π Mathematics 3D Gallery

NUM007 Complex Numbers Classes 11–12Graph → NUM006 Number Systems Classes 6–123D → −3 … +5NUM003 Integers Classes 6–82D → ←0→NUM008 Number Line Classes 1–82D → H T ONUM012 Place Value Classes 2–53D → 0.37NUM014 Decimal Place Value Classes 4–72D → 1, 2, 3, …NUM001 Natural numbers Classes 1–52D → 0, 1, 2, …NUM002 Whole numbers Classes 1–62D → p/qNUM004 Rational numbers Classes 6–102D → √2, √3, √5NUM005 Irrational numbers Classes 8–102D → |−4|NUM009 Absolute value Classes 6–92D → 3 ↔ −3NUM010 Opposites Classes 6–82D → −3 < ½ < 2NUM011 Ordering numbers Classes 3–82D → 500 + 70 + 2NUM013 Expanded form Classes 2–53D → MCMXCIVNUM015 Roman numerals Classes 3–62D → 1101₂NUM016 Binary numbers Classes 6–123D → 100₅NUM017 Base systems Classes 7–123D → 347 ≈ 350NUM018 Rounding numbers Classes 3–72D → ≈ 900NUM019 Estimation Classes 3–72D → [−2, 3)NUM020 Interval notation Classes 9–122D →

AR019 Ratios and Proportions Classes 6–103D → 6 + 3AR001 Addition Classes 1–53D → 439 − 127AR002 Subtraction Classes 1–53D → 4 × 6AR003 Multiplication Classes 2–63D → 23 ÷ 5AR004 Division Classes 3–63D → 3 + 4 × 5AR005 Order of Operations (BODMAS) Classes 5–83D → 48 + 2 + 25AR006 Mental addition Classes 2–52D → 82 − 30 − 7AR007 Mental subtraction Classes 2–52D → 23 × 14AR008 Long multiplication Classes 4–72D → 156 ÷ 4AR009 Long division Classes 4–72D → a + b = b + aAR010 Properties of addition Classes 3–63D → a × b = b × aAR011 Properties of multiplication Classes 3–62D → a(b + c)AR012 Distributive property Classes 5–82D → ₹ changeAR013 Arithmetic word problems Classes 3–72D → −5 + 8AR014 Negative number arithmetic Classes 6–82D → − × + = −AR015 Signed multiplication Classes 7–92D → −12 ÷ 3AR016 Signed division Classes 7–92D → +5 ↔ −5AR017 Inverse operations Classes 3–72D → ₹/kgAR018 Unit rates Classes 5–82D → ≈ 50 × 20AR020 Arithmetic estimation Classes 4–82D →

FR002 Fractions Classes 3–73D → FR012 Decimals Classes 5–82D → FR019 Percentages Classes 6–102D → 2/3 = 4/6FR005 Equivalent Fractions Classes 4–72D → 1/4FR001 Unit fractions Classes 2–52D → 7/3FR003 Improper fractions Classes 4–72D → 2¾FR004 Mixed numbers Classes 4–72D → 12/18 = 2/3FR006 Simplifying fractions Classes 5–72D → ½ + ⅓FR007 Fraction addition Classes 5–82D → ¾ − ⅓FR008 Fraction subtraction Classes 5–82D → ⅔ × ¾FR009 Fraction multiplication Classes 6–82D → ¾ ÷ ½FR010 Fraction division Classes 6–82D → ⅔ ? ⅗FR011 Fraction comparison Classes 4–72D → 0.75 = ¾FR013 Decimal to fraction Classes 5–72D → 2.5 + 1.7FR014 Decimal addition Classes 5–72D → 5.3 − 2.8FR015 Decimal subtraction Classes 5–72D → 1.5 × 0.4FR016 Decimal multiplication Classes 6–82D → 4.8 ÷ 0.6FR017 Decimal division Classes 6–82D → 0.(142857)FR018 Recurring decimals Classes 7–92D → ⅜ = 37.5%FR020 Fraction-decimal-percent conversion Classes 6–82D →

