Exponents and Indices
Term 1
Index laws · Negative & fractional indices · Scientific form
Learning Objectives
PrintIndex Laws
- 1. Apply the index laws for multiplication, division and power of a power with positive integer indices.
- 2. Evaluate expressions involving zero and negative integer indices (e.g. $a^0 = 1$, $a^{-n} = 1/a^n$).
- 3. Evaluate expressions involving fractional indices (e.g. $a^{1/2}$, $a^{2/3}$).
- 4. Simplify algebraic expressions that combine the index laws, including negative and fractional indices.
Solving Index Equations
- 5. Solve equations by writing both sides with the same base and comparing exponents.
- 6. Solve equations of the form $a^{x} = k$ where the answer is a fraction or negative.
- 7. Solve equations of the form $a^{-2/3} = 1/25$ using fractional indices.
- 8. Convert between ordinary numbers and scientific (standard) form, including with negative powers of $10$.
- 9. Multiply and divide numbers in scientific form, expressing the answer in standard form.
Surds (Extended)
- 10. Simplify surds by extracting the largest square factor (e.g. $\sqrt{50} = 5\sqrt{2}$).
- 11. Add, subtract, multiply and divide surds, including expanding brackets containing surds.
- 12. Rationalise a denominator of the form $1/\sqrt{a}$.
- 13. Rationalise a denominator of the form $1/(a + \sqrt{b})$ using the conjugate.
- 14. Apply surds and index laws inside sequence problems and other algebraic contexts.
Assessments
Exponents and indices end-of-unit test
Criterion A
50 min
Written test on the index laws, negative and fractional indices, and converting between standard and scientific form.
Review Pack
Open review hub
Fluency Pack A — 40 questions
Fluency Pack B — 40 questions
Problem-solving — 12 unfamiliar tasks
Worked solutions (Pack A + B + problems)