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GCSE OCR Maths Paper 6 Higher 2018 – Fun Compound Interest Questions & More

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GCSE OCR Maths Paper 6 Higher 2018 – Fun Compound Interest Questions & More

This OCR GCSE Maths Paper 6 (Higher) from June 2018 covers a range of advanced mathematical topics, including compound interest, algebraic fractions, graphing, statistics, geometry proofs, and more. The paper tests students' problem-solving skills and mathematical reasoning across 20 questions of varying difficulty.

17/05/2023

2794

Page 9: Statistics and Ratio Problems

This page contains two separate questions:

  1. Find four numbers given their mode, range, and mean
  2. Calculate the percentage of blue pens in a box given ratios of red:blue and blue:green pens

Vocabulary: Mode - the most frequent value in a dataset; Range - the difference between the highest and lowest values; Mean - the average of a set of numbers.

Highlight: These questions test students' ability to work with statistical measures and ratios, important OCR Maths Paper 6 topics.

15
15 Ratna invests £1200 for 2 years in a bank account paying r % per year compound interest.
At the end of 2 years, the amount in the bank

Page 8: Function Analysis

This page presents a function and asks students to:

a) Write an algebraic expression for the input of the function when the output is x b) Find the value of k when k is both the input and output of the function

Example: Function A: Input → ((x - 5) / 2) + 14 → Output

Highlight: This question tests students' understanding of function notation and algebraic manipulation, key skills in OCR Maths GCSE exams.

15
15 Ratna invests £1200 for 2 years in a bank account paying r % per year compound interest.
At the end of 2 years, the amount in the bank

View

Page 10: Significant Figures and Indices

This page includes two questions:

  1. Evaluate the reasonableness of a calculation result using significant figures
  2. Simplify algebraic expressions involving indices and write a fraction as a power

Example: Show that a⁵ × (a³)² can be expressed as a¹¹

Highlight: These questions test students' understanding of number representation and laws of indices, crucial skills in OCR GCSE Maths.

15
15 Ratna invests £1200 for 2 years in a bank account paying r % per year compound interest.
At the end of 2 years, the amount in the bank

View

Page 5: Exam Information and Instructions

This page provides essential information about the exam:

  • It's the OCR GCSE (9-1) Mathematics J560/06 Paper 6 (Higher Tier)
  • The exam date is Tuesday 12 June 2018 (Morning)
  • Time allowed is 1 hour 30 minutes
  • Students may use a scientific or graphical calculator, geometrical instruments, and tracing paper
  • The total mark for the paper is 100

Highlight: This information is crucial for students to understand the exam format and requirements.

15
15 Ratna invests £1200 for 2 years in a bank account paying r % per year compound interest.
At the end of 2 years, the amount in the bank

View

Page 3: Cubic Function Graph Analysis

This page presents a graph of a cubic function y = x³ - 7x - 12 and asks students to:

a) Calculate y when x = 3 b) Show that 3 < p < 4, where p is the root of the equation x³ - 7x - 12 = 0 c) Find a smaller interval containing p, showing calculations

Definition: A root of an equation is a value of x that makes the equation equal to zero.

Highlight: This question combines graphical interpretation with algebraic problem-solving, common in OCR Maths GCSE exams.

15
15 Ratna invests £1200 for 2 years in a bank account paying r % per year compound interest.
At the end of 2 years, the amount in the bank

View

Page 2: Algebraic Fraction Simplification

The final question on the paper involves simplifying an algebraic fraction:

  • Students must show that (2x² + 13x + 20) / (2x² + x - 10) simplifies to (x + a) / (x - b)
  • a and b are integers that need to be determined

Example: This type of question often appears in OCR Maths Paper 6 topics and requires strong algebraic manipulation skills.

Highlight: The question tests students' ability to factor quadratic expressions and simplify complex fractions.

15
15 Ratna invests £1200 for 2 years in a bank account paying r % per year compound interest.
At the end of 2 years, the amount in the bank

View

Page 7: Similar Triangles Proof

This question focuses on triangle similarity:

  • Students must prove that triangles PQS and QRS are similar
  • The diagram shows two right-angled triangles with some side lengths given

Vocabulary: Similar triangles have the same shape but may be different sizes, with corresponding angles equal and sides proportional.

Highlight: This question combines knowledge of right-angled triangles with proof techniques, typical of OCR GCSE Maths higher tier papers.

15
15 Ratna invests £1200 for 2 years in a bank account paying r % per year compound interest.
At the end of 2 years, the amount in the bank

View

Page 4: Box Plot and Salary Distribution

This question focuses on statistical analysis and data representation:

  • Students must draw a box plot for salary data from Camford Cookies
  • The data includes information on the highest and lowest salaries, quartiles, and median
  • Students then need to make two comparisons between salary distributions at Camford Cookies and Bexbridge Biscuits

Vocabulary: Box plot - A graphical representation of data that displays the median, quartiles, and extremes of a dataset.

