Explore structured mathematics courses, solved problems, simulations and Python activities.
The 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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
These are part of our upcoming paid plans.
Harder problems for the keen: equations that turn into quadratics, the sum and the product of the roots, and the greatest or least value of a quadratic, each with worked solutions and a timed paper.
A polynomial puzzle in an olympiad is usually solved in two lines, if you know the trick. In this course you learn how to find a zero by testing a few numbers, and how to use an identity to avoid a long calculation. Then you solve problems and take a timed paper in the style of an olympiad.