FUTURE INTELLIGENCE STUDENTS OLYMPIAD

Syllabus of Mathematics

(For Final and International Round)

Kindergarten Group (Category 1)
  • Addition with 1-digit numbers without carrying
  • Subtraction on 1-digit numbers without carrying
  • Balance Problem
  • Basic number pattern and figure pattern
  • Odd and Even numbers
  • Counting 2-D and 3-D shapes
  • Arranging the number in order
  • Creating 3 digit numbers
  • Comparing numbers
  • Matching Equation
  • Counting numbers of sides and interior angles
  • Basic Number sequence
Grade 1 – 2 (Category 2)
  • Basic number pattern and sequence
  • Age and Date problem
  • Addition 2 digits with carrying
  • Subtraction 2 digits with carrying
  • Odd and Even
  • Counting on 2D and 3Dshapes
  • Basic Arithmetic pattern
  • Simple Combination
  • Finding squares and triangles
  • Balance problem
  • Counting on numbers of sides and angles
  • Formation of 3-digit numbers
Grade 3 – 4 (Category 3)
  • Addition and subtraction 3 digits with carrying
  • Sum, different and multiples of number sentence
  • IQ age problem and date problem
  • Pigeonhole problem
  • Basic concept about area and perimeter
  • Guess on 3 digits numbers
  • Chicken and rabbit theorem
  • Counting on numbers of 2 D shapes
  • Counting on the number of Vertices, Faces and Edges of 3-D figure
  • Finding lines segments and intersection point
  • Basic routing problem
  • L.C.M and H.C.F
Grade 5 – 6 (Category 4)
  • Chicken and rabbit problem
  • Pigeon Hole problem
  • Speed and Time problem
  • Calculation with decimal and fraction
  • Area and perimeter of 2D shapes
  • Excess and shortage problems
  • Finding volume and surface area of 3D shapes
  • Sum of positive numbers series
  • Combinations and permutation
  • Basic probability
  • Method of difference equation
  • Guess on 4 digits numbers
Grade 7 – 8 (Category 5)
  • Speed, distance and time problems
  • Algebraic expression
  • Basic Inequalities
  • Pigeonhole theorem (Hard)
  • Routing problem (Hard)
  • Linear equation
  • Volume and surface area of 3D shapes
  • Factor theorem
  • Distributions (Hard)
  • Combination and permutations
  • Counting on possible solution on Indefinite equations
  • Pythagorean Theorem
Grade 9 – 10 (Category 6)
  • Four arithmetical operations on rational numbers and irrational numbers; HCF, LCM, square roots, cube roots, primes, prime factorization and relatively prime
  • Length, mass, volume, time, money; percentage (including simple and compound interest formulae), ratio, rate, distance, speed, map scales, direct and inverse proportions
  • Expansion and factorization of algebraic expressions; three perfect squares identities; linear and quadratic expressions, equations (including quadratic formula) and inequalities; solving word problems using algebra
  • Graphs of linear (including distance-time and speed-time graphs, and gradient of straight line), quadratic and power functions (y = a xn for n = –2, –1, 0, 1, 2, 3)
  • Standard form, indices (including zero, negative and fractional indices) and surds (including rationalizing denominator)
  • Remainder and factor theorems; solving of cubic equations by factorization; two perfect cubes identities (i.e. sum and difference of perfect cubes); partial fractions; binomial theorem
  • Properties of rectangle, square, triangle, parallelogram, rhombus, trapezium, kite and regular polygons; perpendicular bisector and angle bisector; exterior angle of triangle, sum of interior angles of polygon and sum of exterior angles of polygon; angles associated with parallel lines (corresponding angles, alternate angles and interior angles)
  • Congruence tests for triangles, Area and perimeter of triangle, rectangle, square, parallelogram and trapezium;
  • Probability of single events
  • Circumference of circle; volume and surface area of prism, cylinder, pyramid, cone and sphere; arc length, sector area and area of segment of circle (where angles are in degrees and in radians)
  • Pythagoras’ theorem and its converse; and generalized Pythagoras’ theorem
  • Trigonometric ratios of acute and obtuse angles; sine rule; cosine rule; 3D problems
  • Picture graphs (or pictograms), bar graphs, tables of values, line graphs, pie charts, histograms for ungroupped and grouped data; average (mean, median and mode)
  • Simple Venn diagrams
  • Divisibility tests and combined divisibility tests
  • Number sequences and patterns (including formula to find 1 + 2 + 3 + … + n, i.e. (𝑛+1)2, and formula for general term of arithmetic progression, i.e. Tn = a + (n – 1) d, although students can use other methods)
  • Counting (e.g. no. of terminal zeros)
  • Logarithms
  • Derivative and Integrals
  • Logic problems and Cryptarithms
Grade 11 – 12 (Category 7)
  • Four arithmetical operations on rational numbers and irrational numbers; HCF, LCM, square roots, cube roots, primes, prime factorization and relatively prime
  • Length, mass, volume, time, money; percentage (including simple and compound interest formulae), ratio, rate, distance, speed, map scales, direct and inverse proportions
  • Expansion and factorization of algebraic expressions; three perfect squares identities; linear and quadratic expressions, equations (including quadratic formula) and inequalities; solving word problems using algebra; modulus functions (excluding graphs)
  • Graphs of linear (including distance-time and speed-time graphs), quadratic and power functions (y = a xn for n = –2, –1, 0, 1, 2, 3)
  • Coordinate geometry formulae (gradient, length of line segment, midpoint, perpendicular lines, and shoelace formula)
  • Standard form, indices (including zero, negative and fractional indices) and surds (including rationalizing denominator); logarithms (including product law, quotient law, power law and change of base formula)
  • Remainder and factor theorems; solving of cubic equations by factorization; two perfect cubes identities (i.e. sum and difference of perfect cubes); partial fractions; binomial theorem
  • Properties of rectangle, square, triangle, parallelogram, rhombus, trapezium, kite and regular polygons; perpendicular bisector and angle bisector
  • Exterior angle of triangle, sum of interior angles of polygon and sum of exterior angles of polygon; angles associated with parallel lines (corresponding angles, alternate angles and interior angles)
  • Symmetric and angle properties of circles
  • Congruence and similarity tests for triangles
  • Area and perimeter of triangle, rectangle, square, parallelogram and trapezium; area and
  • Circumference of circle; volume and surface area of prism, cylinder, pyramid, cone and sphere; arc length, sector area and area of segment of circle (where angles are in degrees and in radians)
  • Pythagoras’ theorem and its converse; and generalized Pythagoras’ theorem
  • Trigonometric ratios of angles in all quadrants; sine rule; cosine rule; 3D problems; angle of elevation, angle of depression and bearings; graphs of sine, cosine and tangent functions; cosecant, secant and cotangent; trigonometric identities, formulae and equations
  • Picture graphs (or pictograms), bar graphs, tables of values, line graphs, pie charts, histograms for ungroupped and grouped data; average (mean, median and mode)
  • Probability of single and combined events (including additive law for mutually exclusive events, multiplicative law for independent events, possibility diagrams, tree diagrams and probability trees for independent and dependent events; but excluding non-mutually exclusive events and
  • Bayes’ theorem (for conditional probabilities)
  • Divisibility tests and combined divisibility tests
  • Number sequences and patterns (including formula to find 1 + 2 + 3 + … + n, i.e. (𝑛+1)2, and formula for general term of arithmetic progression, i.e. Tn = a + (n – 1) d, although students can use other methods)
  • Counting (e.g. no. of terminal zeros)
  • Simple Venn diagrams
  • Logarithms, Derivative and Integrals
  • Logic problems and Cryptarithms
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