Year 9 Maths Worksheets

Classify rational, irrational and real numbers; compare and order rationals on number lines; convert between decimals and fractions; square roots; cube roots; irrational numbers on number lines.

Add, subtract, multiply and divide integers; evaluate numerical and variable expressions involving integers and rational numbers; order of operations with rationals.

Powers with integer, decimal and fractional bases; multiplication, division and power rules with positive exponents; negative exponents (a⁻ⁿ = 1/aⁿ); all exponent laws with integer exponents; evaluate and identify equivalent exponential expressions.

Convert between standard and scientific notation; compare numbers in scientific notation; add, subtract, multiply and divide in scientific notation.

Sets, subsets and complements; unions and intersections; set-builder notation and Venn diagrams.

Equivalent ratios; unit rates and prices; proportions and word problems; estimating populations; scale drawings.

Convert between %, fraction and decimal; percent equations and word problems; percent change; simple interest (NEW v9); GST and discount; multi-step percent problems.

Mixed word problems; money and financial modelling (NEW v9); consecutive integers; rate of travel; weighted averages.

Add and subtract multi-digit whole numbers up to 100 million.

Find a percentage of a given whole (single-digit and round percentages).

Model direct and inverse proportion; solve real-world proportion and rate problems.

Commutative, associative, identity, inverse and zero properties of addition and multiplication; distributive property; simplify variable expressions using properties; properties of equality.

Translate words into algebraic expressions and equations; simplify with like terms and the distributive property; identify equivalent expressions; check solutions by substitution; solve multi-step linear equations; rearrange formulas.

Algebra tiles; equations from diagrams; one-step, two-step and multi-step linear equations; brackets and fractions; variables on both sides; complete a worked solution; number of solutions (one/none/infinite — NEW v9); word problems and mixed review.

Convert between tables/graphs/mappings/lists; independent/dependent variables; identify functions; vertical line test; evaluate functions in formal f(x) notation; substitute expressions; complete function tables; interpret real-world function graphs (NEW v9).

Find the constant of proportionality k = y/x from tables and graphs; write y = kx equations; identify whether relationships are proportional; interpret k as a unit rate; solve proportional word problems.

Identify linear vs nonlinear; gradient from graph and from two points; missing coordinate from gradient; gradient and y-intercept from y = mx + c; graph y = mx + c; write equations from graphs, tables and word problems; rearrange into y = mx + c.

Identify monomials; multiply, divide, multiply and divide monomials using index laws; raise a monomial to a power.

Polynomial vocabulary; algebra-tile models; add, subtract and multiply polynomials; FOIL for binomials; perfect squares and difference of squares; HCF of monomials; factor out a monomial; factorise monic quadratics (NEW v9).

Distinguish linear and quadratic from graphs and tables; vertex, axis of symmetry, max/min; complete a quadratic table; graph y = ax² + k; solve x² = k by square roots; zero product property; solve monic quadratics by factorising (NEW v9); transformations of quadratics (NEW v9).

Experiment with changing the parameters m and c in y = mx + c and observe the effects on the graph.

Convert rates and measurements; precision and significant figures; greatest possible error; minimum and maximum area and volume; percent error (NEW v9).

Perimeter and area of polygons and circles; compound and inscribed figures; interior angles of polygons; transversal angles; volume and surface area of cylinders (NEW v9) and prisms.

Find hypotenuse and missing legs; perimeter; word problems; converse of Pythagoras.

sin, cos and tan ratios; special angles; trigonometric calculator use; find sides and angles in right triangles; combined Pythagoras-trig problems; angles of elevation and depression (NEW v9).

Calculate absolute, relative and percentage errors in measurement contexts.

Quadrants and coordinates; midpoint formula (NEW v9); distance formula (NEW v9).

Congruent figures; SSS, SAS, ASA and RHS rules; dilations (NEW v9); similarity statements; side and angle ratios; indirect measurement; scaling effects on perimeter, area and volume (NEW v9).

Apply ruler-and-compass construction algorithms to bisect angles, segments and construct perpendiculars.

Interpret and create bar, line, circle and stem-and-leaf plots; histograms (NEW v9); back-to-back stem-and-leaf plots (NEW v9).

Mean, median, mode and range; missing data values; quartiles and IQR (NEW v9); biased samples and comparing distributions.

Design and report on full statistical investigations.

Construct and compare parallel boxplots to compare distributions of multiple datasets.

Select and justify the most appropriate data display for a given dataset and purpose.

Theoretical and experimental probability; two-way tables; sample spaces and outcome counting; independent and dependent events; two-step experiments with and without replacement (NEW v9).

Repeated chance experiments and simulations for compound events.

Calculate relative frequencies for AND and OR events; use P(A∪B) = P(A)+P(B)−P(A∩B).