Starter - Pascal’s Triangle
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Pascal’s Triangle
A Level Maths Induction
Course Structure
• At Hardenhuish School we follow the Edexcel Advanced GCE in Mathematics Syllabus.
• This is a linear course with a mixture of Pure and Applied Mathematics
• Two thirds of the course is Pure Mathematics and one third is Applied Mathematics.
• Three 2 hour exams at the end of Year 13
Lesson Structure
• You will have five 50 minute lessons each week, plus one lesson of independent study.
• You will have two teachers who teach different parts of the course.
• It is your responsibility to catch up with any work you may miss.
• You will be set homework by each teacher each week.
Equipment
• You should have an A4 folder for your notes
• There are 43 chapters over the 2 years (21 in Year 1, 22 in Year 2)
• You will have a login for electronic resources
• You will need a Casio Classwiz calculator
Summer Work
• During the summer you will be expected to complete a small booklet of work to prepare yourself for September.
• All the topics in the booklet you will have covered for your GCSE exams.
• It will be important that you are confident and comfortable with these topics.
• There will be a short test in your second lesson in September to ensure you have prepared yourself for starting the A-Level work.
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Binomial Expansion
We will introduce a pure topic which extends what you know about expanding brackets
from GCSE
Binomial Expansion
• Expand and simplify the following
(𝑎 + 𝑏)0
(𝑎 + 𝑏)1
(𝑎 + 𝑏)2
(𝑎 + 𝑏)3
(𝑎 + 𝑏)4
1
1𝑎 + 1𝑏
1𝑎2 + 2𝑎𝑏 + 1𝑏2
1𝑎3 + 3𝑎2𝑏 + 3𝑎𝑏2 + 1𝑏3
1𝑎4 + 4𝑎3𝑏 + 6𝑎2𝑏2 + 4𝑎𝑏3 + 1𝑏4
Binomial Expansion
• Expand and simplify the following
(𝑎 + 𝑏)0
(𝑎 + 𝑏)1
(𝑎 + 𝑏)2
(𝑎 + 𝑏)3
(𝑎 + 𝑏)4
𝟏
𝟏𝑎 + 𝟏𝑏
𝟏𝑎2 + 𝟐𝑎𝑏 + 𝟏𝑏2
𝟏𝑎3 + 𝟑𝑎2𝑏 + 𝟑𝑎𝑏2 + 𝟏𝑏3
𝟏𝑎4 + 𝟒𝑎3𝑏 + 𝟔𝑎2𝑏2 + 𝟒𝑎𝑏3 + 𝟏𝑏4
(𝑎 + 𝑏)5
1𝑎5
Binomial Expansion
+5𝑎4𝑏 +10𝑎3𝑏2+10𝑎2𝑏3 +5𝑎𝑏4+1𝑏5
(𝑎 + 𝑏)5
1𝑎5
(𝑥 + 3)4
Binomial Expansion
1
4
6
4
1
+5𝑎4𝑏 +10𝑎3𝑏2+10𝑎2𝑏3 +5𝑎𝑏4+1𝑏5
81 + 108𝑥 + 54𝑥2 + 12𝑥3 + 𝑥4
(𝑥)0
(𝑥)1
(𝑥)2
(𝑥)3
(𝑥)4
(3)4
(3)3
(3)2
(3)1
(3)0
Exam Question• Find the binomial expansion of (𝑥 + 2)6,
giving each term in its simplest form.(Total 4 marks)
• Challenge, find the expansion of 2𝑥 − 3 4
Exam Question• Find the binomial expansion of (𝑥 + 2)6,
giving each term in its simplest form.(Total 4 marks)
64 + 192𝑥 + 240𝑥2 + 160𝑥3 + 60𝑥4 + 12𝑥5 + 𝑥6
• Challenge, find the expansion of 2𝑥 − 3 4
Binomial Expansion
• Where do we go from here?• Year 1 pure using a formula instead of drawing
the triangle – very useful for things like 2 + 𝑥 25 and uses factorial (!)
• Year 2 binomial expansion with fractional & negative powers and estimating square roots
• Year 1 stats binomial distribution to find probabilities
• Further Maths links with complex numbers and trigonometry
Summer Work
• During the summer you will be expected to complete a small booklet of work to prepare yourself for September.
• All the topics in the booklet you will have covered for your GCSE exams.
• It will be important that you are confident and comfortable with these topics.
• There will be a short test in your second lesson in September to ensure you have prepared yourself for starting the A-Level work.
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