Year 9 Indices and Quadratics

Simplify algebraic expressions using the product, quotient, and power-of-a-power index laws.

Simplify powers of products containing numerical coefficients and multiple variables.

Rewrite and simplify expressions containing zero or negative indices so that the final answer has positive indices.

Determine the first whole-number input for which an exponential growth model exceeds a given value.

Convert numbers between ordinary decimal form and scientific notation.

Round ordinary numbers and values in scientific notation to a specified number of significant figures.

Calculate products of quantities in scientific notation and express the result to a specified number of significant figures.

Expand and simplify the product of two linear binomials containing positive or negative terms.

Expand perfect-square binomials using the appropriate algebraic identity.

Expand conjugate binomials using the difference-of-two-squares identity.

Factorise an algebraic expression fully by removing its highest common factor.

Factorise a difference of two squares fully.

Factorise a four-term algebraic expression by grouping terms in pairs.

Factorise a monic quadratic trinomial by finding two integers with the required sum and product.

Simplify algebraic fractions involving multiplication or division by factorising and cancelling common factors.

Add or subtract algebraic fractions by forming a common denominator and simplifying the result.

Solve quadratic equations of the form x² = k, including equations first rearranged into that form.

Solve a monic quadratic equation by factorising and applying the zero-product rule.

Form and solve a quadratic equation representing the dimensions and area of a rectangle, rejecting solutions that are invalid in context.