Math Basics

Topic	Sub-Topic / Details
Tables till 30	Reference list for rapid calculation
Squares till 30	Essential for Algebra/Geometry
Square roots of 1, 2, 3, 4, 9	Common irrational & rational roots
Cubes till 11	Volume & Algebra basics
Types of Numbers & Systems
Real Numbers Includes all possible numbers on a continuous number line (rational + irrational).	Rational Numbers Fractions with terminating or repeating decimals (Integers > Whole > Natural).
	Irrational Numbers Cannot be expressed as fractions; non-repeating infinite decimals (e.g., π, √2, √10).
Roman Numerals, Even, Odd, Prime, & Composite	Classification and properties
Fractions (p/q)	Proper (Numerator < Denominator) Improper (Numerator > Denominator) Mixed Numbers
Decimals, Powers & Roots	Decimal Indices (powers/exponents) (a raise to power b) Surds (irrational roots or underroot)
Number Systems & Notation	Place value & expanded form Number system (India & International) (reading & writing) Scientific notation / Standard form
Order of Operations & Rules	Order of operations (BODMAS / BIDMAS / PEMDAS) Divisibility Rules BODMAS for Natural Numbers, Whole, Integer, Fractions, decimal, Indices, Surds
Arithmetic Foundations	Unitary method LCM, HCF, Factors, Multiples Average (mean)
Ratios & Applied Math	Ratio & Proportions Ages problems Time & work / Pipes & cisterns problems
Commercial Mathematics	% & taxes Interest (simple, compound) Profit, loss, discount
Motion & Speed	Time, speed, distance Boats & Trains problems Streams (Upstream/Downstream)
1	Numbers & Number Systems
2	Arithmetic
3	Geometry
4	Coordinate Geometry
5	Mensuration (2D, 3D)
6	Trigonometry
7	Statistics
8	Probability
9	Algebra
Numbers & Number Systems
Basic Number Concepts	Counting, reading & writing numbers Place value & expanded form Even & odd numbers Factors, multiples, prime & composite numbers HCF & LCM Divisibility rules
Number Classification	Fractions — types, operations, comparison Decimals — operations & conversion Integers & negative numbers Rational numbers — properties & operations Irrational numbers & real numbers
Exponents & Theorems	Square roots & cube roots Surds, indices & laws of exponents Scientific notation / Standard form Euclid's Lemma & Fundamental Theorem of Arithmetic
Arithmetic
Basic Operations & Rules	Basic operations — addition, subtraction, multiplication, division Order of operations (BODMAS / BIDMAS / PEMDAS) Roman numerals Unitary method
Commercial Concepts	Ratio & proportion Percentage Profit, loss & discount Simple interest & compound interest Average (Mean)
Applied Word Problems	Time & work / Pipes & cisterns Time, speed & distance Trains, boats & streams (applied speed problems)
Business & Real-world Math	Partnership Mixture & alligation Ages problems Financial literacy (budgeting, tax, GST, bills)
Geometry
Geometric Foundations	Basic 2D & 3D shape recognition Lines, line segments, rays & angle types Parallel lines & transversals Symmetry & reflection
Polygons & Triangles	Triangles — types, properties, congruence Quadrilaterals — types & properties Polygons — interior & exterior angles Similarity of triangles & Basic Proportionality Theorem (BPT) Pythagoras theorem & applications
Circles & Drafting	Circles — chord, arc, tangent, angles, secant Circle theorems Geometric constructions with compass & straightedge
Transformations & Proofs	Congruence, similarity & transformations (rotation, reflection, translation) Vectors — introduction Geometric proof (Euclidean)
Coordinate Geometry
Points & Planes	Plotting points on a number line Cartesian plane — axes, quadrants, plotting points
Key Formulas	Distance formula Section / midpoint formula Area of triangle using coordinates
Lines & Graphing	Slope & equation of a straight line Parallel & perpendicular lines (coordinate) Graphing linear & quadratic functions
