Year 10 - Maths
Accuracy of final answers
Surds
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit pupils will learn how to recognise surds, handle them in calculations and rationalise fractions with surds as denominators.
Lesson Summary
You will learn to appreciate the accuracy in leaving an answer without carrying out the final operation.
Key Notes
- There is always a choice regarding how you represent a value.
- You need to consider the most suitable way for the situation.
- Rounding reduces accuracy so a rounded answer is not always useful.
- There are agreed forms: one operation remaining and the result of the operation would produce a non-terminating decimal.
- Surd form is one such acceptable way.
Vocabulary To Learn
- Recurring decimal: A recurring decimal is one that has a digit or sequence of digits that repeat endlessly.
- Terminating decimal: A terminating decimal is one that has a finite number of digits after the decimal point.
- Rational number: A rational number is one that can be written in the form a/b where a and b are integers and b is not equal to 0.
- Irrational number: An irrational number is one that cannot be written in the form a/b where a and b are integers and b is not equal to 0.
- Surd: A surd is an irrational number expressed as the root of a rational number.
Common Mistakes To Avoid
- Surds are any number with a root symbol.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
There is always a choice regarding how you represent a value. You need to consider the most suitable way for the situation.
2. Use this key word in a maths sentence and explain it clearly. 'Recurring decimal'
A recurring decimal is one that has a digit or sequence of digits that repeat endlessly. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Surds are any number with a root symbol. Correction: √4 is not a surd as it is equivalent to 2.
More Lessons In This Unit
- Addition with surds Study Guide
- Applying the underlying structure of multiplication and division of surds Study Guide
- Identifying square factors to support simplifying surds Study Guide
- Multiplication of surds Study Guide
- Problem solving with surds Study Guide
- Rationalising a single term denominator Study Guide
- Rationalising a two term denominator Study Guide
- Simplifying surds Study Guide
- Solving equations with surds Study Guide
- The distributive law with surds Study Guide
- The distributive law with two or more binomials Study Guide
Browse all guides in the Year 10 Maths guide library.