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Learn to calculate the gravitational force between two masses, use the value of G and predict how the force changes, separate mass from weight properly, and explain free fall, weightlessness and how g varies.
Read articleLearn to calculate momentum and its change, derive F = ma from the rate of change of momentum, convert between the newton and the kilogram-force, and find the action-reaction pair in any situation.
Read articleLearn what a force can do to a body and how to sort forces into contact and non-contact kinds, state the first law and use it on everyday observations, tell the three kinds of inertia apart, and spot balanced and unbalanced forces.
Read articleLearn to pick the right equation of motion for a numerical, find the distance covered in the nth second, solve free-fall and thrown-upward problems with the correct signs, and see why every body falls at the same rate.
Read articleLearn to read speed from the slope of a distance-time graph, find acceleration and distance from a velocity-time graph, sketch both graphs for four kinds of motion, and derive the equations of motion from a graph.
Read articleLearn to sort quantities into scalars and vectors and draw a vector properly, tell distance from displacement, calculate average speed and average velocity, and handle acceleration and retardation with the right signs.
Read articleLearn the terms that describe a simple pendulum and their units, calculate time period and frequency from a count of oscillations, apply the formula relating period to length and gravity, and see what the period does and does not depend on.
Read articleLearn to calculate the least count of a vernier calliper and a screw gauge, take a full reading from the main and auxiliary scales, identify and correct positive and negative zero error, and choose the right instrument.
Read articleLearn which physical quantities are fundamental and which are derived, the rules for writing SI symbols correctly, how to convert between SI, CGS and FPS and use prefixes, and how to derive the unit of any derived quantity.
Read articleLearn to test whether a sequence is a geometric progression and state its common ratio, find any term of a GP, model doubling growth and decay, and write the sequence for a self-similar pattern.
Read articleLearn to test whether a sequence is an arithmetic progression, find its nth term and locate a given value, derive the sum of the first n natural numbers by pairing, and apply the rule to real growing patterns.
Read articleLearn to spot the pattern in a sequence and continue it, write the explicit rule for the nth term, write the recursive rule including the Fibonacci sequence, and convert between the two descriptions.
Read articleLearn to list the sample space for a random experiment, write an event as a set of outcomes and find its probability, draw a tree diagram for a two-stage experiment, and handle at-least-one questions.
Read articleLearn to place events on a scale from 0 to 1, calculate experimental probability from a table of trials, calculate theoretical probability by counting favourable outcomes, and see why the two values converge.
Read articleLearn to find the area of a circle and work backwards to its radius, calculate sector and segment areas for a given angle, apply Brahmagupta's formula to a cyclic quadrilateral, and solve composite area problems.
Read articleLearn to find areas and missing sides of rectangles and squares, derive the parallelogram formula and apply it to rhombuses and trapeziums, use Heron's formula from three side lengths, and build a square equal in area to a rectangle.
Read articleLearn to find the perimeter of polygons and composite shapes, the circumference of a circle both ways, the length of an arc and the perimeter of a sector, and to solve running-track and fencing problems.
Read articleLearn to use the angle-at-the-centre theorem, prove that the angle in a semicircle is a right angle and that angles in the same segment are equal, test whether four points are concyclic, and find angles in a cyclic quadrilateral.
Read articleLearn why equal chords subtend equal angles at the centre, how the perpendicular from the centre bisects a chord, how to find a chord length from the radius and distance by Pythagoras, and why equal chords are equidistant.
Read articleLearn to name every part of a circle, describe its lines of symmetry and rotational symmetry, construct the one circle through three non-collinear points, and count how many circles pass through one point or two.
Read articleLearn to derive the identity for the cube of a sum, expand cubic brackets and cube numbers near 100, simplify a rational expression by factorising, and state the values that make it undefined.
Read articleLearn the identity for the product of two binomials and the square of three terms, build a factorisation with algebra tiles, split the middle term of a quadratic, and multiply 52 by 53 in your head.
Read articleLearn the three basic identities for squares and the difference of squares, see why the square of a sum works as an area picture, factorise by recognising the matching identity, and square numbers near 100 mentally.
Read articleLearn to convert a fraction into its decimal form, predict from the denominator whether it terminates, find the repeating block of one seventh and one thirteenth, and turn any repeating decimal back into a fraction.
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