Mensuration (2D, 3D)
2D Shapes (Area & Perimeter)	Perimeter of basic shapes Area of square, rectangle, triangle Area of parallelogram, rhombus, trapezium Circumference & area of circle Area of sector & segment
3D Solids & Volumes	Surface area & volume — cube & cuboid Surface area & volume — cylinder, cone, sphere, hemisphere Combinations of solids & frustum of cone Composite / compound figures
Trigonometry
Trig Foundations	Trigonometric ratios — sin, cos, tan (right triangles) Trigonometric identities Complementary angle relationships
Applications & Rules	Heights & distances — elevation & depression Sine & cosine rules (non-right triangles) Bearings & directions
Statistics
Data Representation	Data collection & tally marks Pictographs & bar graphs Pie charts & line graphs
Central Tendency & Spread	Mean, median, mode for ungrouped data Mean, median, mode for grouped data Range, IQR & measures of spread
Statistical Analysis	Histograms, box plots & cumulative frequency Scatter plots, correlation & line of best fit
Applied Statistics	Data Interpretation (tables, charts — applied) Two-way tables & categorical data
Probability
Probability Foundations	Basic concept — likely, unlikely, equally likely Probability scale 0 to 1 Classical definition of probability
Probability Types & Events	Experimental vs theoretical probability Simple & compound events, complementary events
Tools & Advanced Theory	Tree diagrams & Venn diagrams Conditional probability (basic) Combinatorics / counting principles (intro)
Algebra
Algebraic Basics	Introduction to variables & algebraic expressions Exponents & powers Algebraic identities Factorisation of algebraic expressions
Linear Equations	Linear equations — one variable Linear equations — two variables & graphing Pair of linear equations — graphical & algebraic methods
Higher Degree Equations	Polynomials — zeros, remainder & factor theorem Quadratic equations — factorising, formula, discriminant
Advanced Topics	Inequalities — linear Functions — definition, notation, linear functions Sequences — arithmetic & geometric Algebraic fractions
Multiplication Tables (2 to 30) * Swipe left/right to view all columns (x1 to x10)	Table x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 2 2 4 6 8 10 12 14 16 18 20 3 3 6 9 12 15 18 21 24 27 30 4 4 8 12 16 20 24 28 32 36 40 5 5 10 15 20 25 30 35 40 45 50 6 6 12 18 24 30 36 42 48 54 60 7 7 14 21 28 35 42 49 56 63 70 8 8 16 24 32 40 48 56 64 72 80 9 9 18 27 36 45 54 63 72 81 90 10 10 20 30 40 50 60 70 80 90 100 11 11 22 33 44 55 66 77 88 99 110 12 12 24 36 48 60 72 84 96 108 120 13 13 26 39 52 65 78 91 104 117 130 14 14 28 42 56 70 84 98 112 126 140 15 15 30 45 60 75 90 105 120 135 150 16 16 32 48 64 80 96 112 128 144 160 17 17 34 51 68 85 102 119 136 153 170 18 18 36 54 72 90 108 126 144 162 180 19 19 38 57 76 95 114 133 152 171 190 20 20 40 60 80 100 120 140 160 180 200 21 21 42 63 84 105 126 147 168 189 210 22 22 44 66 88 110 132 154 176 198 220 23 23 46 69 92 115 138 161 184 207 230 24 24 48 72 96 120 144 168 192 216 240 25 25 50 75 100 125 150 175 200 225 250 26 26 52 78 104 130 156 182 208 234 260 27 27 54 81 108 135 162 189 216 243 270 28 28 56 84 112 140 168 196 224 252 280 29 29 58 87 116 145 174 203 232 261 290 30 30 60 90 120 150 180 210 240 270 300
Powers & Roots Reference * Squares (1-30), Cubes (1-11), & Key Square Roots	No. Squares Cubes Square Root 1 1 1 1 2 4 8 1.4142 3 9 27 1.732 4 16 64 2 5 25 125   6 36 216   7 49 343   8 64 512   9 81 729 3 10 100 1000   11 121 1331   12 144     13 169     14 196     15 225     16 256     17 289     18 324     19 361     20 400     21 441     22 484     23 529     24 576     25 625     26 676     27 729     28 784     29 841     30 900