In Year 3 of high school the programme changes trade: you move from calculation to functions, and every exercise begins with the same question: for which does this make sense? The answer is always a radical to read or a quadratic inequality to solve. If one of the two costs you effort, it costs you effort in every single exercise of the year, not just in the revision chapter. In physics the jump is even sharper: the subject goes up to three hours and becomes quantitative, starting with motion in the plane, which is kinematics on two axes at once. Nothing new, if kinematics on a single axis is already automatic.
The programme, block by block
Radicals. They are the classic pre-Christmas crash of Year 2, and in Year 3 they come straight back: as soon as there is a root inside a function the domain is an inequality, and as soon as there is a root in a denominator it has to be rationalised.
The absolute value is not a whim: , not . And the root does not distribute over a sum: , not .
Quadratic inequalities. They decide the domain of every irrational or rational function of the year. You don’t learn them by heart: you draw the parabola and read where it lies above or below the -axis.
Outside the roots the trinomial has the same sign as (“same sign outside, opposite sign inside”); and doesn’t mean impossible, it almost always means all the real numbers.
Kinematics of straight-line motion. In Year 3 physics opens with motion in the plane (parabolic, circular, harmonic), and all three are solved by splitting onto the two axes and applying the straight-line motion formulas you already know.
The last one is the formula to use when the problem doesn’t mention time: it saves you half the exercise.
The mistakes that cost the most
” and ” doesn’t exist: it is an “or”. The parabola lies above the axis in two separate zones, and the answer is the union of the two, not the intersection, since no number is both less than 2 and greater than 3.
holds only for uniform motion. With constant acceleration you need the full equation of motion: for a car braking from in the real distance is , not , because the average speed is . It is the most common mistake in problems with braking or starting from rest.
To revise radicals and quadratic inequalities you will find practice tests on radicals and on quadratic inequalities, as well as the one on kinematics for the chapter that motion in the plane rests on; on the parabola as the first new topic of the year there is the guide to tangents and pencils of parabolas. After quadratic inequalities come rational ones (rational inequalities in Year 3) and those with absolute values and radicals (absolute value and irrational equations in Year 3); the circle, which follows the parabola, is in the circle in the Cartesian plane.
The Italian version of this post comes with a companion document (in Italian) that covers all nine topics in full: every formula, one worked example per topic, the typical mistake where needed and thirty exercises with the complete step-by-step solution.
If you would rather have a guided revision than go it alone, tutoring in maths and physics starts exactly from here: write to me and we will see where to concentrate the first lessons.