Highlight: This question tests students' ability to interpret and represent statistical data, a key skill in OCR Maths Paper 6 topics.

15
15 Ratna invests £1200 for 2 years in a bank account paying r % per year compound interest.
At the end of 2 years, the amount in the bank

View

Page 1: Compound Interest Question

This page presents a compound interest problem:

  • Ratna invests £1200 for 2 years in a bank account with r% per year compound interest
  • After 2 years, the amount in the account is £1379.02
  • Students must calculate the value of r (the interest rate)

Highlight: This question tests understanding of compound interest calculations, a key topic in OCR GCSE Maths.

Vocabulary: Compound interest - Interest calculated on the initial principal and accumulated interest from previous periods.

15
15 Ratna invests £1200 for 2 years in a bank account paying r % per year compound interest.
At the end of 2 years, the amount in the bank

View

Page 6: Triangle Congruence Proof

This geometry question requires students to:

  • Prove that triangle ABC is congruent to triangle ACD
  • The diagram shows two triangles with given angle measurements

Definition: Congruent triangles are identical in shape and size.

Highlight: Geometric proofs are a common feature in OCR Maths Paper 6 topics, testing students' logical reasoning skills.

15
15 Ratna invests £1200 for 2 years in a bank account paying r % per year compound interest.
At the end of 2 years, the amount in the bank

View

Page 11: Sphere Volume Calculation

The final visible question on this page asks students to calculate the volume of a sphere.

Vocabulary: The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius.

Highlight: This question tests students' ability to apply geometric formulas, a common feature in OCR Maths Paper 6 topics.

15
15 Ratna invests £1200 for 2 years in a bank account paying r % per year compound interest.
At the end of 2 years, the amount in the bank

View

15
15 Ratna invests £1200 for 2 years in a bank account paying r % per year compound interest.
At the end of 2 years, the amount in the bank

View

15
15 Ratna invests £1200 for 2 years in a bank account paying r % per year compound interest.
At the end of 2 years, the amount in the bank

View

15
15 Ratna invests £1200 for 2 years in a bank account paying r % per year compound interest.
At the end of 2 years, the amount in the bank

View

15
15 Ratna invests £1200 for 2 years in a bank account paying r % per year compound interest.
At the end of 2 years, the amount in the bank

View

15
15 Ratna invests £1200 for 2 years in a bank account paying r % per year compound interest.
At the end of 2 years, the amount in the bank

View

15
15 Ratna invests £1200 for 2 years in a bank account paying r % per year compound interest.
At the end of 2 years, the amount in the bank

View

15
15 Ratna invests £1200 for 2 years in a bank account paying r % per year compound interest.
At the end of 2 years, the amount in the bank

View

15
15 Ratna invests £1200 for 2 years in a bank account paying r % per year compound interest.
At the end of 2 years, the amount in the bank

View

15
15 Ratna invests £1200 for 2 years in a bank account paying r % per year compound interest.
At the end of 2 years, the amount in the bank

View

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

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App Store

Knowunity is the #1 education app in five European countries

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Average app rating

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Pupils love Knowunity

#1

In education app charts in 11 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.

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

13 M

Pupils love Knowunity

#1

In education app charts in 11 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.

View

GCSE OCR Maths Paper 6 Higher 2018 – Fun Compound Interest Questions & More

GCSE OCR Maths Paper 6 Higher 2018 – Fun Compound Interest Questions & More

This OCR GCSE Maths Paper 6 (Higher) from June 2018 covers a range of advanced mathematical topics, including compound interest, algebraic fractions, graphing, statistics, geometry proofs, and more. The paper tests students' problem-solving skills and mathematical reasoning across 20 questions of varying difficulty.

17/05/2023

2794

Page 9: Statistics and Ratio Problems

This page contains two separate questions:

  1. Find four numbers given their mode, range, and mean
  2. Calculate the percentage of blue pens in a box given ratios of red:blue and blue:green pens

Vocabulary: Mode - the most frequent value in a dataset; Range - the difference between the highest and lowest values; Mean - the average of a set of numbers.

Highlight: These questions test students' ability to work with statistical measures and ratios, important OCR Maths Paper 6 topics.

15
15 Ratna invests £1200 for 2 years in a bank account paying r % per year compound interest.
At the end of 2 years, the amount in the bank

Register

Sign up to get unlimited access to thousands of study materials. It's free!

Access to all documents

Join milions of students

Improve your grades

By signing up you accept Terms of Service and Privacy Policy

Page 8: Function Analysis

This page presents a function and asks students to:

a) Write an algebraic expression for the input of the function when the output is x b) Find the value of k when k is both the input and output of the function

Example: Function A: Input → ((x - 5) / 2) + 14 → Output

Highlight: This question tests students' understanding of function notation and algebraic manipulation, key skills in OCR Maths GCSE exams.

