Number Manipulation
Overview
Every calculation you do at IGCSE, from a percentage change to a quadratic solution, rests on a small set of number skills: knowing which operation to apply first, breaking numbers into their prime building blocks, and handling roots that refuse to simplify to a whole number. This topic gathers those foundations into one toolkit.
You will practise the order of operations, use prime factorisation to find the highest common factor and lowest common multiple, apply the laws of indices to integer, negative and fractional powers, and learn to simplify and rationalise surds so that every answer is left in its neatest, exact form.
Objectives
- Use the ordinary processes of number manipulation including the four operations and combination of them by use of brackets
- Understand and use prime numbers, factors and multiples, including finding HCF and LCM in simple cases
- Use index notation and index laws for multiplication and division involving integer, fractional and negative powers
- Perform simple manipulation of surds, understanding what surds represent and their use for exact answers
- Rationalise the denominator
- Recognise and use natural numbers, integers, rational and irrational numbers
Mind map
This topic is mapped out so you can see how the ideas connect.
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Flashcards
Quick recall practice on the facts this topic is tested on.
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Lesson Note
Complete Note Available on the Green Bridge App
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Lesson Evaluation
Congratulations on completing the lesson on Number Manipulation. Now that you've explored the key concepts and ideas, it's time to put your knowledge to the test. This section offers a variety of practice questions designed to reinforce your understanding and help you gauge your grasp of the material.
You will encounter a mix of question types, including multiple-choice questions, short answer questions, and essay questions. Each question is thoughtfully crafted to assess different aspects of your knowledge and critical thinking skills.
Use this evaluation section as an opportunity to reinforce your understanding of the topic and to identify any areas where you may need additional study. Don't be discouraged by any challenges you encounter; instead, view them as opportunities for growth and improvement.
- What is the value of 4 + 2 x (9 - 6)^2? A) 22 B) 40 C) 46 D) 108 Answer: A
- The prime factorisation of 60 is 2^2 x 3 x 5. What is the LCM of 60 and 2^3 x 3^2? A) 12 B) 180 C) 360 D) 720 Answer: C
- Which of the following is equal to 5^(-2)? A) -10 B) -25 C) 1/10 D) 1/25 Answer: D
- Which number is a surd? A) The square root of 49 B) The square root of 11 C) The square root of 100 D) The cube root of 27 Answer: B
- Simplify the square root of 45. A) 3 times the square root of 5 B) 5 times the square root of 3 C) 9 times the square root of 5 D) 15 times the square root of 3 Answer: A
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Recommended Books
Further learning from open sources
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Textbook section
Real Numbers: Algebra Essentials
Classify a real number as a natural, whole, integer, rational, or irrational number.
"Algebra and Trigonometry: Real Numbers: Algebra Essentials" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/algebra-and-trigonometry/pages/1-1-real-numbers-algebra-essentials. Access for free at https://openstax.org/books/algebra-and-trigonometry/pages/1-introduction
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Textbook section
Introduction to Whole Numbers
Use place value with whole numbers
"Elementary Algebra: Introduction to Whole Numbers" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/elementary-algebra/pages/1-1-introduction-to-whole-numbers. Access for free at https://openstax.org/books/elementary-algebra/pages/1-introduction
Published by other organisations under open licences, credited as they ask. Links open their websites.
Practice Mock Questions
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