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Evelyn Ridley
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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
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
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
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
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
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
10
673
8/9
Nth term
Arithmetic, Geometric and Quadratic Sequences
29
763
11/9
Nth term
Explanation of different types of sequences and how to find the nth term from linear and quadratic sequences.
12
633
11/10
Error intervals
Explanation on what error intervals are and how to find error intervals with examples
3
28
S5
Recurrence Relations - word problems notes
notes for higher maths on recurrence relations word problems
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Evelyn Ridley
@ev_alice
·
161 Followers
Follow
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
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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
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
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
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
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
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
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
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
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
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
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
Maths - Nth term
Arithmetic, Geometric and Quadratic Sequences
10
673
2
Maths - Nth term
Explanation of different types of sequences and how to find the nth term from linear and quadratic sequences.
29
763
1
Maths - Error intervals
Explanation on what error intervals are and how to find error intervals with examples
12
633
0
Maths - Recurrence Relations - word problems notes
notes for higher maths on recurrence relations word problems
3
28
0
Average app rating
Pupils love Knowunity
In education app charts in 12 countries
Students have uploaded notes
iOS User
Philip, iOS User
Lena, iOS user
