Combinatorics, Series and Vectors
- Syllabus
- 0606–2028–2029
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- Level
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Topic 11
11. Permutations and combinations
Objectives in this topic
11.1. Distinguish permutations and combinations
- Recognise the difference between permutations and combinations and know when each should be used.
11.2. Use n! and nPr/nCr expressions
- Know and use the notation n! and the expressions for permutations and combinations of n items taken r at a time.
- Includes 0! = 1.
11.3. Solve arrangement and selection problems
- Solve arrangement and selection problems using permutations or combinations.
- Problems will be in everyday contexts or based on algebraic problems.
- Problems involving repeated objects, circular arrangements, or both permutations and combinations are not included.
Topic 12
12. Series
Objectives in this topic
12.1. Use the binomial theorem
- Use the binomial theorem to expand (a + b)^n for positive integer n.
- Includes simplification of coefficients.
- The formula is given in the List of formulas.
12.2. Use the general binomial term
- Use the general term in a binomial expansion.
- Includes finding a specified term such as the term independent of x.
- Knowledge of the greatest term and properties of coefficients is not required.
12.3. Recognise arithmetic and geometric progressions
- Recognise arithmetic and geometric progressions and understand the difference between them.
12.4. Use finite progression formulas
- Use formulas for the nth term and the sum of the first n terms to solve problems involving arithmetic or geometric progressions.
- Problems may be in context.
- Formulas are given in the List of formulas.
12.5. Use convergence and sum to infinity
- Use the condition for convergence of a geometric progression and the formula for the sum to infinity of a convergent geometric progression.
- Explain why a particular geometric progression has or does not have a sum to infinity.
- The formula is given in the List of formulas.
Topic 13
13. Vectors in two dimensions
Objectives in this topic
13.1. Use vector notation
- Understand and use vector notation in forms including column vectors, directed line segments, p, and ai - bj.
- Use correct vector notation.
13.2. Use position and unit vectors
- Know and use position vectors and unit vectors.
- Find the unit vector in the same direction as a given vector.
13.3. Calculate and combine vectors
- Find the magnitude of a vector.
- Add and subtract vectors and multiply vectors by scalars.
- Includes equating like vectors and solving vector-geometry problems, with diagrams given in more complex cases.
13.4. Compose and resolve velocities
- Compose and resolve velocities.
- Determine a resultant vector by adding two or more vectors.
- Use a velocity vector to determine position and solve contextual problems such as particles colliding.