CDS
Elementary Mathematics
Matriculation-level arithmetic, algebra, trigonometry, geometry, mensuration and statistics.
100Questions
120Minutes
100Marks
Skills209
Arithmetic
61 skills
- Introduce a common factor for a ratioTechnique
- HCF LCM = product of the two numbersIdentity
- Prime factorisationProcedure
- Percentage change as a multiplierTechnique
- Take total work as the LCM of the timesTechnique
- Place-value expansion of a numeralIdentity
- Maximise one digit by minimising the othersTechnique
- Fermat's little theoremTheorem
- of a quantityFormula
- Remainders all short of their divisors by the same amountTechnique
- Least multiplier that makes a fraction a whole numberTechnique
- When a rational number's decimal expansion terminatesTheorem
- Over a fixed distance, time varies inversely with speedTheorem
- Counting overtakes on a circular trackTechnique
- Unitary method: find one unit, then scaleTechnique
- Gain percent is measured on the cost priceFormula
- Coprime means no shared prime factorDefinition
- Speed, distance and timeFormula
- Still-water speed and current from the two legsFormula
- Write an odd number as Technique
- Profit is shared in the ratio of capital timeFormula
- Unit digit of a power from its cycleTechnique
- Relative speed: add when opposed, subtract when alikeFormula
- What a train covers when it crosses somethingTechnique
- km/hour to m/secondFormula
- Enumerate a residue class within a boundTechnique
- A number is congruent to its digit sum modulo Theorem
- Reduce a large power by the cycle of its base modulo Technique
- Direct variation as a power: Formula
- The work-equivalence chain rule Formula
- A loan repaid in equal instalments under compound interestTechnique
- Comparing two fractionsTechnique
- Two-year difference between compound and simple interestFormula
- Closed form of a repeated-digit numberFormula
- Head starts and winning margins in a raceTechnique
- Last digit of a perfect squareTheorem
- Euclid's lemmaTheorem
- Average speed over two equal distancesFormula
- Consumption cut that absorbs a price riseFormula
- Convert a recurring decimal to a fractionProcedure
- Angle between the hands of a clockFormula
- Simple interest Formula
- Least perfect square not below a given boundTechnique
- Join two ratios on their shared termTechnique
- Unit digit of a product from its factors' unit digitsTechnique
- Exponent of a prime in (Legendre's formula)Formula
- Divisibility by from the alternating digit sumTheorem
- Compound interest amount Formula
- LCM and HCF of several numbers from prime powersProcedure
- LCM and HCF of fractionsFormula
- Dividend divisor quotient remainderTheorem
- The age difference between two people never changesTechnique
- is irrational unless is a perfect squareTheorem
- Highest power of a number dividing a productTechnique
- Prime, composite, and the status of Definition
- Primality by trial division up to Procedure
- One quantity as a percentage of anotherFormula
- A perfect square has every prime exponent evenTheorem
- Count ordered factorisations by handing out the primesTechnique
- HCF by Euclid's algorithmProcedure
- is irrationalTheorem
Algebra
60 skills
- Difference of two squaresIdentity
- Square of a sum and of a differenceIdentity
- Quadratic formulaFormula
- Sum and product of roots (Vieta)Formula
- Rationalise a denominator using the conjugateProcedure
- denotes the non-negative rootConvention
- Logarithm to exponential formDefinition
- Negative exponent is a reciprocalIdentity
- Locate roots by the sign of at test pointsTechnique
- Denest Procedure
- Complete each equation to the common sumTechnique
- Turn a worded condition into a linear equation in one unknownProcedure
- Set difference Definition
- Sum and difference of two cubesIdentity
- Telescoping a sum by writing each term as a differenceTechnique
- Power of a power, and the move to a common baseIdentity
- Identity
- A product is zero only when a factor is zeroTheorem
- A product with a fixed sum is largest when the factors are equalTheorem
- Factorise a quadratic by splitting the middle termProcedure
- Number of digits from a common logarithmFormula
- Range of a quadratic by completing the squareTechnique
- divides for odd Identity
- Sums of the first natural numbers, their squares and their cubesFormula
- Evaluate a nested fraction from the inside outProcedure
- and Identity
- Factor and remainder theoremTheorem
- and Identity
- When a pair of linear equations meets, is parallel, or coincidesTheorem
- HCF and LCM of polynomials from their complete factorisationsProcedure
- An evenly spaced run averages to its middle termTheorem
- Common root of two quadratics by eliminationTechnique
- Degree of a product of polynomialsTheorem
- Linearise a system by substituting reciprocalsTechnique
- A set is not its element, and is not Convention
- Inclusion-exclusion for two setsFormula
- Value of an infinite nested radicalTechnique
- A positive number plus its reciprocal is at least Theorem
- Pair four linear factors so one quadratic repeatsTechnique
- Clear the denominators of an equationProcedure
- , and the case Identity
- Add and subtract when the coefficients are reversedTechnique
- Cube of a sum and of a differenceIdentity
- Bar notation for a negative characteristicConvention
