Pure 1 - Chapter 7+8
thomas.payne
Created on November 8, 2023
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Transcript
Related
New
Old
LO's
Knowledge check 1
Ans A
Ans C
Ans B
AS
Chapter 7 - Algebraic methods
y dπ₯
A = lw
b2-4ac
Rules
AS
y dπ₯
A = lw
b2-4ac
7.1 - ALgebraic fractions
Rules
AS
y dπ₯
A = lw
b2-4ac
7.2 - Dividing polynomials
Rules
AS
y dπ₯
A = lw
b2-4ac
7.2 - Dividing polynomials
Rules
AS
y dπ₯
A = lw
b2-4ac
7.2 - Dividing polynomials
Rules
AS
y dπ₯
A = lw
b2-4ac
7.3 - The factor theorem
Rules
AS
y dπ₯
A = lw
b2-4ac
7.3 - The factor theorem
Rules
AS
y dπ₯
A = lw
b2-4ac
7.3 - The factor theorem
AS
Rules
y dπ₯
A = lw
b2-4ac
7.4 - Mathematical proof
AS
Rules
y dπ₯
A = lw
b2-4ac
7.4 - Mathematical proof
AS
Rules
y dπ₯
A = lw
b2-4ac
7.4 - Mathematical proof
AS
Rules
y dπ₯
A = lw
b2-4ac
7.4 - Mathematical proof
AS
Rules
y dπ₯
A = lw
b2-4ac
7.5 - methods of proof
AS
Rules
y dπ₯
A = lw
b2-4ac
7.5 - methods of proof
AS
Rules
y dπ₯
A = lw
b2-4ac
7.5 - methods of proof
Related
New
Old
LO's
Knowledge check 1
Ans A
Ans C
Ans B
AS
Chapter 8 - The binomial expansion
y dπ₯
A = lw
b2-4ac
AS
y dπ₯
A = lw
b2-4ac
8.1 - Pascal's triangle
AS
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
8.1 - Pascal's triangle
Rules
AS
y dπ₯
A = lw
b2-4ac
8.2 - Factorial notation
Rules
AS
y dπ₯
A = lw
b2-4ac
8.2 - Factorial notation
Rules
AS
y dπ₯
A = lw
b2-4ac
8.3 - The binomial expansion
AS
Rules
y dπ₯
A = lw
b2-4ac
8.3 - The binomial expansion
Rules
AS
y dπ₯
A = lw
b2-4ac
8.3 - The binomial expansion
AS
Rules
y dπ₯
A = lw
b2-4ac
8.4 - Solving binomial problems
Rules
AS
y dπ₯
A = lw
b2-4ac
8.4 - Solving binomial problems
Rules
AS
y dπ₯
A = lw
b2-4ac
8.4 - Solving binomial problems
AS
Rules
y dπ₯
A = lw
b2-4ac
8.5 - binomial estimation
y dπ₯
Logs
dx
dy
f(π₯+a)
b2-4ac
Foundation
Higher
A Level
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
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
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.
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
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
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
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
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
Foundation
Higher
A Level
Foundation
Higher
A Level
y dπ₯
Logs
dx
dy
f(π₯+a)
b2-4ac
Foundation
Higher
A Level
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
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
y dπ₯
Logs
dx
dy
f(π₯+a)
b2-4ac
Foundation
Higher
A Level