Syllabus
Topics covered in each age group of the Lion Cubs Mathematical Contest.
Jump to Age Group
Group A — Ages 7–8
Addition & Subtraction of Numbers
Master fundamental operations. Explore mental arithmetic strategies, number bonds, and place value up to 100.
Geometrical Shapes
Study 2D shapes, their sides, vertices, and symmetry — triangles, squares, rectangles, and circles.
Odd One Out & Classification
Sharpen analytical skills by identifying sorting rules, anomalies, and shared attributes in sets.
Patterns & Sequences
Investigate numerical and visual patterns. Learn to predict and extend repeating and growing sequences.
Ordering of Sets
Solve problems related to arranging elements in order of magnitude, rank, and position.
Combinatorial Problems
Tackle simple arrangements and selections using systematic listing.
Logical Tasks & Riddles
Develop deduction abilities. Solve mathematical clues, family relationship puzzles, and balance scales.
Measuring Units, Money & Time
Compare lengths, weights, and volumes. Read clocks, calculate elapsed time, and solve money change problems.
Group B — Ages 8–9
Arithmetic Operations within 1,000
Master addition, subtraction, multiplication tables, and division with remainders.
Special Methods for Arithmetic Problems
Smart calculation methods: grouping terms, compensation, and distributive decomposition.
Lines, Shapes & Solids
Angles, perimeter of polygons, line symmetry, and counting faces, edges, and vertices of simple solids.
Measurement & Data Displays
Convert units of length, capacity, and mass. Interpret pictograms and simple bar charts.
Combinatorial Problems & Pigeonhole Principle
Systematic counting, tree diagrams, and introduction to worst-case reasoning (Dirichlet principle).
Logical Problems & Planning Tasks
Multi-step planning, river-crossing riddles, and logical grid deduction.
Group C — Ages 9–10
Multi-Digit Numbers & Divisibility
Numbers up to 100,000. Divisibility rules for 2, 3, 5, 9, 10. Factor pairs and multiples.
Fractions & Decimals Introduction
Equivalent fractions, proper/improper fractions, tenths and hundredths as decimals.
Area & Perimeter
Area of rectangles and composite figures made of rectangles. Perimeter problem-solving.
Working Backward & Inversion
Solving word problems by reversing operations from a given end state.
Elementary Statistics & Probability
Averages (mean), range, interpreting double bar graphs, and likelihood of simple events.
Group D — Ages 10–11
Operations with Fractions & Decimals
Addition, subtraction, multiplication of fractions and decimals. Percentage basics.
Number Theory & Prime Numbers
Prime vs composite numbers, prime factor trees, GCD (HCF) and LCM applications.
Geometry & Angles
Angles on lines, around points, and within triangles. Area of triangles and parallelograms.
Logic Puzzles: Knights & Knaves
Classic truth-teller vs liar scenarios, assumption-testing, and contradiction proofs.
Combinatorics & Permutations
Multiplication principle of counting, arrangements with constraints, and set intersections.
Group E — Ages 11–12
Year 7 / Grade 6 • 9 Curriculum Strands
1. Numbers and Operations
Order of operations with brackets, ×, ÷, + and − (BODMAS/PEMDAS). Mixed operations with whole numbers, decimals and fractions. Fraction comparison and determining proper/improper fractions without full computation.
2. Number Theory and Digits
Divisibility, multiples and factors; lowest common multiple (LCM, counting in tens and dozens). Prime numbers and prime factorization. Units digit of a product. Place value and digit puzzles, including letter-for-digit cryptarithms.
3. Fractions, Ratio, Proportion and Percentages
Fraction of a quantity and whole from a known part. Sharing amounts in given ratios. Direct proportion with whole numbers and decimals. Percentages of quantities and successive percentage changes. Concentration and mixture problems.
4. Word Problems and Algebraic Reasoning
Multi-step problems with unknown quantities using the bar model or units’ method. Age problems across past, present, and future. Averages: change in mean when scores increase. Money and best-value problems. Working backwards through operation sequences.
5. Rates: Motion and Work
Speed, distance and time, including meeting point and catch-up problems. Joint work and cooperative productivity. Workers and time calculations (painters and fences, hummingbirds and flowers).
6. Measurement
Converting units of length, area, volume (m³ to cm³), mass (kg and g) and liquid capacity. Time and calendar mathematics: hours across days, fractions of a day, and elapsed durations.
7. Geometry and Spatial Reasoning
Angles in parallel lines cut by a transversal, angle bisectors, and adjacent angles. Properties of quadrilaterals (parallelograms with equal diagonals) and circles (radius, diameter, chord). Area of rectangles and triangles, including shaded and composite regions. Cutting figures on a grid into identical parts. 3-D visualisation: cubes built from unit cubes; opposite faces of standard dice.
8. Counting, Sets and Patterns
Counting arrangements and selections (e.g. captain and deputy from 11; routes between cities). Venn diagrams with two sets, including “neither”. Number sequences: identifying the inductive rule and extending sequences (e.g. 2, 6, 12, 20, 30, …).
