THE ASCENT LIBRARY
High School MathematicsOne idea at a time.
Build your foundations, find the topic you need, and take the next step with confidence.
Years 7–10 · Australian Curriculum01 / YOUR YEAR LEVEL
Start where you are.
02 / EXPLORE THE TOPICS
85 lessons availableYear 9 starts here.
Develop quadratic thinking, use trigonometry, and investigate the evidence behind statistics.
85 subtopics
01
Real numbers
5 subtopics1.1Rational and irrational numbers1.2Placing real numbers on number lines1.3Estimating non-perfect square roots1.4Exact answers versus approximations1.5Calculations in practical contexts using suitable digital tools
Topic review3 practice tests02
Indices and scientific notation
6 subtopics2.1Integer index laws2.2Zero/negative powers and reciprocals2.3Index laws with variables2.4Scientific notation and decimal conversion2.5Comparing/calculating very large and small quantities2.6Measurement and time-scale applications
Topic review3 practice tests03
Algebra
5 subtopics3.1Simplifying algebraic expressions3.2Expanding single brackets3.3Common-factor factorisation3.4Substitution and rearranging formulas3.5Checking equivalent expressions
Topic review3 practice tests04
Ratio, rates and similarity
7 subtopics4.1Direct proportion4.2Rates and unit conversions4.3Scale drawings/maps4.4Corresponding lengths in similar figures4.5Finding missing lengths by similarity4.6Enlargement and scale factors4.7Practical proportional models and limitations
Topic review3 practice tests05
Pythagoras and Trigonometry
9 subtopics5.1Pythagoras review5.2Exact/rounded missing lengths5.3Opposite, adjacent and hypotenuse5.4Similarity and fixed trigonometric ratios5.5Sine, cosine and tangent5.6Finding a side5.7Finding an angle5.8Selecting the right method5.9Practical right-triangle problems and interpreting diagrams
Topic review3 practice tests06
Linear equations and graphs
9 subtopics6.1Equation-solving consolidation6.2Gradient as rise/run6.3Midpoint6.4Distance between points using Pythagoras6.5Straight-line equations and intercepts6.6Finding a line from information6.7Parallel/perpendicular lines as a natural school extension6.8Interpreting linear models6.9Testing parameter changes digitally
Topic review3 practice tests07
Quadratics and Parabolas
9 subtopics7.1Expanding two brackets7.2Special binomial products7.3Factorising monic quadratics7.4Zero-product principle and integer-root equations7.5Quadratic tables and graphs7.6Roots, intercepts, symmetry and turning point7.7Parameter changes and transformations using graphing tools7.8Graphical/numerical solutions7.9Simple area and financial/application models
Topic review3 practice tests08
Financial mathematics
6 subtopics8.1Percentage change consolidation8.2Simple interest8.3Comparing linear growth/cost models8.4Budgeting and financial assumptions8.5Interpreting linear versus quadratic financial models8.6Checking whether a model's answer makes practical sense
Topic review3 practice tests09
Surface area, volume and measurement
7 subtopics9.1Nets and surface area of right prisms9.2Cylinder surface area9.3Prism/cylinder volume and capacity9.4Unit conversion9.5Absolute, relative and percentage error9.6Interpreting precision and reasonable answers9.7Multi-step measurement problems
Topic review3 practice tests10
Geometry and transformations
7 subtopics10.1Angle reasoning consolidation10.2Enlargements using coordinates/digital geometry10.3Invariant and changing properties10.4Geometric constructions10.5Sequences of steps and decisions10.6Testing/refining construction algorithms10.7Explaining geometric reasoning
Topic review3 practice tests11
Statistics
8 subtopics11.1Sampling and survey quality11.2Population estimates and uncertainty11.3Comparing data sets11.4Comparative stem-and-leaf/dot/frequency displays11.5Centre, spread, shape and outliers11.6Misleading graphs and representations11.7Choosing a display for the data11.8Designing and reporting an investigation
Topic review3 practice tests12
Probability
7 subtopics12.1Compound-event sample spaces12.2Systematic lists, arrays, tables and trees12.3With/without replacement12.4“and” versus inclusive/exclusive “or”12.5Theoretical and relative-frequency estimates12.6Simulations of simple versus related compound events12.7Interpreting results
Topic review3 practice testsSchools may teach these topics in a different order.
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