UNIT 5: The binomial theorem SPECIFICATION REFERENCES Understand and use the binomial expansion of (a for rational including its use for 4.1 + bx)n n, approximation; be aware that the expansion is valid for < 1 (proof not required) KNOWLEDGE Covered so far Series and sequences (See Unit 4 of the SoW) GCSE (9-1) in Mathematics at Higher Tier A4 Algebraic fractions AS Mathematics Pure Mathematics content – 2.6 Algebraic division, factor theorem (See Unit 3a of the SoW) 4.1 Binomial expansion of the form (a + , where is a positive integer (See Unit 3b of the SoW) bx)n n KEYWORDS Binomial, expansion, theorem, integer, rational, power, index, coefficient, validity, modulus, factorial, combinations, Pascal’s triangle, partial fractions, approximation, converges, diverges, root. nCr, The formula book includes formulae for the binomial expansion: (a + = 1b + 2b2 + + + + b)n an + an – an – … an – rbr … bn where = nCr (1 + = 1 + + (|x| < 1, ) x)n nx n This unit links with the binomial distribution in the statistics section of the remaining A level Mathematics content of statistics. Teaching time 5a. Expanding (a + for rational knowledge of range of validity bx)n n; (4.1) 4 hours
UNIT 5: The binomial theorem SPECIFICATION REFERENCES 4.1 Understand and use the binomial expansion of (a + bx)n for rational n, including its use for approximation; be aware that the expansion is valid for < 1 (proof not required) KNOWLEDGE Covered so far Series and sequences (See Unit 4 of the SoW) GCSE (9-1) in Mathematics at Higher Tier A4 Algebraic fractions AS Mathematics – Pure Mathematics content 2.6 Algebraic division, factor theorem (See Unit 3a of the SoW) 4.1 Binomial expansion of the form (a + bx)n , where n is a positive integer (See Unit 3b of the SoW) KEYWORDS Binomial, expansion, theorem, integer, rational, power, index, coefficient, validity, modulus, factorial, nCr, combinations, Pascal’s triangle, partial fractions, approximation, converges, diverges, root. The formula book includes formulae for the binomial expansion: (a + b)n = an + an – 1b + an – 2b2 + … + an – rbr + … + bn where nCr = (1 + x)n = 1 + nx + (|x| < 1, n ) This unit links with the binomial distribution in the statistics section of the remaining A level Mathematics content of statistics. 5a. Expanding (a + bx)n for rational n; knowledge of range of validity (4.1) Teaching time 4 hours
A_level_Maths_2_years_SoW.docx