EXAM TOPICS

Academic competition preparation for students (ages 6–17) seeking a clear outline of subject areas and concepts covered in the International Math Challenge (IMC).

Category Kids (Grades 1 & 2)

4 TOPIC AREAS
  • NumbersMatching, Ordering, Comparison.
  • MeasurementMoney, Time, Length, Weight.
  • GeometryPaper cutting and folding, Figure relations, Position and transformation, Comparison.
  • Non-Routine Problem SolvingMental math, brain teasers, shapes, patterns, and pictograms.

Category 1 (Grades 3 & 4)

6 TOPIC AREAS
  • NumbersOperations and properties, Counting and sequences, Fractions, Decimals, Percentage, Ratio and Proportion, Place value, Ordering and Rounding, Integers and Power, Money.
  • AlgebraExpressions, Equations, Inequalities.
  • Geometry and MeasurementPosition and Transformation, Geometrical reasoning, Shapes and Measurements, Time.
  • Data Collection and AnalysisProbability, Statistics, Average, Handling data.
  • Word ProblemsVerbal equations, Age, Number, Money, Distance, Time, Speed problems.
  • Non-Routine Problem SolvingNumber patterns, Divisibility tests, Spatial visualization, Logic problems, Simple cryptarithms, Mental math, Brain teasers.

Category 2 (Grades 5 & 6)

6 TOPIC AREAS
  • NumbersOperations and properties, BEDMAS rule, Counting and sequences, Fractions, Decimals, Percentages, Ratio and Proportion, Place value, Ordering and Rounding, Integers and Power, Money.
  • AlgebraExpressions, Factorizations, Equations, Inequalities, Exponents, Radicals, Polynomials.
  • Statistics and ProbabilityCombinatorics, Permutation, Presenting and interpreting data, Mean, Median, Range, Mode, Handling data.
  • Word ProblemsVerbal equations, Age, Number, Money, Distance, Time, Speed problems.
  • Geometry and MeasurementPolygons, Angles, Circles, Solids, Length and Width, Area, Perimeter, Volume, Congruent figures.
  • Non-Routine Problem SolvingNumber patterns, Divisibility tests, Spatial visualization, Logic problems, Cryptarithms, Mental math, Brain teasers

Category 3 (Grades 7 & 8)

7 TOPIC AREAS
  • NumbersRational numbers, Operations and properties, Counting and sequences, Fractions, Decimals, Percentages, Ratio and Proportion, Place value, Ordering and Rounding, Integers and Power, Money.
  • SetsSet language and notation, Concepts of sets, Set theory.
  • FunctionsProperties of functions, Transformation of graph, Graph of a function, Applied problems.
  • Statistics and ProbabilityCombinatorics, Permutation, Probability, Statistics, Presenting and interpreting data, Average, Handling data.
  • Word ProblemsVerbal equations, Age, Number, Money, Distance, Time, Speed problems.
  • Geometry and MeasurementPolygons, Angles, Circles, Solids, Area, Perimeter, Volume, Similarity, Pythagorean formula.
  • Non-Routine Problem SolvingNumber patterns, Divisibility tests, Spatial visualization, Logic problems, Cryptarithms, Mental math, Brain teasers.

Category 4 (Grades 9 & 10)

8 TOPIC AREAS
  • NumbersOperations and properties, Counting and sequences, Fractions, Decimals, Percentages, Ratio and Proportion, Place value, Integers and Power, Money.
  • AlgebraExpressions, Factorizations, Equations, Inequalities, Exponents, Radicals, Polynomials.
  • SetsSet language and notation, Concepts of sets, Set theory.
  • FunctionsComposition of functions, Inverse functions, Properties of functions, Transformation of graphs, Graph of a function, Applied problems.
  • TrigonometryFundamentals of trigonometry, Trigonometric functions, Trigonometric theorems and formulas, Trigonometric equations, Trigonometric inequalities.
  • Statistics and ProbabilityCombinatorics, Permutation, Probability, Statistics, Presenting and interpreting data, Average.
  • Geometry and MeasurementPolygons, Area, Perimeter, Coordinate geometry, Analytic analysis of lines, Similarity, Analytic analysis of circles, Solids.
  • Non-Routine Problem SolvingNumber patterns, Divisibility tests, Spatial visualization, Logic problems, Cryptarithms, Word problems

Category 5 (Grades 11 & 12)

10 TOPIC AREAS
  • Quadratic Equations and FunctionsOperations and properties, Counting and sequences, Fractions, Decimals, Percentages, Ratio and Proportion, Place value, Integers and Power, Money.
  • AlgebraExpressions, Factorizations, Equations, Inequalities, Exponents, Radicals, Polynomials.
  • TrigonometryFundamentals of trigonometry, Trigonometric functions, Trigonometric theorems and formulas, Trigonometric equations, Trigonometric inequalities.
  • Series and SequencesSeries, Arithmetic sequences, Geometric sequences.
  • Logarithmic and Exponential FunctionsProperties and graphs of exponential functions, Exponential equations, Properties and graphs of logarithmic functions, Logarithmic equations, Exponential and logarithmic inequalities.
  • DerivativesLimit of a function, Indeterminate forms, Continuous functions, Techniques of differentiation, Applications of derivatives, Optimization problems, Plotting graphs.
  • IntegralsAntiderivative and indefinite integral, Integration methods.
  • Statistics and ProbabilityCombinatorics, Permutation, Probability, Statistics, Presenting and interpreting data, Average.
  • Geometry and MeasurementPolygons, Coordinate geometry, Analytic analysis of lines, Symmetry, Analytic analysis of circles, Solids, Vectors.
  • Non-Routine Problem SolvingNumber patterns, Divisibility tests, Spatial visualization, Logic problems, Cryptarithms, Word problems