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
88 lessons availableYear 8 starts here.
Connect algebra with graphs, extend your geometry, and make sense of data and chance.
88 subtopics
01
Integers and rational numbers
7 subtopics1.1Four operations with integers1.2Signed fraction/decimal calculations1.3Order of operations1.4Terminating and recurring decimals1.5Rational and irrational numbers1.6Estimating square roots and recognising pi1.7Choosing efficient exact/decimal representations
Topic review1 practice test02
Index laws
6 subtopics2.1Exponent notation review2.2Multiplying same-base powers2.3Dividing same-base powers2.4Powers of powers2.5Zero index2.6Combining numerical index laws
Topic review1 practice test03
Percentages and financial mathematics
6 subtopics3.1Percentage increase/decrease3.2Finding an original amount3.3Discounts and mark-ups3.4Percentage comparisons3.5Budgets and purchase decisions3.6Modelling and checking financial problems with digital tools
Topic review1 practice test04
Ratios and rates
7 subtopics4.1Ratio scaling and division review4.2Unit rates4.3Comparing rates and best buys4.4Speed, distance and time4.5Converting compatible units4.6Direct-proportion tables and graphs4.7Modelling practical rate problems and checking assumptions
Topic review1 practice test05
Algebraic expressions
7 subtopics5.1Combining like terms5.2Substitution with signed/rational values5.3Multiplying/dividing algebraic terms5.4Expanding a single bracket5.5Factorising common factors5.6Equivalent linear expressions5.7Rearranging simple formulas
Topic review1 practice test06
Linear equations and graphs
10 subtopics6.1Multi-step equations6.2Brackets and variables on both sides6.3Equations with rational solutions6.4Substitution checks6.5One-variable inequalities and number-line solutions6.6Tables and straight-line graphs6.7Horizontal/vertical lines6.8How coefficients change a graph6.9Graphical solutions and intersection checks6.10Real-world linear models with digital exploration
Topic review1 practice test07
Pythagoras' theorem
7 subtopics7.1Hypotenuse and right-angled triangles7.2Why the theorem works7.3Finding the hypotenuse7.4Finding a shorter side7.5Exact roots versus rounded answers7.6Checking whether a triangle is right-angled7.7Practical length problems
Topic review1 practice test08
Circles, area and volume
6 subtopics8.1Circumference and area of circles8.2Perimeter/area of composite shapes8.3Choosing and converting area units8.4Cross-sections of prisms8.5Prism volume and capacity8.6Mixed measurement applications
Topic review1 practice test09
Congruence and similarity
7 subtopics9.1Congruent shapes and matching parts9.2Triangle congruence tests9.3Similar shapes and corresponding sides9.4Triangle similarity9.5Properties of quadrilaterals established using triangles9.6Testing congruence/similarity with transformations9.7Decision-tree algorithms and digital geometry
Topic review1 practice test10
Coordinates and three-dimensional space
5 subtopics10.1Coordinate transformations review10.2Identifying positions using three coordinates10.3Interpreting 3D axes10.4Describing routes and relative positions10.5Comparing diagrams, views and digital representations
Topic review1 practice test11
Time and time zones
6 subtopics11.1Converting 12-/24-hour time11.2Elapsed time across midnight11.3Timetables and journeys11.4Time-zone differences11.5Date changes11.6Checking real-world scheduling answers
Topic review1 practice test12
Statistics and sampling
8 subtopics12.1Population, census and sample12.2Observational versus experimental data12.3Random and non-random sampling12.4Primary/secondary data12.5Reviewing numerical displays and summary statistics12.6Comparing samples and sample sizes12.7Bias, variation and uncertainty12.8Planning, conducting and reporting a fair investigation
Topic review1 practice test13
Probability
6 subtopics13.1Complementary events13.2Two-stage sample spaces13.3Tables, trees and Venn diagrams13.4Probabilities of combined outcomes13.5Experimental versus theoretical results13.6Compound-event simulations and describing results
Topic review1 practice testSchools may teach these topics in a different order.
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