Syllabus of Mathematics Olympiads Assam Academy of Mathematics

Syllabus of Mathematics Olympiads
Assam Academy of Mathematics
Category - I (Classes V - VI)

• Number system. Concepts and problems related to place value and face
value in decimal number system. Use of the symbols =, < and >. Es-
timation of numbers, identifying smaller, larger etc. Natural numbers,
whole numbers, integers. Properties of numbers (commutative, asso-
ciative, distributive, additive identity, multiplicative identity, additive
inverse, multiplicative inverse). Representation of integers on number
line.
• Statement problems involving the basic rules of addition, subtraction,

multiplication and division. Conversions of units of length & mass
(from the larger to the smaller units and vice-versa).
• Simplification of brackets, multiples and factors, divisibility rules and

related problems. Even numbers, odd and prime numbers, compos-
ite numbers, co-prime numbers. Factorisation of numbers. HCF and
LCM, prime factorization and division methods for HCF and LCM, the
property LCM × HCF = product of two numbers.
• Fractions, representation of fractions (pictorially and on number line),

fraction as a division, proper, improper & mixed fractions, equivalent
fractions, comparison of fractions, addition and subtraction of fractions.
Idea of a decimal fraction, place value in the context of decimal frac-
tion, inter conversion of fractions and decimal fractions, word problems
involving arithmetic operations on decimals. Ratio and Proportion,
Unitary method, statement problems.
• Line, line segment, ray. Open and closed figures. Interior and exte-
rior of closed figures. Angles - acute, obtuse, right, straight, reflex,
complete and zero angle. Triangles — vertices, sides, angles, altitude
1
and median. Classification of triangles (on the basis of sides and of
angles). Quadrilaterals — sides, vertices, angles, diagonals, adjacent
sides and opposite sides. Trapezium, parallelogram, rectangle, square,
rhombus. Circles — centre, radius, diameter, arc, sector, chord, seg-
ment, semicircle, circumference. Intersecting and perpendicular lines,
Parallel lines
• Knowledge of 3-D shapes: Cubes, Cuboids, cylinder, sphere, cone,

prism, pyramid and tetrahedrons. Symmetry of geometrical shapes,
letters, words, numbers. Constructions (using straight edge, protrac-
tor, compasses) - line segment, circle, perpendicular bisector, angles,
angle bisection, angle equal to a given angle (using compass), drawing
a line perpendicular to a given line from a point on the line and from
a point outside the line.
• Areas and perimeters of standard geometrical figures - triangle, rect-

angle, rhombus, square, parallelogram, circle, trapezium. Shapes of
different kinds with the same perimeter/area. Patterns of geometrical
shapes and designs.
• Data handling, collection and organisation of data in tally bars and a

table, making bar graphs for given data interpreting bar graphs.
Category - II (Classes VII - VIII)

• Properties of integers (including identities for addition & multiplica-
tion, commutative, associative, distributive). Word problems including
integers. Rational numbers - representation on number line, properties
of rational numbers , operations on rational numbers, finding rational
numbers between two rational numbers statement problems involving
rational numbers. Number puzzles and games.
• Laws of exponents with integral powers. Square and Square roots.

Square roots using factor method and division method for numbers.
Cubes and cubes roots. Estimating square roots and cube roots.
• Algebraic expressions involving one or two variables. Constants, coef-

ficients, powers, like and unlike terms. Polynomials degree of polyno-
mials, addition, subtraction of polynomials. Algebraic identities, fac-
torisation of polynomials, division of polynomials.
2
• Problems on percentages, profit & loss, overhead expenses, discount,
ratio and proportion, unitary method, simple interest, compound in-
terest, direct and inverse variation, time & work problems.
• Pairs of angles (linear pair, supplementary, complementary, adjacent,

vertically opposite). Properties of parallel lines with transversal (alter-
nate, corresponding, interior, exterior angles). Angle sum property of
triangle, exterior angle property, triangle inequality of sides, Pythago-
ras Theorem. Angle sum property of quadrilateral. Properties of rect-
angles, squares, rhombus, parallelograms.
• Reflection and rotational symmetry. Counting vertices, edges & faces &
verifying Euler’s relation for 3-D figures with flat faces (cubes, cuboids,
tetrahedrons, prisms and pyramids). Congruence of triangles, SSS,
SAS, AAS, ASA and RHS criteria. Construction of triangles, parallel
lines, quadrilaterals using ruler and compass.
• Areas of a square, rectangle, triangle, parallelogram and circle, trapez-

ium, area between two rectangles and two concentric circles, volume of
a cube, cuboid and cylinder, Surface area of a cube, cuboid, cylinder.
Related problems.
• Basic ideas of set theory - types of sets, subsets, null set, finite and
infinite sets, union and intersection of sets, complement of a set. Prin-
ciples of counting - addition rule, subtraction rule, multiplication rule
and division rule. Permutation and combination of objects, related
problems.
• Mean, median and mode of ungrouped and grouped data. Constructing

and interpreting bar-graphs. Simple Pie charts with reasonable data
numbers.
Category - III (Classes IX - X)

