Grade 8 Math Revision

Key ConceptsThis 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 TermsInteger - 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 RecallInteger

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Absolute value

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Power

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Base

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Exponent

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Square root

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Worked Examples1. Adding and subtracting integersCalculate: -8 + 13 - 6

-8 + 13 = 5.

5 - 6 = -1.

Answer: -1

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

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2. Multiplying integersCalculate: (-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 rootsSimplify: 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.

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(Easy) Calculate: (-7) × 4.

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(Medium) Calculate: 18 - (-6) - 11.

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(Medium) Simplify: 5^2 × 5^3.

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(Medium) Find √144 - √25.

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(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 MistakesDo 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 ReferenceRulesSame signs in addition: add and keep the sign.

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