MYP 4Year 10Term 1
Exponents and Indices
Index laws · Negative & fractional indices · Scientific form
Algebra
14 objectives
Learning objectives
What students should be able to do by the end of this unit.
Index Laws
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- Apply the index laws for multiplication, division and power of a power with positive integer indices.
- Evaluate expressions involving zero and negative integer indices (e.g. $a^0 = 1$, $a^{-n} = 1/a^n$).
- Evaluate expressions involving fractional indices (e.g. $a^{1/2}$, $a^{2/3}$).
- Simplify algebraic expressions that combine the index laws, including negative and fractional indices.
Solving Index Equations
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- Solve equations by writing both sides with the same base and comparing exponents.
- Solve equations of the form $a^{x} = k$ where the answer is a fraction or negative.
- Solve equations of the form $a^{-2/3} = 1/25$ using fractional indices.
- Convert between ordinary numbers and scientific (standard) form, including with negative powers of $10$.
- Multiply and divide numbers in scientific form, expressing the answer in standard form.
Surds (Extended)
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- Simplify surds by extracting the largest square factor (e.g. $\sqrt{50} = 5\sqrt{2}$).
- Add, subtract, multiply and divide surds, including expanding brackets containing surds.EXT
- Rationalise a denominator of the form $1/\sqrt{a}$.EXT
- Rationalise a denominator of the form $1/(a + \sqrt{b})$ using the conjugate.EXT
- Apply surds and index laws inside sequence problems and other algebraic contexts.EXT
Review pack
Curated revision materials parents and students can download.
A review pack for this unit is being prepared.