- A linear inequality in two variables is a half-planeTechnique
- Sum and product of the zeros of a cubicFormula
- Square of a sum of several termsIdentity
- Inclusion-exclusion for three setsFormula
- Exactly one, exactly two and at least two of three setsFormula
- Square both sides to clear a radicalTechnique
- Compare with over the natural numbersTechnique
- divides for every Identity
- Eliminate one variable from a linear pairProcedure
- Quotient on dividing by a linear factorProcedure
- Multiplying an inequality by a negative number reverses itTheorem
- Division algorithm for polynomialsTheorem
- Integer solutions of Theorem
- Count integer solutions by fixing one variableTechnique
- Combine algebraic fractions over one denominatorProcedure
- Equate coefficients of like powersTechnique
Trigonometry
12 skills
- Pythagorean trigonometric identitiesIdentity
- Exact trigonometric ratios of the standard anglesConvention
- Sine, cosine and tangent in a right triangleDefinition
- Angles of elevation and depressionTechnique
- Ratios of complementary anglesIdentity
- Reciprocal and quotient relations between the ratiosIdentity
- Converting between degrees and radiansFormula
- How the ratios move across the first quadrantTheorem
- Sine and cosine lie between and Theorem
- Sine rule, with the circumradiusTheorem
- Reading a compass bearing N E as a right triangleConvention
- Identity
Geometry
34 skills
- Pythagoras' theoremTheorem
- Similar triangles have proportional sidesTheorem
- Side of a regular polygon inscribed in a circleFormula
- The perpendicular from the centre bisects a chordTheorem
- The two tangents from an external pointTheorem
- Distance between the centres of touching circlesTheorem
- Pitot's theorem for a tangential quadrilateralTheorem
- Midpoint theoremTheorem
- The circumcentre is the point equidistant from the verticesDefinition
- Triangle inequalityTheorem
- Angle sum of a triangleTheorem
- Base angles of an isosceles triangleTheorem
- Congruence criteria for trianglesTheorem
- Internal angle bisector of a triangleDefinition
- Angles on a straight line and vertically opposite anglesTheorem
- Angles made by a transversal of two parallel linesTheorem
- Angles of a parallelogramTheorem
- The diagonals of a rectangle are equal and bisect each otherTheorem
- The angle at the centre is twice the angle at the circumferenceTheorem
- Length of a common tangent to two circlesFormula
- The orthocentre and the orthocentric systemTheorem
- British flag theoremTheorem
- Interior and exterior angle sums of a polygonFormula
- The centroid divides each median in the ratio Theorem
- The sum of the medians lies between of the perimeter and the perimeterTheorem
- The largest circle that fits inside a squareTheorem
- A circle is the locus of points at a fixed distance from a fixed pointDefinition
- Points equidistant from two intersecting lines form a pair of bisectorsTheorem
- Where two external bisectors meet: Theorem
- Opposite angles of a cyclic quadrilateral are supplementaryTheorem
- Parallel lines cut transversals proportionallyTheorem
- The greater side faces the greater angleTheorem
- Opposite sides of a parallelogram are equalTheorem
- A median bisects the area of a triangleTheorem
Mensuration
23 skills
- Area and circumference of a circleFormula
- Distance covered by a rolling wheelTechnique
- Area of a triangle from base and heightFormula
- Area of a triangle from two sides and the included angleFormula
- Perimeter and area of a squareFormula
- Volume and wall area of a cuboidFormula
- Volume of a right circular cylinderFormula
- Curved and total surface of a cylinderFormula
- Volume of a right circular coneFormula
- Slant height and curved surface of a coneFormula
- Volume and surface area of a sphereFormula
- Volume of a frustum of a coneFormula
- Recasting preserves volumeTechnique
- Volume and surface of a composite solidTechnique
- Perimeter and area of a rectangleFormula
- Area of a trapeziumFormula
- Area and altitude of an equilateral triangleFormula
- Heron's formulaFormula
- Area and arc length of a circular sectorFormula
- Cut a compound plane figure into standard piecesTechnique
- A cube has faces, edges and verticesDefinition
- Space diagonal of a cube and a cuboidFormula
- Area from perpendicular diagonalsFormula
Statistics
19 skills
- Mean of a frequency distributionFormula
- Median of a data setDefinition
- Qualitative, discrete and continuous dataDefinition
- A pie chart sector's angle is proportional to its shareFormula
- Inclusive and exclusive class intervalsDefinition
- Frequency densityFormula
- Empirical relation between mean, median and modeFormula
- Cumulative frequencyDefinition
- Mode: the most frequent value, and it need not be uniqueDefinition
- Geometric mean: the th root of the productDefinition
- Primary and secondary dataDefinition
- Nominal, ordinal, interval and ratio scalesDefinition
- Frequency polygon and the frequency curve it tends toDefinition
- Diagrammatic and graphic presentation of dataDefinition
- Locating the median graphically from an ogiveProcedure
- Mode of a grouped frequency distributionFormula
- Harmonic mean: over the sum of the reciprocalsDefinition
- Deviations about the mean add to zeroTheorem
- for two numbersIdentity