SPI Mathematics Notes

Favourable over total, the faces of a die, coins, the 36 outcomes of two dice, the complement, the 52-card deck, bags, odds and expected counts.

The mean of a list, median and mode, class marks, the assumed mean and step deviation methods, the median and mode formulas, the empirical relation and graphs.

Pictograph keys and part symbols, the axes and scale of a bar graph, and a pie chart's shares, central angles and amounts.

Cuboids and cubes, cylinders and cones, spheres and hemispheres, solids joined together, the frustum, melting into coins and the rise of water.

Number families, place value, digit counts, divisibility rules, primes, prime factorisation, HCF and LCM, fractions, recurring decimals and irrational numbers.

The six ratios of a right triangle, the values at 0°, 30°, 45°, 60° and 90°, the three identities, and complementary angles.

Common difference, the nth term, terms from the end, three terms in AP, the two sum formulas, standard sums, sums written in n, GP and the AM and GM.

One-variable equations, inequalities, solving a pair, the graph of a line, the three ratio cases, finding k, and word problems on ages, coins and fractions.

Tangent and radius, parallel tangents, equal tangents from a point, the angle between tangents, the incircle, chords, angles in a circle and cyclic quadrilaterals.

Lines, rays and opposite rays, complementary and supplementary angles, crossing and parallel lines, polygon angles, dividing a segment and building angles with a compass.

The 360 degree angle sum, angle bisectors, parallelogram angles and height, special quadrilaterals, the mid-point figure and a trapezium cut by a parallel line.

The angle sum, the exterior angle, Pythagoras, the congruence rules, similar triangles, basic proportionality, the angle bisector and the areas of similar triangles.

Axes and quadrants, the distance formula, the section formula, midpoints and centroids, the area of a triangle, slope, collinear points and the equation of a line.

Rectangles, squares, triangles and the hexagon, circles and wheels, wire bent into new shapes, sectors, the clock hand and segments.

The laws of indices, zero and negative powers, fractional powers, equations in powers, simplifying and comparing roots, rationalising, and endless roots.

Angles of elevation and depression, shadows, kite strings and ropes, broken trees, and towers seen at two angles.

Standard form, reducing an equation before naming its type, roots by factorisation and the formula, the discriminant, conditions on k, equal roots, and the sum and product of the roots.

Degree and value, zeroes on a graph, factorising by splitting and grouping, the division algorithm, the remainder and factor theorems, and the zeroes of quadratics and cubics against their coefficients.

Common factors and grouping, (x + a)(x + b), perfect squares, the difference of squares, squares and cubes from a sum and product, a + b + c = 0, and chains of brackets that cancel.