Powers and Roots

A year 10 unit of work covering the following topics.
(1) Rules of Indices: The index form. Evaluating the index form. The multiplication rule. The division rule. The zeroth index rule. Raising a power to another index. The negative index rule. The reciprocal as a negative index. Unitary fraction index rule. Algebra and rules of indices. The general fraction index rule.
(2) Standard Form: Writing numbers 𝑥 ≥ 1 in standard form. Writing numbers 0 < 𝑥 < 1 in standard form. Changing from standard form to an ordinary number. Adding and subtracting in standard form. Almost in standard form. Multiplying and dividing in standard form.
(3) Efficient Percentage Changes: Repeated percentage changes. Calculating compound interest efficiently. Fractional changes. Reverse percentages.
(4) Graph Plotting: Quadratic graphs. Recognising and sketching graphs of the form 𝑦 = 𝑎𝑥² + 𝑏. Graphical method of solving equations of the form 𝑥² + 𝑎𝑥 + 𝑏 = 0. Other graphs.