Year 10 Maths Worksheets

Coordinate plane review; midpoint formula; distance between two points.

Key features of parabolas; graph in standard form; convert to vertex form y=a(x-h)²+k; transformations; axis of symmetry; intercepts.

Identify congruent figures; write congruence statements; use corresponding parts to find missing measures.

SSS, SAS, ASA, AAS, HL congruence criteria; choose the correct criterion; deductive proofs using CPCTC.

Similar figures; scale factor; AA, SAS, SSS similarity criteria for triangles; missing lengths; proportional segments; Triangle Proportionality Theorem.

Equation of a circle (x-h)²+(y-k)²=r²; find centre and radius; write and graph circle equations.

Network vocabulary (vertices, edges, degree); interpret network diagrams; connectedness; Eulerian paths and circuits; real-world network applications.

Apply algorithmic thinking to spatial problems: shortest paths, spanning trees and region-fill.

Powers with integer, decimal and fractional bases; negative exponents; all index laws (product, quotient, power); evaluate and identify equivalent exponential expressions.

Evaluate rational exponents a^(p/q)=(q-th root of a)^p; multiplication, division and power rules with rational exponents; simplify expressions with rational exponents.

Roots of integers and rationals; simplify surds (√50=5√2); multiply and add/subtract surds; rationalise denominators using conjugates; convert between radical and rational exponent form.

One-step through multi-step linear equations; variables on both sides; brackets; fractions; literal equations; word problems; number of solutions; quadratic equations by factorising.

Graph inequalities; identify solutions; solve one-step through multi-step; compound inequalities (AND/OR); absolute value inequalities; graph solution sets.

Domain and range; identify functions; vertical line test; evaluate f(x); function tables; rate of change from tables/graphs; increasing/decreasing; transformations.

Slope from graph and two points; y=mx+b; standard form; point-slope form; parallel/perpendicular lines; transformations; direct/inverse variation; scatter plots; distance from point to line (NEW v9); distance between parallel lines (NEW v9).

Solve systems of two linear equations by graphing, substitution, and elimination; classify systems (one/no/infinite solutions); word problems.

Check if (x,y) satisfies an inequality; solve for y; graph linear inequalities with shaded regions; word problems.

Convert between exponential and logarithmic form; evaluate logs; product, quotient, and power rules; expand and condense expressions; change of base; natural logarithm (ln).

Graph and transform exponential functions; growth/decay models (A=ab^t); solve exponential and logarithmic equations; compound interest; natural exponential (e^x); Richter, pH, decibel word problems.

Multiply, divide and raise monomials to powers using index laws; multiply monomials by polynomials.

Add, subtract, multiply polynomials; special products; evaluate and describe end behaviour; divide polynomials by monomials, synthetic division, and long division.

Factor GCF, difference of squares, perfect square trinomials, monic quadratics, non-monic quadratics (NEW v9), sum/difference of cubes, factor completely, and factor by grouping (NEW v9).

Solve by factorising (monic and non-monic), square roots, graphing, zero product property, completing the square (NEW v9), quadratic formula (MAJOR NEW v9), discriminant Δ=b²-4ac (NEW v9), simultaneous quadratic-linear (NEW v9).

Identify linear, quadratic and exponential functions from equations, tables and graphs; compare growth rates; mathematical modelling.

Consecutive integer problems; rate of travel word problems; weighted averages.

Experiment with linear, quadratic and cubic functions using digital tools; identify key features.

Classify rational and irrational numbers; compare and order rationals; evaluate square and cube roots.

Simple and compound interest (A=P(1+r/n)^nt); continuously compounded interest (A=Pe^rt); GST, discount, markup; financial modelling including superannuation and loans.

Basic probability; theoretical vs experimental; compound events; conditional probability P(A|B) from two-way tables (NEW v9); permutations and combinations; simulations.

Calculate P(A|B) using two-way tables, tree diagrams and repeated experiments.

Pythagorean theorem review and 3D applications; converse; special right triangles 30-60-90 and 45-45-90 (NEW v9).

Convert between degrees and radians; coterminal angles (NEW v9); reference angles (NEW v9).

SOH-CAH-TOA; exact trig values; sine and cosine rules (MAJOR NEW v9); area ½ab sinC; bearings (NEW v9); 3D trigonometry (NEW v9).

SA/V of prisms, cylinders; pyramids and cones V=⅓Bh (NEW v9); spheres SA=4πr² V=⁴⁄₃πr³ (NEW v9); compound figures; effect of scaling.

Circle vocabulary; central angles; arc measure and arc length (NEW v9); radians (NEW v9); sector area; chords; tangents; inscribed angles (NEW v9).

Use mathematical modelling to solve practical problems involving proportion and scaling of objects, including enlargement and reduction.

Analyse absolute, relative and percentage measurement errors in practical contexts.

Mean, median, mode; range and IQR; outliers; mean absolute deviation (NEW v9); variance and standard deviation (NEW v9 — formal).

Frequency tables; bar charts; dot plots; line graphs; two-way tables; back-to-back stem-and-leaf; box plots 5-number summary (NEW v9); scatter plots and line of best fit (MAJOR NEW v9).

Construct scatterplots and comment on the association between 2 numerical variables in terms of direction, form and strength.

Construct two-way tables and discuss the possible relationship between categorical variables.

Investigate bivariate numerical data; identify relationships and report findings.