Mathematics Learning Path
High School (9–10) Mathematics
Explore structured mathematics courses, solved problems, simulations and Python activities.
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Chords, Arcs and the Angles They Make
StemPy LabThe parts of a circle, and how chords and the centre are related. Equal chords, the perpendicular from the centre, and the angle that an arc makes at the centre and at the rim.
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Cyclic Quadrilaterals
A four-sided figure with all its corners on a circle. Why its opposite angles add to 180 degrees, how to tell whether a quadrilateral is cyclic, and problems that use these facts.
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Tangents to a Circle
A line that touches a circle at one point. The tangent is perpendicular to the radius, two tangents from a point are equal, and problems about circles inside triangles and quadrilaterals.
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Lines of Sight, Elevation and Depression
The line of sight, the angle of elevation and the angle of depression. Drawing a right triangle from a word problem and using one trigonometric ratio to find a height or a distance.
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Heights and Distances with Two Triangles
Problems with two observation points or two objects, a tower on a building, a moving aircraft or boat, and a river or bridge to measure. Solving two equations for the height and the distance.
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Congruent Triangles and Their Properties
When two triangles are exactly equal: the SAS, ASA, SSS and RHS rules, the properties of an isosceles triangle, and the inequalities between the sides and angles of a triangle.
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Similar Triangles and the Basic Proportionality Theorem
Similar figures and the two conditions for similar triangles. Then Thales' theorem, its converse, and the way a line parallel to one side cuts the other two in the same ratio.
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Criteria for Similarity, Areas and the Pythagoras Theorem
The AA, SSS and SAS criteria for similarity. Then the ratio of the areas of similar triangles, and the Pythagoras theorem and its converse proved by similar triangles.
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Graphs and Consistency of Pairs of Equations
A pair of linear equations drawn as two lines. When the lines cross, run parallel or coincide, and how the coefficients tell you which without drawing.
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Solving Pairs of Equations Algebraically
Substitution, elimination and cross-multiplication. Then equations that become linear after a change of variable, and word problems about numbers, ages, speeds, money and geometry.
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Probability: Equally Likely Outcomes
Outcomes, events and equally likely outcomes, the probability of an event as favourable over total, the range from 0 to 1, impossible and sure events, and the complement.
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Probability with Coins, Dice and Cards
Listing the outcomes of two coins, two dice and a pack of cards, then problems with balls in a bag, numbers on discs and spinners, the kinds of question boards set most.
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