Teacher Notes

go to unit tests for HL Vectors below ↴

Comparing the syllabus content on vectors for the current Analysis & Approaches course to the old Maths HL and Maths SL courses is simple.
Analysis & Approaches
▪ vectors syllabus content in SL level ... none !
▪ vectors syllabus content in HL level ... everything (that is, all the vectors material in the old Maths HL course is in HL level of Analysis & Approaches)

The difference between no vectors material at SL level to a substantial amount of vectors material at HL level is one of the more distinguishing features between SL and HL for the Analysis & Approaches course.

Vectors are a useful mathematical concept and tool in geometry, trigonometry, kinematics and in physics. Practical applications of vectors arise in many situations.

Teaching approaches

One way to begin the study of vectors (even if students have encountered vectors in a previous mathematics or physics course) is to actually avoid using the word 'vectors', and use some other term or phrase which better fits what a vector actually does. It's the concept of a vector (what information a vector provides) that is most important to get across to students when first starting to teach ectors.

♦ Two initial activities ♦

1. Movement Instructions: This student activity attempts to give an engaging and informative introduction to two-dimensional vectors referring to them as 'movement instructions' rather than 'vectors'. Take a look at this activity (there are six separate sections - each with its own set of instructions) and try it with your students at the very beginning of their study of vectors. 
AA_HL_3.12_movement_instructions

2. Another activity that I like doing with students at the start of their formal study of vectors is answering a question that they should be able to answer using some trigonometry. The question is simple and short: find the measure of the acute angle between two diagonals of a cube. In fact, I prefer to have students do this question as a class 'warm-up' exercise before I've even announced that we're starting a unit on vectors. I simply give them an exercise with no instructions on how to approach it - i.e. an open-ended question. Unless someone in the class has studied vectors before, the expectation is that all students should answer the question using the cosine rule - so, the exercise also serves as good review for an important item in trigonometry. Then what really makes the exercise useful is to re-visit the question at the end of studying vectors (or at least after a thorough study of the scalar product). Answering this question again using knowledge of vectors should give students an appreciation of how using vectors to solve geometric problems (and exam questions) can be very practical and efficient.
[ ANSWER: angle is approximately 70.529 degrees ]

 ♦ Unit Tests

Test1_HL_vectors_v1
Test covering most of the content for HL vectors. Contains 6 questions (total of 50 marks) - 3 questions with no GDC, and 3 questions with GDC allowed. No space is provided for students to show working - so separate answer paper will be needed. Answers included on last page (be sure to remove last page before giving to students!). Solution Key available below.

Test1_HL_vectors_v1_SOL_KEY 
Fully worked solutions for Test1_HL_vectors above

Test2_HL_vectors_v2
Test (longer than Test1 above) covering majority of content for HL vectors. Contains 11 questions (total of 80 marks) - 5 questions with no GDC and 6 questions with GDC allowed. Space is provided below each question for students to show working. Answers provided on last page (so be sure to detach last page before giving to students). Solution Key below.

Test2_HL_vectors_SOL_KEY_v2 
Fully worked solutions for Test2_HL_vectors above.

Test3_HL_vectors_v1
Unit test on vectors with 9 questions - total of 70 marks.  4 questions with no GDC (Part1), and 5 questions with GDC (Part 2).  Worked solutions available below.

Test3_HL_vectors_v1_SOL_KEY
Worked solutions for Test3_HL_vectors above.

♦ Review

AA_HL_3.12(8)_vectors_exam-style_Qs 
Set of six exam-style questions on vectors; answers included