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Fun Recurrence Relations Word Problems for Higher Maths

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Fun Recurrence Relations Word Problems for Higher Maths

Recurrence relations are a crucial topic in Higher Maths, often appearing in GCSE and A Level Maths exams. This guide explores word problems involving recurrence relations, providing examples of loan calculations and drug dosage scenarios. These problems are common in Higher Maths past papers and are essential for understanding sequences and financial mathematics.

31/08/2022

28

value
term
C
20
20
10
convergent
sequence
$
2 3 4 5
term number
RECURRENCE RELATIONS - WORD
Yes, it converges with limit = 3
PROBLEMS
100% +

View

Page 1: Loan Repayment Calculation

This page introduces a recurrence relation word problem focused on loan repayment calculations. It demonstrates how to use recurrence relations to model financial scenarios, a common topic in Higher Maths and A Level Maths.

The problem presents Betty's loan of £2000 with a 1.5% monthly interest rate and £450 monthly repayments. Students are tasked with creating a recurrence relation to model the loan balance over time.

Definition: A recurrence relation for this loan scenario is given as Bn+1 = 1.015Bn - 450, where Bn represents the balance after n months.

The page walks through the calculation process month by month, showing how the loan balance decreases over time. This step-by-step approach is valuable for students learning to apply recurrence relations to real-world problems.

Example: The calculation shows that by the end of May, the balance owed is £281.82058, and the final payment is made in June.

The problem also asks students to calculate the total amount Betty will have paid, which comes to £2086.05. This illustrates the concept of total interest paid on a loan, an important aspect of financial mathematics.

Highlight: For questions involving exceeding or dropping below specific limits, it's crucial to consider the values both before and after each payment or change.

This page effectively demonstrates the application of recurrence relations in financial contexts, providing a practical example that students might encounter in Higher Maths past papers or A Level Maths exams.

value
term
C
20
20
10
convergent
sequence
$
2 3 4 5
term number
RECURRENCE RELATIONS - WORD
Yes, it converges with limit = 3
PROBLEMS
100% +

View

Recurrence Relations - Word Problems

This document covers two main types of recurrence relation word problems: loan repayments and drug dosage calculations. These examples demonstrate the practical applications of recurrence relations in real-world scenarios.

Loan Repayment Problem

The first problem involves a reducing balance loan scenario where Betty borrows £2000 with monthly repayments and interest.

Example: Betty takes out a £2000 loan with 1.5% monthly interest and £450 monthly repayments.

The recurrence relation for the loan balance is derived:

Definition: Bn+1 = 1.015Bn - 450, where Bn is the balance after n months.

The problem is solved step-by-step, showing how the loan balance decreases each month until the final payment in June.

Highlight: The final payment is made in June, with a total repayment of £2086.05.

Drug Dosage Problem

The second problem involves calculating drug levels in a patient's bloodstream using recurrence relations.

Example: A drug with an initial dose of 120ml is administered, with 50% metabolized hourly and 35ml top-ups given each hour.

Two recurrence relations are presented:

  1. Un+1 = 0.5Un + 35 (drug level after top-up)
  2. Un+1 = 0.5Un (drug level before top-up)

Vocabulary: Metabolised - The process by which a drug is broken down in the body.

The problem is solved to determine when the drug level falls below the effective threshold of 58ml.

Highlight: The treatment stops being effective between the 3rd and 4th doses when the drug level drops below 58ml.

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Fun Recurrence Relations Word Problems for Higher Maths

Recurrence relations are a crucial topic in Higher Maths, often appearing in GCSE and A Level Maths exams. This guide explores word problems involving recurrence relations, providing examples of loan calculations and drug dosage scenarios. These problems are common in Higher Maths past papers and are essential for understanding sequences and financial mathematics.

31/08/2022

28

 

S5

 

Maths

3

value
term
C
20
20
10
convergent
sequence
$
2 3 4 5
term number
RECURRENCE RELATIONS - WORD
Yes, it converges with limit = 3
PROBLEMS
100% +

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

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Page 1: Loan Repayment Calculation

This page introduces a recurrence relation word problem focused on loan repayment calculations. It demonstrates how to use recurrence relations to model financial scenarios, a common topic in Higher Maths and A Level Maths.

The problem presents Betty's loan of £2000 with a 1.5% monthly interest rate and £450 monthly repayments. Students are tasked with creating a recurrence relation to model the loan balance over time.

Definition: A recurrence relation for this loan scenario is given as Bn+1 = 1.015Bn - 450, where Bn represents the balance after n months.

The page walks through the calculation process month by month, showing how the loan balance decreases over time. This step-by-step approach is valuable for students learning to apply recurrence relations to real-world problems.

Example: The calculation shows that by the end of May, the balance owed is £281.82058, and the final payment is made in June.

The problem also asks students to calculate the total amount Betty will have paid, which comes to £2086.05. This illustrates the concept of total interest paid on a loan, an important aspect of financial mathematics.

Highlight: For questions involving exceeding or dropping below specific limits, it's crucial to consider the values both before and after each payment or change.

This page effectively demonstrates the application of recurrence relations in financial contexts, providing a practical example that students might encounter in Higher Maths past papers or A Level Maths exams.

value
term
C
20
20
10
convergent
sequence
$
2 3 4 5
term number
RECURRENCE RELATIONS - WORD
Yes, it converges with limit = 3
PROBLEMS
100% +

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Recurrence Relations - Word Problems

This document covers two main types of recurrence relation word problems: loan repayments and drug dosage calculations. These examples demonstrate the practical applications of recurrence relations in real-world scenarios.

Loan Repayment Problem

The first problem involves a reducing balance loan scenario where Betty borrows £2000 with monthly repayments and interest.

Example: Betty takes out a £2000 loan with 1.5% monthly interest and £450 monthly repayments.

The recurrence relation for the loan balance is derived:

Definition: Bn+1 = 1.015Bn - 450, where Bn is the balance after n months.

The problem is solved step-by-step, showing how the loan balance decreases each month until the final payment in June.

Highlight: The final payment is made in June, with a total repayment of £2086.05.

Drug Dosage Problem

The second problem involves calculating drug levels in a patient's bloodstream using recurrence relations.

Example: A drug with an initial dose of 120ml is administered, with 50% metabolized hourly and 35ml top-ups given each hour.

Two recurrence relations are presented:

  1. Un+1 = 0.5Un + 35 (drug level after top-up)
  2. Un+1 = 0.5Un (drug level before top-up)

Vocabulary: Metabolised - The process by which a drug is broken down in the body.

The problem is solved to determine when the drug level falls below the effective threshold of 58ml.

Highlight: The treatment stops being effective between the 3rd and 4th doses when the drug level drops below 58ml.

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.

Ranked #1 Education App

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.