Mathematical Reasoning
About this subject
Mathematical Reasoning tests your ability to apply mathematical concepts to solve problems quickly and accurately. Topics include number operations, fractions, ratios, measurement, geometry, and data.
Unit 1
Patterns and Sequences
Identify rules in number sequences, repeating patterns, and arithmetic progressions. Learn the cycle-remainder shortcut for repeating sequences and the sum formulas for arithmetic series.
Unit 2
Number Theory
Explore the properties of whole numbers — divisibility, factors, multiples, LCM, HCF, primes, and combinatorics. Build the number sense that underpins every other MR topic.
Unit 3
Measurement and Data
Apply units of length, mass, capacity, time, and money to real-world problems. Read and interpret graphs, timetables, and data tables with precision.
Unit 4
Statistics and Probability
Calculate means and averages, interpret column and line graphs, work with Venn diagrams, and apply basic probability reasoning to single and compound events.
Unit 5
Geometry
Calculate areas and perimeters of composite shapes, volumes of solids, surface areas, and angles in polygons. Develop spatial intuition through paper-folding and 3D reasoning.
Unit 6
Algebra
Solve equations, simultaneous conditions, and before-after ratio problems using systematic algebraic thinking. Translate word problems into equations confidently.
Unit 7
Finding Procedures
Master multi-step problem-solving strategies: working backwards, the supposition method, rate-and-worker problems, and percentage applications.
Unit 8
Rates and Ratios
Solve ratio, proportion, distance-speed-time, and work-rate problems. Handle meeting, chasing, and combined-rate scenarios with a systematic approach.
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