Year 10 - Maths
Problem solving with the laws of indices
Arithmetic procedures: index laws
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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 learn how to manipulate indices and perform calculations without conversion by understanding index laws.
Lesson Summary
You will learn to use your knowledge of the laws of indices to solve problems.
Key Notes
- The base could be a number, letter or combination of the two.
- The laws are another way you can simplify an expression.
- Plotting numbers against their squared values can help you estimate unknown amounts.
Vocabulary To Learn
- Power: An alternative word for exponent or index. Used when reading exponents above 3. E.g. 2^4 is read as "2 to the power of 4".
- Vinculum: Vinculum is the horizontal line placed over an expression to show that everything below that line is one group.
Common Mistakes To Avoid
- Using the laws of indices, when dividing by a number with a negative exponent pupils can incorrectly subtract the negative exponent.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
The base could be a number, letter or combination of the two. The laws are another way you can simplify an expression.
2. Use this key word in a maths sentence and explain it clearly. 'Power'
An alternative word for exponent or index. Used when reading exponents above 3. E.g. 2^4 is read as "2 to the power of 4". Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Using the laws of indices, when dividing by a number with a negative exponent pupils can incorrectly subtract the negative exponent. Correction: When the bases of all the numbers are the same, forming an equation with the exponents can reduce errors.
More Lessons In This Unit
- Advanced problem solving with the laws of indices Study Guide
- Checking and securing understanding of calculating with fractions and decimals Study Guide
- Checking and securing understanding of calculations involving negative numbers Study Guide
- Checking and securing understanding of converting between fractions and decimals Study Guide
- Checking and securing understanding of LCM and HCF Study Guide
- Checking and securing understanding of prime factorisation Study Guide
- Checking and securing understanding of roots and integer indices Study Guide
- Converting any recurring decimal to a fraction Study Guide
- The laws of indices - division Study Guide
- The laws of indices - fractional exponents Study Guide
- The laws of indices - multiplication Study Guide
- The laws of indices - negative and zero exponents Study Guide
- The laws of indices - raising a power to a power Study Guide
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