CDS Mathematics Notes

Number System is the single biggest chapter in CDS Elementary Mathematics: 223 past-year questions across all twenty-one sittings from 2016 (II) to 2026 (II), which is roughly eleven of the hundred questions on every paper.

Standard values, right-triangle ratios, complementary angles, the Pythagorean identities, the sec ± tan reciprocal pair, squaring a given sum, equations, maxima and minima, and eliminating θ.

Triangle and quadrilateral areas, re-bent wires and equal perimeters, wheels and rings, sectors and segments, inscribed figures, touching circles and shaded regions.

Cuboids and their diagonals, cylinders, cones, spheres, frustums and joined solids, melting and recasting, water and flow, scaling, and solids inside solids.

Angles, triangle inequalities, congruence and similarity, parallels and the bisector theorem, area ratios, Pythagoras, the altitude to the hypotenuse, medians, the four centres, and the sine and cosine rules.

Squares and cubes of a binomial, x ± 1/x, sums of three variables, the cube identity, sums of squares and least values, conditional identities, rational expressions and cyclic sums.

Forming equations, symmetric functions of the roots, roots in a relation, the discriminant, perfect squares and signs of roots, common roots, maxima and minima, reducible equations and word problems.

Recurring decimals, laws of indices, exponential equations, square roots of surds, rationalising and telescoping sums, equations with surds, cube-root expressions, continued fractions and nested radicals.

Types of data and scales, classes and histograms, cumulative tables, properties of the mean, the median of a list, grouped mean, median and mode, and choosing an average.

Degree and zeros, the remainder theorem, the factor theorem, factorising cubics and quartics, and the HCF and LCM of polynomials.

Chaining and dividing by ratios, incomes and ages, equal-ratio algebra, direct and inverse variation, partnership, and mixtures with alligation.

Average speed, speed–time ratios, speed-change equations, chasing and meeting, trains crossing, boats and streams, races, and clock angles.

Chords and the centre, angles in a circle, cyclic quadrilaterals, the circumcircle and locus, tangents, power of a point, common tangents and touching circles.

Diagonals and triangle bounds, parallelograms and midpoint figures, rhombus and kite, trapeziums, and cyclic quadrilaterals.

Percentages and changes from tables, averages, pie-chart angles and shares, comparing charts with different totals, bar graphs and caselets.

Percentages of a base, more-than and less-than, successive changes, price against consumption, profit and loss, false weights and discounts.

Sum equals count times mean, correcting a misread value, combined and weighted averages, the ratio of group sizes, and averages of consecutive numbers.

Work rates, joining and leaving, taking turns, man-days and man-hours, men and women gangs, and pipes and cisterns.

One line of sight, two observation points, complementary angles, elevation and depression together, and towers on squares, rectangles and hexagons.

Elimination and the 1/x substitution, when a system has one, none or infinitely many solutions, word problems, ages, and whole-number solutions.

Simple interest, compound interest with half-yearly and quarterly periods, doubling times, the CI minus SI gap, and equal instalments.

Product, power and change-of-base laws, bar notation, counting digits and leading zeros, and logarithmic and exponential equations.

Set difference, union and intersection, null and singleton sets, finite and infinite sets, and Venn-diagram counting with two and three groups.

Linear pairs and vertical angles, complements, parallels and transversals, the intercept ratio, and interior and exterior angles of polygons.

AP and GP sums, sums of squares and cubes, telescoping series, and the arithmetic, geometric and harmonic means of two numbers.

Solving linear and quadratic inequalities, the sign of a product, odd and even powers, data-sufficiency reasoning, and x + 1/x ≥ 2.