Chapter 1 Algebraic Expressions

    Cards (21)

    • What can you use the laws of indices for?

      To simplify powers of the same base
    • What is the product rule of indices?

      a<sup>m</sup> × a<sup>n</sup> = a<sup>m+n</sup>
    • What is the quotient rule of indices?

      a<sup>m</sup> ÷ a<sup>n</sup> = a<sup>m-n</sup>
    • What is the power of a power rule of indices?

      (a<sup>m</sup>)<sup>n</sup> = a<sup>mn</sup>
    • What is the product of powers rule of indices?

      (ab)<sup>n</sup> = a<sup>n</sup>b<sup>n</sup>
    • What is the process for expanding brackets?

      • Multiply each term in one expression by each term in the other expression.
      • For example, (x+5)(4x-2y+3) expands to:
      • x(4x-2y+3) + 5(4x-2y+3)
    • How many terms do you get when multiplying (x+5) by (4x-2y+3)?

      6 terms
    • What is the result of expanding (x+5)(4x-2y+3)?

      • 4x² - 2xy + 23x - 10y + 15
    • What is factorising in algebra?

      • Writing expressions as a product of their factors.
      • It is the opposite of expanding brackets.
    • What is the form of a quadratic expression?

      ax² + bx + c where a, b, and c are real numbers and a ≠ 0
    • How do you factorise a quadratic expression?

      Find two factors of ac that add up to b
    • What is the difference of two squares formula?

      - = (x + y)(x - y)
    • What is the notation for real numbers?

      All positive and negative numbers, or zero, including fractions and surds
    • What is the value of a<sup>0</sup>?

      1
    • What is a surd?
      A surd is a multiple of √n where n is not a square number
    • Give examples of surds.

      √2, √19, and 5√2
    • What characterizes the decimal expansion of a surd?

      It is never-ending and never repeats
    • What are irrational numbers?

      Numbers that cannot be written in the form a/b where a and b are integers
    • What are the rules for manipulating surds?

      • √ab = √a × √b
      • √a/√b = √a/b
    • What is rationalising the denominator?

      • Rearranging a fraction with a surd in the denominator to make the denominator a rational number.
      • Common methods include:
      • Multiply by √a for 1/√a
      • Multiply by a - √b for 1/(a - √b)
      • Multiply by a + √b for 1/(a + √b)
    • What are the key points about indices and surds?

      1. Laws of indices simplify powers of the same base.
      2. Factorising is the opposite of expanding brackets.
      3. Quadratic expressions are of the form ax² + bx + c.
      4. Difference of two squares: x² - y² = (x + y)(x - y).
      5. Laws of indices apply to rational powers.
      6. Surds can be manipulated using specific rules.
      7. Rationalising denominators is useful for fractions with surds.