Algebraic Techniques Flashcards
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Questions and Answers

What does the index law state for multiplication of exponents?

  • m^a x m^b = m^(a-b)
  • m^a x m^b = m^(a+b) (correct)
  • m^a x m^b = 1
  • m^a x m^b = a + b

    • What is the value of m^0?

    1

    What does m^-1 equal?

    1/m

    The expression 2/(8x-y)^5 can be written as 2(8x-y)^5.

    <p>False</p> Signup and view all the answers

    What is the relationship expressed in fractional indices?

    <p>m^(1/2) x m^(1/2) = m</p> Signup and view all the answers

    Write in surd form: m^2/3.

    <p>3√m^2</p> Signup and view all the answers

    Write √2m in index form.

    <p>2m^(1/2)</p> Signup and view all the answers

    The formula for the difference of two squares is a^2 - b^2 = ______

    <p>(a+b)(a-b)</p> Signup and view all the answers

    What is factorisation (HCF)?

    <p>A method to rewrite an expression as a product of its highest common factor.</p> Signup and view all the answers

    What does 'trinomials' refer to?

    <p>Turning three terms into a bracketed equation.</p> Signup and view all the answers

    What is meant by 'rationalising the denominator'?

    <p>To eliminate any radicals in the denominator of a fraction.</p> Signup and view all the answers

    Study Notes

    Index Laws

    • m^a x m^b results in m^(a+b)
    • m^a ÷ m^b results in m^(a-b)

    Zero Indices

    • Any base raised to the power of zero equals one: m^0 = 1

    Negative Indices

    • m^-1 is equivalent to 1/m
    • To express a negative exponent in a fraction, flip the fraction to make it positive, e.g., (2/3)^-1 = 3/2

    Expressions with Negative Indices

    • An expression like 2/(8x - y)^5 can be rewritten as 2(8x - y)^-5

    Fractional Indices

    • The expression √m multiplied by itself equals m
    • m^(1/2) multiplied by m^(1/2) also equals m, establishing that √m = m^(1/2)
    • The cube root of m, 3√m, multiplied by itself three times also equals m; therefore, 3√m = m

    Writing in Surd Form

    • The expression m^(2/3) can be expressed as the cube root of m squared: 3√(m^2)

    Writing in Index Form

    • The square root of 2m can be denoted as 2m^(1/2)

    Factorisation (HCF)

    • Revisiting factorisation methods is essential; concepts are usually straightforward.

    Grouping in Pairs

    • Practice problems related to grouping in pairs to enhance understanding.

    Trinomials

    • Trinomials can be transformed into bracketed equations, facilitating easier factorisation.

    Perfect Squares

    • Review perfect squares to strengthen algebraic manipulation skills.

    Difference of Two Squares

    • The formula a^2 - b^2 factors into (a+b)(a-b), a crucial algebraic identity to remember.

    Algebraic Fractions

    • Go through related questions to gain a better grasp of simplifying and manipulating algebraic fractions.

    Simplifying Surds

    • Practice examples focused on simplifying surds, reinforcing techniques learned.

    Rationalising the Denominator

    • It's crucial to fully revise methods of rationalising denominators to eliminate roots from the bottom of fractions.

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    Description

    This quiz consists of flashcards covering essential algebraic techniques, specifically index laws, zero, negative, and fractional indices. Each card provides a definition and examples to help reinforce your understanding of these concepts. Test your knowledge and master the fundamentals of algebra.

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