9. Logical Reasoning
Solving “who is who” association puzzles with elimination tables. Truth-teller and liar statements. Arrangement puzzles with positional clues (next to, between, opposite). Precision reading of carefully worded statements (“all except”, “at least”).
Group F — Ages 12–13
Year 8 / Grade 7 • 9 Curriculum Strands
1. Numbers and Operations
Order of operations with brackets, whole numbers and decimals. Evaluating newly defined mathematical operations and binary functions. Squares and square roots of whole numbers.
2. Number Theory and Digits
Divisibility rules for 3 and 4, and combining them. Counting the divisors of a composite number. Prime factorization into canonical powers. Highest common factor (HCF) and lowest common multiple (LCM), including fraction pairs.
3. Fractions, Ratio, Proportion and Percentages
Fraction of quantity, fraction of a remainder, and the whole from a part. Equations with fractions of two related quantities. Sharing in a ratio, including tracking adjustments after individual shares change. Percentage decrease followed by the increase that restores original price. Mixtures: concentration of solutions and price per kilogram of blends.
4. Word Problems and Algebraic Reasoning
Formulating and solving linear equations in one unknown from practical scenarios. Combining two given totals to deduce a third related total. Working backwards through a chain of operations. Reuse, remainder, and leftover inventory problems.
5. Rates and Work
Inlet and outlet rate problems: filling and emptying reservoirs simultaneously. Comparing and synthesizing work rates across different tasks.
6. Measurement and Time
Converting units of length and area. Clock angles: calculating the exact angular displacement the hour and minute hands turn in a given time.
7. Geometry
Angle sum of a triangle and quadrilateral; interior angles in a given ratio. Isosceles triangles, angle bisectors and altitudes, including from the right angle. The 30–60–90 triangle: the shorter side is half the hypotenuse. Pythagorean theorem, including distance between two points on a grid. Trapezoid midline and how a diagonal divides it. Area of triangles and rectangles; equal areas giving equal products of base and height. Perimeter changes when a piece is cut off. Counting triangles and quadrilaterals in complex figures.
8. Counting, Probability and Sets
Arrangements in order, including keeping two specific items together. Selections where orders do not matter. Probability of an event with dice, and of a range from two given probabilities. Venn diagrams with two sets.
9. Logic and Patterns
Logic grids with clues. Deductive scenarios with two true statements and one false. Repeating decimals: finding the digit in any given decimal position.
Group G — Ages 13–14
Year 9 / Grade 8 • 9 Curriculum Strands
1. Numbers and Operations
Find a missing number in a calculation using the order of operations. Compute cleverly with algebraic patterns and factorization identities.
2. Number Theory and Digits
Prime and composite numbers; prime factorization. Divisibility rules for 3, 5 and 15; divisibility of digit-swap sums. Remainders: finding a divisor from two remainders; the smallest number with given remainders. Units digit and periodic cycles of integer powers.
3. Fractions, Ratio, Proportion and Percentages
Percentage reduction and markup dynamics. Ratios change when the same amount is added to both parts. Chained ratios. Quantities whose products with given numbers are equal. Direct and inverse proportion. Percentage change in area when length and width change.
4. Algebra and Word Problems
Form and solve linear equations, and pairs of simultaneous linear equations, from a story. Substitute and simplify multi-variable expressions. Age problems, including ages in months against years. Heads-and-legs and parts-of-a-route problems. Averages: effect of adding, removing or changing values.
5. Rates: Motion and Work
Two objects moving towards each other, including staggered start times. Boats against and with the current. Filling and emptying a pool at the same time.
6. Measurement
Time calculations across the hour (e.g. 155 minutes before 14:00). Map scale (1 : 500,000) and conversion to kilometres. Circumference and distance travelled by a clock-hand tip (using π = 22/7). Volume of cuboids: water displacement and scaling dimensions.
7. Geometry
Angles in triangles, squares and equilateral triangles combined. Interior and exterior angles of polygons. Area of a rhombus from its diagonals; area of parallelograms and trapezoids. Pythagorean theorem in a trapezium with perpendicular diagonals. Translations on the coordinate plane, including negative coordinates. Solids: edges after cutting corners; cuboids built from identical unit blocks.
8. Counting, Probability and Sets
Count numbers in a range with a digit condition (contain 7; exactly one 5). Ordered selections (favourite and second favourite of 7) and sequences with restrictions (no button twice in a row). Count regions formed by lines on a sphere (parallels and meridians). Probability from given ratios and from counts. Two overlapping sets given as percentages.
9. Logic and Patterns
Find the generative rule of a sequence of fractions and continue it. Extremal reasoning: the largest share when all shares differ.
Remember: Practice and perseverance are key to excelling. Fostering curiosity and a positive attitude toward problem-solving is just as important as the topics themselves.
Next: View Sample Questions or read the Contest Rules.