Subjects

Maths

Algebra

Sequences

Fun GCSE Maths Guide: Higher Tier Formulae Sheet

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Fun GCSE Maths Guide: Higher Tier Formulae Sheet

Evelyn Ridley

@ev_alice

161 Followers

Top of the class Student

Let me create SEO-optimized summaries for this mathematics exam content.

A comprehensive guide to higher tier formulae sheet for GCSE maths and advanced mathematical problem-solving techniques.

• The document covers essential mathematical concepts including geometric formulas, solving simultaneous equations step by step, and nth term non-linear sequences practice questions

• Key topics include compound interest calculations, quadratic formula applications, non-linear sequences, and circle equations

• Assessment materials feature both calculator and non-calculator sections with detailed worked examples

27/05/2023

212

Rossett School
Sam
Mathematics
Department
Teacher Comment:
Strength:
Target (DIRT):
Crossover:
A12
Assessment 5-HIGHER
30
CALCULATOR
Higher:

View

Page 2: Sequence Analysis and Problem-Solving

This page covers various types of sequences and their applications, including non-linear sequences and pattern recognition problems.

Example: For the sequence with nth term 2n², the 4th term is calculated as 2(4²) = 2(16) = 32

Definition: An arithmetic sequence has a constant difference between consecutive terms

Highlight: When determining if a number is in a sequence, divide the number by the coefficient and check if the result is a perfect square

View

Page 3: Advanced Equation Solving

This section focuses on solving simultaneous equations and exploring Fibonacci sequences.

Definition: Fibonacci sequence - Each number is the sum of the two preceding ones

Example: In the Fibonacci sequence 1,1,2,3,5,8, the 9th term is found by adding the 7th and 8th terms

Highlight: When solving simultaneous equations, matching coefficients is a crucial strategy for elimination

View

Page 4: Word Problems and Sequence Applications

This page demonstrates practical applications of simultaneous equations through word problems and explores complex sequence problems.

Example: In the paint and brush problem, using algebraic methods to solve 3P + 4B = 23 and 2P + 3B = 16

Highlight: When comparing sequences, equating their nth terms can help find common values

View

Page 5: Advanced Sequence Analysis

The final page focuses on quadratic sequences and their nth term expressions.

Definition: A quadratic sequence has second differences that are constant

Example: Finding the nth term of a quadratic sequence requires analyzing first and second differences

Highlight: The nth term of a quadratic sequence takes the form an² + bn + c, where a, b, and c are constants

View

Page 5: Advanced Sequence Analysis

The content focuses on quadratic nth terms and non-linear simultaneous equations, demonstrating complex problem-solving techniques.

Example: Finding the nth term of a sequence requires analyzing first and second differences

Definition: Non-linear simultaneous equations involve at least one equation with variables of degree higher than one

Highlight: Solutions require systematic approach and careful algebraic manipulation

View

Page 1: Essential Mathematical Formulae

This page presents a comprehensive collection of essential mathematical formulae for higher-tier mathematics. The content focuses on key areas including geometry, trigonometry, and probability.

Definition: Compound Interest formula P(1+r)ⁿ where P is principal amount, r is interest rate, and n is number of compound periods

Highlight: The quadratic formula (-b±√(b²-4ac))/2a is essential for solving quadratic equations where a≠0

Example: For circle calculations, the area is πr² and circumference is 2πr or πd where r is radius and d is diameter

Vocabulary: Principal amount - The initial sum of money invested or borrowed before interest is applied

Can't find what you're looking for? Explore other subjects.

Knowunity is the #1 education app in five European countries

Knowunity has been named a featured story on Apple and has regularly topped the app store charts in the education category in Germany, Italy, Poland, Switzerland, and the United Kingdom. Join Knowunity today and help millions of students around the world.

Download in

Google Play

Download in

App Store

Knowunity is the #1 education app in five European countries

4.9+

Average app rating

15 M

Pupils love Knowunity

#1

In education app charts in 12 countries

950 K+

Students have uploaded notes

Still not convinced? See what other students are saying...

iOS User

I love this app so much, I also use it daily. I recommend Knowunity to everyone!!! I went from a D to an A with it :D

Philip, iOS User

The app is very simple and well designed. So far I have always found everything I was looking for :D

Lena, iOS user

I love this app ❤️ I actually use it every time I study.

Subjects

Maths

Algebra

Sequences

Fun GCSE Maths Guide: Higher Tier Formulae Sheet

Evelyn Ridley

@ev_alice

161 Followers

Top of the class Student

Let me create SEO-optimized summaries for this mathematics exam content.

A comprehensive guide to higher tier formulae sheet for GCSE maths and advanced mathematical problem-solving techniques.

• The document covers essential mathematical concepts including geometric formulas, solving simultaneous equations step by step, and nth term non-linear sequences practice questions

• Key topics include compound interest calculations, quadratic formula applications, non-linear sequences, and circle equations

• Assessment materials feature both calculator and non-calculator sections with detailed worked examples

27/05/2023

212

10/11

Maths

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Page 2: Sequence Analysis and Problem-Solving

This page covers various types of sequences and their applications, including non-linear sequences and pattern recognition problems.

