Combinatorics, Series and Vectors
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11. Permutations and combinations
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.
12. Series
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.
13. Vectors in two dimensions
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.