• Number systems, rational numbers, irrational numbers, real numbers.
Number theory - well ordering principle, division algorithm, divisibility
theory, GCD and LCM, Euclidean algorithm, Diophantine Equation,
prime numbers and their properties, fundamental theorem of arith-
metic, theory of congruences, linear congruences, Fermat’s little theo-
rem, Wilson’s theorem. Number theoretic functions τ, σ and Euler’s φ
function, Euler’s theorem. Greatest integer function.
3
• Sets, relations and functions. One-one functions, onto functions, bi-
jections, inverse of a bijection. Counting principles - addition rule,
subtraction rule, multiplication rule, division rule. Permutation and
combination of distinct objects. Permutations and combinations with
repetitions. Inclusion-Exclusion principle. Pigeonhole principle.
• Polynomials in one variable, coefficients, terms, degree of a polyno-

mial. Constant, linear, quadratic, cubic polynomials; monomials, bi-
nomials, trinomials etc. Factors and multiples. Zeros/roots of a poly-
nomial/equation. Relation between roots and coefficients. Remainder
Theorem, Factor Theorem and related problems. Algebraic identities
involving several variables. Linear equations in two variables, the cases
of unique solution, no solution and infinitely many solutions. Quadratic
equations. Statement problems.
• Arithmetic, geometric and harmonic progressions. Inequalities involv-

ing arithmetic mean, geometric mean and harmonic mean. Cauchy
Schwartz inequality.
• Euclidean Geometry, lines and angles, triangles, quadrilaterals, circles

and their properties, congruence and similarity of triangles. Mensura-
tion - area, perimeter, surface area and volumes of standard geometrical
objects.
Recommended books
• NCERT / SEBA / AHSEC recommended textbooks.
• Elementary Number Theory; David M. Burton; McGraw Hill Educa-

tion.
• Introductory combinatorics; Richard A. Brualdi; Pearson Education

Inc.
• Mathematical Circles (Russian Experience); Dmitri Fomin, Sergey Genkin,

Ilia Itenberg; Universities Press.
• A Moscow Math Circle; Sergey Dorichenko; Universities Press.
• Functional Equations; B.J.Venkatachala; Prism Books Pvt. Ltd.
• International Mathemtical Olympiad (Volumes I to III); Istvan Reiman;

Anthem Press.
4
• Problem Solving Strategies; Arthur Angel; Springer.
• Challenge and thrill of pre-college mathematics; V.K.Krishnamurthy

et.al.; New Age International Publishers.

Syllabus of Mathematics Olympiads Assam Academy of Mathematics

Uploaded by

Copyright:

Available Formats

Syllabus of Mathematics Olympiads Assam Academy of Mathematics

Uploaded by

Document Information

Original Description:

Original Title

Copyright

Available Formats

Share this document

Share or Embed Document

Sharing Options

Did you find this document useful?

Is this content inappropriate?

Copyright:

Available Formats

Syllabus of Mathematics Olympiads Assam Academy of Mathematics

Uploaded by

Copyright:

Available Formats

Syllabus of Mathematics Olympiads

Assam Academy of Mathematics

Category - I (Classes V - VI)

• Statement problems involving the basic rules of addition, subtraction,

• Simplification of brackets, multiples and factors, divisibility rules and

• Fractions, representation of fractions (pictorially and on number line),

• Knowledge of 3-D shapes: Cubes, Cuboids, cylinder, sphere, cone,

• Areas and perimeters of standard geometrical figures - triangle, rect-

• Data handling, collection and organisation of data in tally bars and a

Category - II (Classes VII - VIII)

• Laws of exponents with integral powers. Square and Square roots.

• Algebraic expressions involving one or two variables. Constants, coef-

• Pairs of angles (linear pair, supplementary, complementary, adjacent,

• Areas of a square, rectangle, triangle, parallelogram and circle, trapez-

• Mean, median and mode of ungrouped and grouped data. Constructing

Category - III (Classes IX - X)

• Polynomials in one variable, coefficients, terms, degree of a polyno-

• Arithmetic, geometric and harmonic progressions. Inequalities involv-

• Euclidean Geometry, lines and angles, triangles, quadrilaterals, circles

• Elementary Number Theory; David M. Burton; McGraw Hill Educa-

• Introductory combinatorics; Richard A. Brualdi; Pearson Education

• Mathematical Circles (Russian Experience); Dmitri Fomin, Sergey Genkin,

• A Moscow Math Circle; Sergey Dorichenko; Universities Press.

• Functional Equations; B.J.Venkatachala; Prism Books Pvt. Ltd.

• International Mathemtical Olympiad (Volumes I to III); Istvan Reiman;

• Challenge and thrill of pre-college mathematics; V.K.Krishnamurthy

You might also like