2 3 5 7DIV003 Prime Numbers Classes 5–82D → 2² × 3 × 5DIV005 Prime Factorisation Classes 6–102D → HCFDIV013 Highest Common Factor (HCF) Classes 6–102D → LCMDIV014 Least Common Multiple (LCM) Classes 6–102D → 1 2 3 4 6 12DIV001 Factors Classes 4–72D → 4, 8, 12, …DIV002 Multiples Classes 3–62D → 15 = 3 × 5DIV004 Composite numbers Classes 5–82D → …8 ÷ 2DIV006 Divisibility by 2 Classes 4–72D → 4+7+1 = 12DIV007 Divisibility by 3 Classes 4–72D → …16 ÷ 4DIV008 Divisibility by 4 Classes 5–72D → …5 ÷ 5DIV009 Divisibility by 5 Classes 4–72D → ÷2 and ÷3DIV010 Divisibility by 6 Classes 5–72D → 7+3+6+2 = 18DIV011 Divisibility by 9 Classes 5–72D → …0 ÷ 10DIV012 Divisibility by 10 Classes 4–62D → HCF = 1DIV015 Coprime numbers Classes 6–92D → 84 → 2·2·3·7DIV016 Factor trees Classes 6–92D → SieveDIV017 Sieve of Eratosthenes Classes 5–82D → 144 = 12²DIV018 Perfect squares Classes 6–82D → 216 = 6³DIV019 Perfect cubes Classes 7–93D → 28: perfectDIV020 Number properties Classes 6–92D →

Extra Logarithmic Spiral Class 12Graph → EXP015 Logarithms Classes 11–12Graph → 2⁵EXP001 Exponents Basics Classes 6–93D → 10³EXP002 Powers of 10 Classes 6–93D → n²EXP003 Square Numbers Classes 5–82D → n³EXP004 Cube Numbers Classes 6–93D → aᵐ·aⁿEXP005 Exponent Product Rule Classes 7–92D → a⁻ⁿEXP009 Negative Exponents Classes 8–102D → ∛27EXP010 Fractional Exponents Classes 9–112D → 3×10⁸EXP012 Scientific Notation Classes 8–102D → ↗ (1+r)ᵗEXP013 Exponential Growth Classes 9–12Graph → ↘ (1−r)ᵗEXP014 Exponential Decay Classes 9–12Graph → log xEXP016 Common Logarithm (base 10) Classes 9–12Graph → ln xEXP017 Natural Logarithm (base e) Classes 11–12 + B.TechGraph → log abEXP018 Log Product Rule Classes 9–122D → log a/bEXP019 Log Quotient Rule Classes 9–122D → log aⁿEXP020 Log Power Rule Classes 9–122D → aᵐ ÷ aⁿEXP006 Exponent quotient rule Classes 7–92D → (aᵐ)ⁿEXP007 Power of a power Classes 8–102D → a⁰ = 1EXP008 Zero exponent Classes 7–92D → √72 = 6√2EXP011 Radicals and roots Classes 8–102D →

3x + 5ALG001 Variables and constants Classes 6–82D → 2x² − 3x + 5ALG002 Terms and coefficients Classes 6–82D → 4xALG003 Monomials Classes 6–82D → 3x + 2ALG004 Binomials Classes 6–82D → x² + 5x + 6ALG005 Trinomials Classes 7–92D → P(x)ALG006 Polynomials Classes 8–102D → 3x + 4xALG007 Like terms Classes 6–82D → 5x + 3 − 2x − 7ALG008 Simplifying expressions Classes 7–92D → 4x − 3ALG009 Evaluating expressions Classes 6–92D → 3(x + 4)ALG010 Distributive expansion Classes 7–92D → x → −3ALG011 Algebraic substitution Classes 7–92D → deg = 2ALG012 Polynomial degree Classes 8–102D → P + QALG013 Polynomial addition Classes 8–102D → P − QALG014 Polynomial subtraction Classes 8–102D → (x + 2)(x + 3)ALG015 Polynomial multiplication Classes 8–102D → ÷ (x − r)ALG016 Polynomial division Classes 9–11Graph → 4(x + 3)ALG017 Factorization by common factor Classes 8–102D → x(x+2) + 3(x+2)ALG018 Factorization by grouping Classes 9–102D → (x² − 9)/(x − 3)ALG019 Algebraic fractions Classes 9–11Graph → √48 = 4√3ALG020 Surds Classes 9–112D →

