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Compare metals and non-metals on lustre, malleability, ductility, conductivity, sonority and melting point, classify an unknown element from its stated properties, and name the six exceptions that break the rules.
Read articleRead the pH scale and rank solutions by acidity, see why pH matters for teeth, digestion, soil and stings, work out whether a salt is acidic or basic from its parents, and learn the four important sodium and calcium compounds.
Read articlePredict indicator colours for acids and bases, write the reactions of acids with metals, carbonates and hydrogencarbonates, name the salt from a neutralisation, and explain why an acid conducts only when dissolved in water.
Read articleSort reactions into combination, decomposition, displacement and double displacement, tell the three kinds of decomposition apart by their energy source, label what is oxidised and reduced, and explain corrosion and rancidity.
Read articleRecognise from observation that a chemical reaction has taken place, turn a word equation into a balanced one with physical states, and balance a skeletal equation by hit and trial while checking that mass is conserved.
Read articleDerive the distance formula from the Pythagoras theorem, measure from the origin and the axes, prove points collinear or a triangle isosceles or right-angled, and find a missing coordinate or an equidistant point.
Read articleDraw two simultaneous equations on one pair of axes and read the solution from their crossing point, find where each line meets the axes, compute the area of the triangle they enclose, and check the answer algebraically.
Read articleTell dependent from independent variables, plot points and name their quadrants, identify the figure formed by given vertices, and draw the graph of a linear equation from a table of values.
Read articleFind every unknown side and angle of a right-angled triangle from two given parts, use standard angles to compute a length, solve pole and shadow problems, and pick the right triangle out of a larger figure.
Read articleUse the complementary-angle relations to swap sine for cosine and tangent for cotangent, collapse expressions like sin 35 over cos 55 to a single number, and solve equations where a sine equals a cosine.
Read articleDerive the ratios of 0, 30, 45, 60 and 90 degrees from a square and an equilateral triangle, evaluate numerical expressions in them, verify given relations, and solve for a standard angle.
Read articleWrite the six trigonometric ratios from a right-angled triangle, rebuild all six when only one is given, prove the basic identities from the Pythagoras theorem, and evaluate expressions from a single ratio.
Read articleFind the volume and surface areas of cubes and cuboids, handle open boxes and painting costs, work out the material in a hollow box, and use cross-section times length for beams, pipes and canals.
Read articleFind a circle's area and circumference either way round, compute the area of a ring, solve path-and-cost problems for rectangular and circular fields, and count the revolutions of a wheel.
Read articleFind a triangle's area from its base and height or from its three sides, handle equilateral, isosceles and right-angled cases, compute areas of quadrilaterals, and split a composite figure into parts.
Read articleFind the mean of raw data and of a frequency distribution, locate the median for an odd or even number of observations, and recover a missing value or correct a mean after a misread entry.
Read articleTell raw, arrayed and grouped data apart, build a frequency table with tally marks, convert discontinuous class intervals into continuous ones, and draw a frequency polygon that closes properly.
Read articleShow that exactly one circle passes through three non-collinear points and construct it, link equal central angles to equal arcs and equal chords, and solve riders on arcs, chords and angles.
Read articleProve that a line from the centre bisecting a chord is perpendicular to it, find chord lengths and distances with the Pythagoras theorem, show equal chords are equidistant, and handle two parallel chords.
Read articleProve that parallelograms on the same base between the same parallels are equal in area, that a triangle is half of one, and use equal areas to prove riders and to deduce equal altitudes.
Read articleConstruct a quadrilateral from four sides and a diagonal, build a parallelogram from sides, diagonals and angles, draw a rhombus from its diagonals, and step off a regular hexagon with the compass alone.
Read articleProve that the diagonals of a rhombus meet at right angles and those of a rectangle are equal, name a quadrilateral from its stated properties, and solve trapezium riders with the mid-point theorem.
Read articleProve that opposite angles of a parallelogram are equal and that its diagonals bisect each other, use the equal-and-parallel test to prove a figure is a parallelogram, and find unknown sides, angles and diagonal segments.
Read articleProve the Pythagoras theorem by comparing areas, find any missing side of a right-angled triangle, use the converse to test for a right angle, and solve ladder, pole, rhombus and diagonal problems.
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