15
15 Ratna invests £1200 for 2 years in a bank account paying r % per year compound interest.
At the end of 2 years, the amount in the bank

Register

Sign up to get unlimited access to thousands of study materials. It's free!

Access to all documents

Join milions of students

Improve your grades

By signing up you accept Terms of Service and Privacy Policy

Page 10: Significant Figures and Indices

This page includes two questions:

  1. Evaluate the reasonableness of a calculation result using significant figures
  2. Simplify algebraic expressions involving indices and write a fraction as a power

Example: Show that a⁵ × (a³)² can be expressed as a¹¹

Highlight: These questions test students' understanding of number representation and laws of indices, crucial skills in OCR GCSE Maths.

15
15 Ratna invests £1200 for 2 years in a bank account paying r % per year compound interest.
At the end of 2 years, the amount in the bank

Register

Sign up to get unlimited access to thousands of study materials. It's free!

Access to all documents

Join milions of students

Improve your grades

By signing up you accept Terms of Service and Privacy Policy

Page 5: Exam Information and Instructions

This page provides essential information about the exam:

  • It's the OCR GCSE (9-1) Mathematics J560/06 Paper 6 (Higher Tier)
  • The exam date is Tuesday 12 June 2018 (Morning)
  • Time allowed is 1 hour 30 minutes
  • Students may use a scientific or graphical calculator, geometrical instruments, and tracing paper
  • The total mark for the paper is 100

Highlight: This information is crucial for students to understand the exam format and requirements.

15
15 Ratna invests £1200 for 2 years in a bank account paying r % per year compound interest.
At the end of 2 years, the amount in the bank

Register

Sign up to get unlimited access to thousands of study materials. It's free!

Access to all documents

Join milions of students

Improve your grades

By signing up you accept Terms of Service and Privacy Policy

Page 3: Cubic Function Graph Analysis

This page presents a graph of a cubic function y = x³ - 7x - 12 and asks students to:

a) Calculate y when x = 3 b) Show that 3 < p < 4, where p is the root of the equation x³ - 7x - 12 = 0 c) Find a smaller interval containing p, showing calculations

Definition: A root of an equation is a value of x that makes the equation equal to zero.

Highlight: This question combines graphical interpretation with algebraic problem-solving, common in OCR Maths GCSE exams.

15
15 Ratna invests £1200 for 2 years in a bank account paying r % per year compound interest.
At the end of 2 years, the amount in the bank

Register

Sign up to get unlimited access to thousands of study materials. It's free!

Access to all documents

Join milions of students

Improve your grades

By signing up you accept Terms of Service and Privacy Policy

Page 2: Algebraic Fraction Simplification

The final question on the paper involves simplifying an algebraic fraction:

  • Students must show that (2x² + 13x + 20) / (2x² + x - 10) simplifies to (x + a) / (x - b)
  • a and b are integers that need to be determined

Example: This type of question often appears in OCR Maths Paper 6 topics and requires strong algebraic manipulation skills.

Highlight: The question tests students' ability to factor quadratic expressions and simplify complex fractions.

15
15 Ratna invests £1200 for 2 years in a bank account paying r % per year compound interest.
At the end of 2 years, the amount in the bank

Register

Sign up to get unlimited access to thousands of study materials. It's free!

Access to all documents

Join milions of students

Improve your grades

By signing up you accept Terms of Service and Privacy Policy

Page 7: Similar Triangles Proof

This question focuses on triangle similarity:

  • Students must prove that triangles PQS and QRS are similar
  • The diagram shows two right-angled triangles with some side lengths given

Vocabulary: Similar triangles have the same shape but may be different sizes, with corresponding angles equal and sides proportional.

Highlight: This question combines knowledge of right-angled triangles with proof techniques, typical of OCR GCSE Maths higher tier papers.

15
15 Ratna invests £1200 for 2 years in a bank account paying r % per year compound interest.
At the end of 2 years, the amount in the bank

Register

Sign up to get unlimited access to thousands of study materials. It's free!

Access to all documents

Join milions of students

Improve your grades

By signing up you accept Terms of Service and Privacy Policy

Page 4: Box Plot and Salary Distribution

This question focuses on statistical analysis and data representation:

  • Students must draw a box plot for salary data from Camford Cookies
  • The data includes information on the highest and lowest salaries, quartiles, and median
  • Students then need to make two comparisons between salary distributions at Camford Cookies and Bexbridge Biscuits

Vocabulary: Box plot - A graphical representation of data that displays the median, quartiles, and extremes of a dataset.

Highlight: This question tests students' ability to interpret and represent statistical data, a key skill in OCR Maths Paper 6 topics.

