Grade 8 Math Revision by benjamin manani

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Chapter 1

Integers, Powers, and Square Roots

Key Concepts

This chapter covers operations with integers, laws of powers, and square roots. You need these skills to simplify expressions, calculate accurately, and solve measurement problems in exams.

• Integers include negative numbers, zero, and positive numbers.

• Add integers with the same sign, then keep the sign. For different signs, subtract and keep the sign of the larger absolute value.

• For multiplication and division: same signs give a positive answer; different signs give a negative answer.

• Laws of powers: a^m × a^n = a^(m+n); a^m ÷ a^n = a^(m-n); (a^m)^n = a^(mn).

• A square root is a number that gives the original number when multiplied by itself.

• Use correct order of operations: brackets, powers or roots, multiplication/division, addition/subtraction.

Before you continue: How would you simplify -3^2 and (-3)^2 differently?

Key Terms

• Integer - A whole number, including negative numbers and zero.

• Absolute value - The distance of a number from zero, written without its sign.

• Power - A number written using a base and an exponent, such as 2^4.

• Base - The number being multiplied repeatedly in a power.

• Exponent - The small number showing how many times the base is used.

• Square root - A number which, when squared, gives the original number.

• Perfect square - A number with a whole-number square root, such as 49.

Active Recall

• Integer

__________________________________________________

• Absolute value

__________________________________________________

• Power

__________________________________________________

• Base

__________________________________________________

• Exponent

__________________________________________________

• Square root

__________________________________________________

Worked Examples

1. Adding and subtracting integers

Calculate: -8 + 13 - 6

• -8 + 13 = 5.

• 5 - 6 = -1.

• Answer: -1

Now you try: Calculate -12 + 7 + 9.

__________________________________________________

2. Multiplying integers

Calculate: (-4) × (-3) × 2

• (-4) × (-3) = 12 because two negative signs give a positive.

• 12 × 2 = 24.

• Answer: 24

Now you try: Calculate (-5) × 6 × (-2).

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3. Powers and square roots

Simplify: 2^3 × 2^4 + √81

• Apply the power law: 2^3 × 2^4 = 2^7.

• 2^7 = 128.

• √81 = 9.

• 128 + 9 = 137.

Now you try: Simplify 3^2 × 3^3 + √64.

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Practice Questions

• (Easy) Calculate: -15 + 8.

__________________________________________________

• (Easy) Calculate: (-7) × 4.

__________________________________________________

• (Medium) Calculate: 18 - (-6) - 11.

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• (Medium) Simplify: 5^2 × 5^3.

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• (Medium) Find √144 - √25.

__________________________________________________

• (Hard) Simplify: 2^5 ÷ 2^2 + (-3)^2.

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Answer Key

• -7

• -28

• 13

• 5^5 = 3,125

• 7

• 8 + 9 = 17

Exam Tips & Common Mistakes

• Do not confuse -3^2 with (-3)^2. The first is -9; the second is 9.

• When subtracting a negative, change it to addition: 7 - (-4) = 7 + 4.

• Do not add exponents when adding powers. The law a^m × a^n applies to multiplication only.

• Check the sign separately before completing multiplication or division.

• For measurement problems, write the correct square units for area and cubic units for volume.

• Show each step. Markers can award method marks even when the final answer is incorrect.

• Keep answers exact when possible, especially square roots. Check calculations using inverse operations.

Quick Reference

Rules

• Same signs in addition: add and keep the sign.

• Different signs in addition: subtract absolute values and use the sign of the larger absolute value.

• Same signs in multiplication/division = positive.

• Different signs in multiplication/division = negative.

• a^m × a^n = a^(m+n)

• a^m ÷ a^n = a^(m-n)

• (a^m)^n = a^(mn)

• √a × √a = a

Mnemonic: “Same Sign Plus; Different Sign Minus.”

Remember

• Integers include negative numbers, zero, and positive numbers.

• Powers show repeated multiplication.

• Square roots undo squaring.

• Follow the order: brackets, powers/roots, multiplication/division, addition/subtraction.

• Check signs and units before submitting.

Exam Practice

• Simplify expressions carefully.

End of chapter one. 4 more chapters and about 3,927 words in the full book.

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What's inside: 5 chapters

1. Integers, Powers, and Square Roots
2. Linear Equations and Inequalities
3. Proportionality, Ratios, and Rates
4. Percentages and Simple Interest
5. Geometry: Angles, Triangles, and Perimeter

About this book

"Grade 8 Math Revision" is a study guide book by benjamin manani with 5 chapters and approximately 3,927 words. Revision mathematics for Grade 8 under Kenya CBE curriculum.

This book was created using Inkfluence AI, an AI-powered book generation platform that helps authors write, design, and publish complete books. It was made with the Study Guide Generator.

Frequently Asked Questions

What is "Grade 8 Math Revision" about?

Revision mathematics for Grade 8 under Kenya CBE curriculum

How many chapters are in "Grade 8 Math Revision"?

The book contains 5 chapters and approximately 3,927 words. Topics covered include Integers, Powers, and Square Roots, Linear Equations and Inequalities, Proportionality, Ratios, and Rates, Percentages and Simple Interest, and more.

Who wrote "Grade 8 Math Revision"?

This book was written by benjamin manani and created using Inkfluence AI, an AI book generation platform that helps authors write, design, and publish books.

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