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Number - Integers, powers and roots

Grade 7IGCSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Integers: Positive and negative whole numbers including zero.

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Directed Numbers: Using the number line to add and subtract integers; rules for multiplying and dividing signs (e.g., negative × negative = positive).

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Prime Numbers: Numbers with exactly two factors (1 and itself). Note: 1 is not a prime number.

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Prime Factorization: Breaking a number down into a product of its prime factors (Factor Trees).

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HCF and LCM: Highest Common Factor (largest number that divides into others) and Lowest Common Multiple (smallest number that is a multiple of others).

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Powers (Indices): The base is the number being multiplied, the exponent/index is how many times it is multiplied.

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Square and Cube Roots: The inverse operations of squaring (x2x^2) and cubing (x3x^3) a number.

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Order of Operations (BIDMAS/BODMAS): Brackets, Indices, Division/Multiplication, Addition/Subtraction.

📐Formulae

am×an=am+na^m \times a^n = a^{m+n}

am÷an=am−na^m \div a^n = a^{m-n}

a0=1a^0 = 1

x2=x\sqrt{x^2} = x

x33=x\sqrt[3]{x^3} = x

💡Examples

Problem 1:

Calculate: −12+(−5)×(−3)-12 + (-5) \times (-3)

Solution:

3

Explanation:

Follow BIDMAS. First, multiply the directed numbers: (−5)×(−3)=15(-5) \times (-3) = 15. Then, perform the addition: −12+15=3-12 + 15 = 3.

Problem 2:

Find the HCF and LCM of 12 and 18 using prime factorization.

Solution:

HCF = 6, LCM = 36

Explanation:

Prime factors of 12=2×2×312 = 2 \times 2 \times 3. Prime factors of 18=2×3×318 = 2 \times 3 \times 3. HCF is the product of common factors: 2×3=62 \times 3 = 6. LCM is the product of the highest powers of all factors present: 22×32=4×9=362^2 \times 3^2 = 4 \times 9 = 36.

Problem 3:

Evaluate: 23+81−6432^3 + \sqrt{81} - \sqrt[3]{64}

Solution:

13

Explanation:

Calculate each term individually: 23=82^3 = 8, 81=9\sqrt{81} = 9, and 643=4\sqrt[3]{64} = 4. Then substitute back into the expression: 8+9−4=17−4=138 + 9 - 4 = 17 - 4 = 13.