CAT (entrance exam)Indian Institutes of Management
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SubjectQuantitative Ability

## Topics with syllabus and resources

100.00 Numbers
• Classification of Real Numbers - 1. Rational, 2. Iirational, 3. Integers, 4. Prime, 5. Prime factorization theorem, 6. Composite, 7. Relative Primes, 8. Perfect numbers.
• BODMAS,
• Rules for Divisibility,
• Recurring decimals,
• Square root.
• Factors of a number, Product of two factors, power cycle, sum of all factors, product of all factors, largest power of a prime number in a factorial.
• Basic algebra formulae.
200.00 LCM and HCF
• HCF by factorization method and division method.
• LCM models, HCF models,successive division.
• HCF and LCM of fractions
300.00 Complex Numbers
• Last digit of a number, Last 2 digits of a number.
• Remainder theorem.
• Binomial theorem
• Fermat's Little Theorem
• Wilson's Theorem.
400.00 Number Systems
• Decimal to binary and vice versa,
• decimal to octal and vice versa,
• decimal to hexa-decimal and vice versa,
• decimal to duodenay and vice versa,
• binary to octal,
• binary to hexa decimal,
• binary arithmetic.
500.00 Equations
• 1,2 and 3 unknown equations.
• Finding roots of quadratic equations by factorisation and formula.
• Nature,sum and product of roots.
• Maximum and minimum value of a quadratic equation.
• Polynomial division.
• Descarte's rule.
600.00 Percentages, Profit and Loss
• Percentage as a fraction and decimal as percentage.
• Percentage increase and decrease.
• Constant product rule
• Successive percentage changes
• Percentage points.
• Profit and loss, discount, successive discounts.
• Partnership
• Stocks and shares
700.00 Interest
• Simple interest.
• Compound interest, compounding more than once a year.
• Present value under simple interest and compound interest.
• Instalments.
800.00 Time Distance and speed
• Average speed, relative speed.
• Boats and streams.
• Races and circular tracks.
• Clocks.
• Trains.
900.00 Time and Work
• Unitary method and concept of mandays.
• Pipes and cisterns.
1000.00 Averages Mixtures and Alligations
• Averages and weighted average.
• Mixtures.
• Rule of alligations.
1100.00 Ratio and Proportion
• Ratio, proportion, direct, inverse and joint variation, continued ratio, compounded ratio.
• Invertendo, alternendo, componendo, dividendo,
1200.00 logarithms
• Formulae and application
1300.00 Progression and Series
• Arithmetic progression
• Geometric Progression
• Infinite geometric progression
• Harmonic progression.
• Sequence and series
1400.00 Indices and Surds
• Laws of indices
• Rationalization of surds.
• Square roots of surds.
• Comparison of surds.
1500.00 Inequalities
• Symbols and notationsm, interval notation
• Absolute value, properties of modulus.
1600.00 Permutation and Combination
• Permutations and combinations.
• Repetitions, circular table, circular wire, ranks, selection, arrangements.
1700.00 Probability
• Equally likely outcomes,mutually exclusive events,independent events,collectively exhaustive events.
• Conditional probability.
• Multiplication theorem.
• Baye's Theorem.
• Expected value.
1800.00 Functions
• Roster form, Set builder form.
• Types of sets-Null set, Finite infinite sets, cardinaity of a set, singleton sets, equal sets, Subsets, supersets, power set, universal set.
• Set operations- union intersection, division and difference of sets, Complement of a set, Symmetric difference of two sets, Cartesian product of sets
• Relations- domain and range of relations, Inverse of a relation.
• Functions- One-one function, many-one function, Onto function, Into function, Bijection, Constant function, Identity Function, Inverse Function, Composition of functions, real Functions, Explicit implicit functions, even and odd functions, periodic functions, Increasing decreasing functions, Polynomial functions, modulus functions, Signum functions, Trigonometric functions, Functional equations.
• Graphs
1900.00 Geometry
• Angles and lines.
• Circumcentre, Incentre and Excentre, orthocentre, centroid
• Triangles, Similarity of triangles, Congruency of triangles.
• Quadrilaterals, Trapezium, Parallelogram law, Rhombus, Rectangle, Square, Polygon, cirlces,ellipse, kites, hemispheres.
• Arcs and sectors.
• Areas and perimeters of plane figures.
2000.00 Mensuration
• Volumes and surface area of solids- prism, cubes, cuboids,cylinder, pyramid, cones, cone frustum,pyramid, torus, sphere
2100.00 Trigonometry
• Law of sines and conversions.
• Signs of trigonometric ratios, maximum and minimum value of trigonometric ratios.
• trigonometric identities.
• Addition and subtraction formulae, double angle formulae, half angle formulae, triple angle formulae, changing product into sum or difference formulae, changing sum or difference into product formulae.
• Heights and distances.
2200.00 Co-ordinate Geometry
• x and y co-ordinate and quadrants.
• Ordered pairs, distance between two points formula, Area of triangle formula, centroid formula.
• Internal division,external division.
• Collinearity of points.
• Intercept formula,point-slope formula,two point slope formula, slope intercept formula.
• Angle between two lines.
• Perpendicular distance from a point to line formula, distance between two parallel lines formula.
• Locus.
• Change of axes, translation of axes, rotation of axes.

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