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Year 10 · Term 1

Exponents and Indices

Learning Objectives

Index Laws

  1. 1. Apply the index laws for multiplication, division and power of a power with positive integer indices.
  2. 2. Evaluate expressions involving zero and negative integer indices (e.g. $a^0 = 1$, $a^{-n} = 1/a^n$).
  3. 3. Evaluate expressions involving fractional indices (e.g. $a^{1/2}$, $a^{2/3}$).
  4. 4. Simplify algebraic expressions that combine the index laws, including negative and fractional indices.

Solving Index Equations

  1. 5. Solve equations by writing both sides with the same base and comparing exponents.
  2. 6. Solve equations of the form $a^{x} = k$ where the answer is a fraction or negative.
  3. 7. Solve equations of the form $a^{-2/3} = 1/25$ using fractional indices.
  4. 8. Convert between ordinary numbers and scientific (standard) form, including with negative powers of $10$.
  5. 9. Multiply and divide numbers in scientific form, expressing the answer in standard form.

Surds (Extended)

  1. 10. Simplify surds by extracting the largest square factor (e.g. $\sqrt{50} = 5\sqrt{2}$).
  2. 11. Add, subtract, multiply and divide surds, including expanding brackets containing surds.
  3. 12. Rationalise a denominator of the form $1/\sqrt{a}$.
  4. 13. Rationalise a denominator of the form $1/(a + \sqrt{b})$ using the conjugate.
  5. 14. Apply surds and index laws inside sequence problems and other algebraic contexts.