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Knowledge check, do now:

LO's

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Chapter 8 - The binomial expansion

y dπ‘₯

A = lw

b2-4ac

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y dπ‘₯

A = lw

b2-4ac

AS

y dπ‘₯

A = lw

b2-4ac

AS

y dπ‘₯

A = lw

b2-4ac

Related

New

Old

LO's

Knowledge check 1

Ans A

Ans C

Ans B

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Chapter 8 - The binomial expansion

y dπ‘₯

A = lw

b2-4ac

AS

y dπ‘₯

A = lw

b2-4ac

8.1 - Pascal's triangle

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y dπ‘₯

A = lw

b2-4ac

8.1 - Pascal's triangle

Rules

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y dπ‘₯

A = lw

b2-4ac

8.1 - Pascal's triangle

Rules

AS

y dπ‘₯

A = lw

b2-4ac

8.1 - Pascal's triangle

Rules

AS

y dπ‘₯

A = lw

b2-4ac

8.2 - Factorial notation

Rules

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y dπ‘₯

A = lw

b2-4ac

8.2 - Factorial notation

Rules

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y dπ‘₯

A = lw

b2-4ac

8.3 - The binomial expansion

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Rules

y dπ‘₯

A = lw

b2-4ac

8.3 - The binomial expansion

Rules

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y dπ‘₯

A = lw

b2-4ac

8.3 - The binomial expansion

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Rules

y dπ‘₯

A = lw

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8.4 - Solving binomial problems

Rules

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y dπ‘₯

A = lw

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8.4 - Solving binomial problems

Rules

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y dπ‘₯

A = lw

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8.4 - Solving binomial problems

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Rules

y dπ‘₯

A = lw

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8.5 - binomial estimation

Foundation

Higher

A Level

y dπ‘₯

Logs

dx

dy

f(π‘₯+a)

b2-4ac

Foundation

Higher

A Level

Foundation

Higher

A Level

y dπ‘₯

Logs

dx

dy

f(π‘₯+a)

b2-4ac

y dπ‘₯

Logs

dx

dy

f(π‘₯+a)

b2-4ac

Foundation

Higher

A Level

Foundation

Higher

A Level

Foundation

Higher

A Level

Foundation

Higher

A Level

y dπ‘₯

Logs

dx

dy

f(π‘₯+a)

b2-4ac

y dπ‘₯

Logs

dx

dy

f(π‘₯+a)

b2-4ac

y dπ‘₯

Logs

dx

dy

f(π‘₯+a)

b2-4ac

y dπ‘₯

Logs

dx

dy

f(π‘₯+a)

b2-4ac

Foundation

Higher

A Level

Who to believe?

A quick google on 'real life uses of the binomial theorem' will throw up a suggestion that it is used in the automatic generation of IP addresses. This sounds mildly interesting so I tried to find out more... but couldn't. I found out a bit about IP addresses, but nothing that related to the binomial theorem. I then thought to try chat gpt. It said "The statement that the binomial theorem is used for the automatic generation of IP addresses appears to be incorrect or misleading.... As of my last knowledge update in September 2021 there is no known connection between the binomial theorem and the automatic generation of IP addresses.

y dπ‘₯

Logs

dx

dy

f(π‘₯+a)

b2-4ac

y dπ‘₯

Logs

dx

dy

f(π‘₯+a)

b2-4ac

y dπ‘₯

Logs

dx

dy

f(π‘₯+a)

b2-4ac

y dπ‘₯

Logs

dx

dy

f(π‘₯+a)

b2-4ac

Foundation

Higher

A Level

Foundation

Higher

A Level

y dπ‘₯

Logs

dx

dy

f(π‘₯+a)

b2-4ac

Foundation

Higher

A Level

Chapter 8 Learning Objectives

  • Use Pascal's triangle to identify binomial coefficients and use them to expand simple binomial expressions.
  • Use combinations and factorial notation.
  • Use the binomial expansion to expand brackets.
  • Find individual coefficients in a binomial expansion.
  • Make approximations using the binomial expansion.

Chapter 7 Learning Objectives

  • Cancel factors in algebraic fractions
  • Divide a polynomial by a linear expression
  • Use the factor theorem to factorise a cubic expression
  • Construct mathematical proofs using algebra
  • Use proof by exhaustion and disproof by counter-example.

Foundation

Higher

A Level

Foundation

Higher

A Level

Foundation

Higher

A Level

y dπ‘₯

Logs

dx

dy

f(π‘₯+a)

b2-4ac

y dπ‘₯

Logs

dx

dy

f(π‘₯+a)

b2-4ac

y dπ‘₯

Logs

dx

dy

f(π‘₯+a)

b2-4ac

Foundation

Higher

A Level

Foundation

Higher

A Level

Foundation

Higher

A Level

y dπ‘₯

Logs

dx

dy

f(π‘₯+a)

b2-4ac

y dπ‘₯

Logs

dx

dy

f(π‘₯+a)

b2-4ac

Foundation

Higher

A Level

y dπ‘₯

Logs

dx

dy

f(π‘₯+a)

b2-4ac