Principles of Mathematics

Find the point where two lines meet: solve systems of two linear equations by graphing, substitution and elimination, tell when a system has one, no or infinitely many solutions, and use systems to solve real problems about money, mixtures and rates.

Use coordinates to measure and prove: find the midpoint and length of a line segment, write the equation of a circle centred at the origin, build perpendicular bisectors, find the shortest distance from a point to a line, and verify properties of triangles and quadrilaterals with algebra.

Multiply binomials and simplify second-degree expressions, then run the process backwards: factor out common factors, group, factor trinomials, and spot perfect squares and differences of squares.

Meet the parabola: recognize quadratic relations from data, tables and equations, read the vertex, axis, zeros and maximum or minimum, graph y = a(x − h)² + k by transforming y = x², use factored form and completing the square, and compare y = x² with y = 2ˣ to make sense of zero and negative exponents.

Solve quadratic equations by factoring, with the quadratic formula and by graphing, use the discriminant to tell whether there are two, one or no real roots, and answer real questions about heights, times, areas and revenue.

Use ratio and proportion to work with similar triangles (shadows, mirrors, scale models, surveying), then build the sine, cosine and tangent ratios from similar right triangles and use them with the Pythagorean theorem to find unknown sides and angles in real situations.