Example: For the sequence with nth term 2n², the 4th term is calculated as 2(4²) = 2(16) = 32

Definition: An arithmetic sequence has a constant difference between consecutive terms

Highlight: When determining if a number is in a sequence, divide the number by the coefficient and check if the result is a perfect square

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Page 3: Advanced Equation Solving

This section focuses on solving simultaneous equations and exploring Fibonacci sequences.

Definition: Fibonacci sequence - Each number is the sum of the two preceding ones

Example: In the Fibonacci sequence 1,1,2,3,5,8, the 9th term is found by adding the 7th and 8th terms

Highlight: When solving simultaneous equations, matching coefficients is a crucial strategy for elimination

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Page 4: Word Problems and Sequence Applications

This page demonstrates practical applications of simultaneous equations through word problems and explores complex sequence problems.

Example: In the paint and brush problem, using algebraic methods to solve 3P + 4B = 23 and 2P + 3B = 16

Highlight: When comparing sequences, equating their nth terms can help find common values

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Page 5: Advanced Sequence Analysis

The final page focuses on quadratic sequences and their nth term expressions.

Definition: A quadratic sequence has second differences that are constant

Example: Finding the nth term of a quadratic sequence requires analyzing first and second differences

Highlight: The nth term of a quadratic sequence takes the form an² + bn + c, where a, b, and c are constants

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Page 5: Advanced Sequence Analysis

The content focuses on quadratic nth terms and non-linear simultaneous equations, demonstrating complex problem-solving techniques.

Example: Finding the nth term of a sequence requires analyzing first and second differences

Definition: Non-linear simultaneous equations involve at least one equation with variables of degree higher than one

Highlight: Solutions require systematic approach and careful algebraic manipulation

Sign up for free!

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Page 1: Essential Mathematical Formulae

This page presents a comprehensive collection of essential mathematical formulae for higher-tier mathematics. The content focuses on key areas including geometry, trigonometry, and probability.

Definition: Compound Interest formula P(1+r)ⁿ where P is principal amount, r is interest rate, and n is number of compound periods

Highlight: The quadratic formula (-b±√(b²-4ac))/2a is essential for solving quadratic equations where a≠0

Example: For circle calculations, the area is πr² and circumference is 2πr or πd where r is radius and d is diameter

Vocabulary: Principal amount - The initial sum of money invested or borrowed before interest is applied

Sign up for free!

Learn faster and better with thousand of available study notes

By signing up you accept Terms of Service and Privacy Policy

Can't find what you're looking for? Explore other subjects.

Knowunity is the #1 education app in five European countries

Knowunity has been named a featured story on Apple and has regularly topped the app store charts in the education category in Germany, Italy, Poland, Switzerland, and the United Kingdom. Join Knowunity today and help millions of students around the world.

Download in

Google Play

Download in

App Store

4.9+

Average app rating

15 M

Pupils love Knowunity

#1

In education app charts in 12 countries

950 K+

Students have uploaded notes

Still not convinced? See what other students are saying...

iOS User

I love this app so much, I also use it daily. I recommend Knowunity to everyone!!! I went from a D to an A with it :D

Philip, iOS User

The app is very simple and well designed. So far I have always found everything I was looking for :D

Lena, iOS user

Fun GCSE Maths Guide: Higher Tier Formulae Sheet

Page 2: Sequence Analysis and Problem-Solving

Page 3: Advanced Equation Solving

Page 4: Word Problems and Sequence Applications

Page 5: Advanced Sequence Analysis

Page 1: Essential Mathematical Formulae

Similar content

Can't find what you're looking for? Explore other subjects.

Knowunity is the #1 education app in five European countries

Knowunity has been named a featured story on Apple and has regularly topped the app store charts in the education category in Germany, Italy, Poland, Switzerland, and the United Kingdom. Join Knowunity today and help millions of students around the world.

4.9+

15 M

#1

950 K+

Still not convinced? See what other students are saying...

I love this app so much, I also use it daily. I recommend Knowunity to everyone!!! I went from a D to an A with it :D

The app is very simple and well designed. So far I have always found everything I was looking for :D

I love this app ❤️ I actually use it every time I study.

Fun GCSE Maths Guide: Higher Tier Formulae Sheet

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Page 1: Essential Mathematical Formulae

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Similar content

Can't find what you're looking for? Explore other subjects.

Knowunity is the #1 education app in five European countries

Knowunity has been named a featured story on Apple and has regularly topped the app store charts in the education category in Germany, Italy, Poland, Switzerland, and the United Kingdom. Join Knowunity today and help millions of students around the world.

4.9+

15 M

#1

950 K+

Still not convinced? See what other students are saying...

I love this app so much, I also use it daily. I recommend Knowunity to everyone!!! I went from a D to an A with it :D

The app is very simple and well designed. So far I have always found everything I was looking for :D

I love this app ❤️ I actually use it every time I study.