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GCSE Direct and Inverse Proportion Questions and Answers

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Question 19 - AQA GCSE Higher Maths Past Paper 2 November 2021

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Question 21 - OCR GCSE Foundation 2017 Past Paper 1 - Ratio, Proportion and Rates of Change Questions By Topic

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Proportions - GCSE Exam

1. What is Proportion?

Proportion is a relationship between two quantities such that a change in one quantity relates to change in another quantity.

1.1 Direct Proportions:

Two variables are said to be directly proportional to each other if increment of one quantity leads to increment in the second quantity similarly decrement of one quantity leads to decrement in the second quantity.

          Represented as  X ∝ Y,     read as ‘X is directly proportional to Y’

                                      X = k X,       where k is proportionality constant.

For Example

Ciara put a 2p coin in her piggy bank daily so she will have 14p in her piggy bank by the week. Here the amount of savings is directly proportional to the number of days.

Golden rule to solve direct proportions: Divide for One then Times for All

Example:

If Mr. John earns £160 per day working 8 hours a day, How much will he earn by working 30 hours?

Direct proportion example 1

1.2 Indirect Proportions:

When two quantities are related to each other in a way that increment in one quantity leads to decrement in another quantity and vice versa, we say they are inversely proportional.

             Represented as  X ∝ 1⁄y,          read as ‘X is indirectly proportional to Y’.

                                     X =k 1⁄y,              where k is proportionality constant.

For Example:

Gia takes 30 minutes to reach school from her home on bicycle. If she doubles her speed she would reach school in 15 minutes. Here we can see the speed is inversely proportional to the time taken to complete the journey.

Golden Rule to solve indirect proportions: Times for One then Divide for All

Example:

5 workers take 3 days to paint a wall. How long will only one worker take to paint the same wall?

Direct proportion example 2

Quiz
GCSE Proportions

GCSE Topics

  • Probability (258)
  • Statistical Measures (5)
  • Numbers (1,084)
  • Data Visualisation (4)
  • Algebra (1,176)
  • Ratio, Proportion and Rates of Change (443)
  • Geometry and Measures (809)
  • Statistics (274)
    • Frequently Asked Questions
    What are the main topics in GCSE Maths?

    The main topics in GCSE Maths are:

    • Numbers
    • Algebra 
    • Ratio, Proportion and Rates of Change 
    • Geometry and Measures
    • Statistics 
    • Probability 
    • Statistical Measures 
    • Data Visualisation 

    With regular practice of GCSE Maths topic-wise questions and GCSE Maths past pacers, you can easily score high marks.

    Is GCSE Maths hard?

    Although many people think of GCSE maths as a difficult subject, with the correct training and preparation,you can master it in time. You can practice GCSE Maths  topic-wise questions daily to improve speed, accuracy, and time and to score high marks in the GCSE Maths exam.

    What is a good grade on GCSE Maths Exam?

    A grade of 4 or 5 would be considered "good" because the government has established a 4 as the passing grade; a grade of 5 is seen as a strong pass. Therefore, anything that exceeds this level would be considered good. You can practice GCSE Maths topic-wise questions to score good grades in the GCSE Maths exam.

    How can I get full marks in GCSE Maths?

    You can get a high score in GCSE Maths through meticulous practice of GCSE Maths topic-wise questions and GCSE Maths past papers.

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