution Guides
I assign this homework: Assignment Grid
I use this class syllabus: Syllabus
I make kids post questions in a forum.

Week 1: Limits
Used sections 12.1-12.3 of this book.  In the past I had begun with an intense algebra review anyway, teaching limits and making kids evaluate derivatives by hand allowed me to have kids practice those skills without numbing their minds too much.  It worked very well.  You can use any introductory limits chapter from any Calculus or Precalculus book.  I did not test on this section.
Note: Eliminate most if not all trig from assigned work.


Weeks 2-3: Fundamentals & Functions (Chapters 1 & 2)
I had students work primarily independently on these chapters.  Most of the content was material they learned in Algebra 2 if not before.  I made a special point to highlight the following:
  • Set theory
  • Formal definition of a function
  • Domain & range
  • Various international notations
  • Domain & Range of composites
  • Domain restriction for inverse functions [powerpoint]
  • Absolute value graphs
Learning Targets:
  • LT A: Function domains, ranges, and inverses [ 2.1 ]
  • LT B: Function compositions and transformations [ 2.1, 2.2, 2.3 ]
    Learning Target exams can be found HERE.

Weeks 4-5: Algebraic Functions, Equations and Inequalities (Chapter 3)
Much of this chapter was also structured around independent learning & review.  I highlighted the following:
  • Relationship between degree & possible extrema
  • Relationship between roots of multiplicity & graphical behavior
  • Rational functions
    [powerpoints]
  • Polynomial & Rational inequalities
  • Discriminant problems that turn into polynomial inequalities
  • Absolute value & rational equations and inequalities
Learning Targets:
  • LT C: Quadratic forms [ 2.6 ]
  • LT D: The discriminant and quadratic inequalities [ 2.6, 2.7 ]
  • LT E: Polynomial & rational functions [ 2.4, 2.5, 2.6 ]
    Learning Target exams can be found HERE.

Weeks 5-9: Sequences & Series
This is a chapter that begins with a pretty pedestrian analysis of sequences & series, and then descends into madness with mathematical induction.  That's the student perspective anyway, madness.  I love it, obviously.

This is where students really start figuring out how to use and how valuable the formula packet can be.

Learning Targets:
  • LT F: Arithmetic Sequences & Series [ 1.1 ]
  • LT H: Geometric Sequences & Series [ 1.1 ]
  • LT G: Counting Principles [ 1.3 ]
  • LT K: Binomial Theorem [ 1.3 ]
  • LT L: Mathematical Induction [ 1.4 ]
    Learning Target exams can be found HERE and HERE.

Weeks 10-11: Exponential & Logarithmic Functions
Again, we have a chapter that was covered pretty well at the Algebra 2 level.  I took care to emphasize the following:
  • Laws of exponents (using the Super Exponent Spectacular)
  • Definitions of and why it shows up when we compound continuously [powerpoint]
  • Tricky log problems. I put them in mixed-ability groups and give them this contest.  Prizes can make it really fun!
Learning Targets:
  • LT I: Exponential Growth & Decay [ 1.2 ]
  • LT J: Logarithmic & Exponential Functions & Equations [ 1.2 ]
    Learning Target exams can be found HERE.

Matrix Algebra: IB dropped this part of the curriculum and although I didn't ignore this completely, I gave it a very superficial reading, making sure that they at least knew how to very quickly solve systems using the reduced row echelon function in their calculators.

Weeks 12-13: Trimester One Review & Final

Weeks 14-17: Circle Trig
This chapter is a monster.  I typically supplement this one quite a bit.  In it are:
Learning Targets:
  • LT K: Circular Functions and Equations
  • LT L: Length of Arcs and Area of Sectors
    Learning Target exams can be found HERE.
Week 18: Triangle Trig
Pretty uneventful chapter.  Tore through it pretty quickly.  Law of sines & cosines is the highlight (powerpoint).

Learning Targets:
  • LT M: Triangle Trigonometry
  • LT N: Trigonometry in 3D Figures
    Learning Target exams can be found HERE.

Weeks 19-21: Vectors (part 1)
This is basically the 2D section and introduction to the dot (scalar) product.  Some notes:

  • IB has very little expectation by way of force applications.  This requires a minimal treatment.
  • It's really important to show all representations throughout, especially graphical representation.
  • Without doing much with them, it's not very fruitful to teach projections.
  • Most emphasis should be on:
    • Graphical & algebraic problem solving
    • Applications involving speed & direction (boats, planes, etc)
Learning Target:
  • LT O: 2D Vectors
    LT exam can be found HERE.






2 comments:

  1. I hope to finish this page sometime in the next three weeks.

    ReplyDelete