15
15 Ratna invests £1200 for 2 years in a bank account paying r % per year compound interest.
At the end of 2 years, the amount in the bank

Register

Sign up to get unlimited access to thousands of study materials. It's free!

Access to all documents

Join milions of students

Improve your grades

By signing up you accept Terms of Service and Privacy Policy

Page 1: Compound Interest Question

This page presents a compound interest problem:

  • Ratna invests £1200 for 2 years in a bank account with r% per year compound interest
  • After 2 years, the amount in the account is £1379.02
  • Students must calculate the value of r (the interest rate)

Highlight: This question tests understanding of compound interest calculations, a key topic in OCR GCSE Maths.

Vocabulary: Compound interest - Interest calculated on the initial principal and accumulated interest from previous periods.

15
15 Ratna invests £1200 for 2 years in a bank account paying r % per year compound interest.
At the end of 2 years, the amount in the bank

Register

Sign up to get unlimited access to thousands of study materials. It's free!

Access to all documents

Join milions of students

Improve your grades

By signing up you accept Terms of Service and Privacy Policy

Page 6: Triangle Congruence Proof

This geometry question requires students to:

  • Prove that triangle ABC is congruent to triangle ACD
  • The diagram shows two triangles with given angle measurements

Definition: Congruent triangles are identical in shape and size.

Highlight: Geometric proofs are a common feature in OCR Maths Paper 6 topics, testing students' logical reasoning skills.

15
15 Ratna invests £1200 for 2 years in a bank account paying r % per year compound interest.
At the end of 2 years, the amount in the bank

Register

Sign up to get unlimited access to thousands of study materials. It's free!

Access to all documents

Join milions of students

Improve your grades

By signing up you accept Terms of Service and Privacy Policy

Page 11: Sphere Volume Calculation

The final visible question on this page asks students to calculate the volume of a sphere.

Vocabulary: The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius.

Highlight: This question tests students' ability to apply geometric formulas, a common feature in OCR Maths Paper 6 topics.

15
15 Ratna invests £1200 for 2 years in a bank account paying r % per year compound interest.
At the end of 2 years, the amount in the bank

Register

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Access to all documents

Join milions of students

Improve your grades

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15
15 Ratna invests £1200 for 2 years in a bank account paying r % per year compound interest.
At the end of 2 years, the amount in the bank

Register

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Access to all documents

Join milions of students

Improve your grades

By signing up you accept Terms of Service and Privacy Policy

15
15 Ratna invests £1200 for 2 years in a bank account paying r % per year compound interest.
At the end of 2 years, the amount in the bank

Register

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Access to all documents

Join milions of students

Improve your grades

By signing up you accept Terms of Service and Privacy Policy

15
15 Ratna invests £1200 for 2 years in a bank account paying r % per year compound interest.
At the end of 2 years, the amount in the bank

Register

Sign up to get unlimited access to thousands of study materials. It's free!

Access to all documents

Join milions of students

Improve your grades

By signing up you accept Terms of Service and Privacy Policy

15
15 Ratna invests £1200 for 2 years in a bank account paying r % per year compound interest.
At the end of 2 years, the amount in the bank

Register

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Access to all documents

Join milions of students

Improve your grades

By signing up you accept Terms of Service and Privacy Policy

15
15 Ratna invests £1200 for 2 years in a bank account paying r % per year compound interest.
At the end of 2 years, the amount in the bank

Register

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Access to all documents

Join milions of students

Improve your grades

By signing up you accept Terms of Service and Privacy Policy

15
15 Ratna invests £1200 for 2 years in a bank account paying r % per year compound interest.
At the end of 2 years, the amount in the bank

Register

Sign up to get unlimited access to thousands of study materials. It's free!

Access to all documents

Join milions of students

Improve your grades

By signing up you accept Terms of Service and Privacy Policy

15
15 Ratna invests £1200 for 2 years in a bank account paying r % per year compound interest.
At the end of 2 years, the amount in the bank

Register

Sign up to get unlimited access to thousands of study materials. It's free!

Access to all documents

Join milions of students

Improve your grades

By signing up you accept Terms of Service and Privacy Policy

15
15 Ratna invests £1200 for 2 years in a bank account paying r % per year compound interest.
At the end of 2 years, the amount in the bank

Register

Sign up to get unlimited access to thousands of study materials. It's free!

Access to all documents

Join milions of students

Improve your grades

By signing up you accept Terms of Service and Privacy Policy

15
15 Ratna invests £1200 for 2 years in a bank account paying r % per year compound interest.
At the end of 2 years, the amount in the bank

Register

Sign up to get unlimited access to thousands of study materials. It's free!

Access to all documents

Join milions of students

Improve your grades

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.

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

13 M

Pupils love Knowunity

#1

In education app charts in 11 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.