EQ005 Linear Equations Classes 8–12Graph → EQ008 Quadratic Equations Classes 10–12Graph → EQ006 Simultaneous Equations Classes 9–12Graph → x + 5 = 12EQ001 One-step linear equations Classes 6–83D → 3x + 4 = 19EQ002 Two-step linear equations Classes 7–93D → 2(x + 3) = 16EQ003 Linear equations with brackets Classes 7–93D → x/3 + 2 = 6EQ004 Linear equations with fractions Classes 8–103D → ∩EQ007 Graphical solution of equations Classes 9–10Graph → x = (−b ± √D)/2aEQ009 Quadratic formula Classes 10–12Graph → (x − h)² + kEQ010 Completing the square Classes 10–12Graph → (x − 2)(x − 3) = 0EQ011 Factor method for quadratics Classes 10–112D → D = b² − 4acEQ012 Discriminant Classes 10–12Graph → α + β, αβEQ013 Roots and coefficients Classes 10–12Graph → P(x) = 0EQ014 Polynomial equations Classes 10–12Graph → 12/x = 4EQ015 Rational equations Classes 10–12Graph → |x − 1| = 3EQ016 Absolute value equations Classes 9–11Graph → 2x + 3 < 11EQ017 Linear inequalities Classes 8–102D → −1 < x + 2 ≤ 7EQ018 Compound inequalities Classes 9–112D → x ≥ −2EQ019 Inequality number line Classes 7–92D → 2x + 10 = 50EQ020 Word problems with equations Classes 7–103D →

(a+b)²ID001 (a + b)² Classes 8–102D → (a−b)²ID002 (a − b)² Classes 8–102D → a² − b²ID003 a² − b² Classes 8–102D → (a+b)³ID004 (a + b)³ Classes 9–103D → (a−b)³ID005 (a − b)³ Classes 9–103D → a³ + b³ID006 a³ + b³ Classes 9–103D → a³ − b³ID007 a³ − b³ Classes 9–103D → (x+a)(x+b)ID008 (x + a)(x + b) Classes 8–102D → x² + 6x + 9ID009 Perfect square trinomials Classes 8–102D → (3 + 2)³ID010 Cube of a binomial Classes 9–103D → (a + b)ⁿID011 Binomial expansion Classes 11–12 + B.Tech2D → 1 5 10 10 5 1ID012 Pascal triangle Classes 8–122D → LHS = RHS ?ID013 Identity verification Classes 8–102D → □ = a² + 2ab + b²ID014 Geometric proof of square identity Classes 8–102D → L → ▭ID015 Geometric proof of difference of squares Classes 8–102D → x² + bx + cID016 Factorization identities Classes 9–102D → a + b, abID017 Symmetric expressions Classes 9–112D → 103²ID018 Algebraic simplification identities Classes 8–102D → p(r)ID019 Remainder theorem Classes 9–11Graph → p(r) = 0ID020 Factor theorem Classes 9–11Graph →

SET011 Set Theory Classes 11–122D → SET018 Logic and Truth Tables Classes 11–122D → A = {…}SET001 Set notation Classes 9–112D → {x : …}SET002 Roster and set-builder forms Classes 9–112D → ∅SET003 Empty set Classes 9–112D → A ⊆ BSET004 Subset Classes 9–112D → A ⊂ BSET005 Proper subset Classes 9–112D → USET006 Universal set Classes 9–112D → A ∪ BSET007 Union of sets Classes 9–112D → A ∩ BSET008 Intersection of sets Classes 9–112D → A − BSET009 Set difference Classes 9–112D → A′SET010 Complement of a set Classes 9–112D → A ∪ B ∪ CSET012 Venn diagrams: three sets Classes 11–122D → A × BSET013 Cartesian product Classes 11–122D → a R bSET014 Relations Classes 11–122D → dom → ranSET015 Domain and range Classes 11–122D → x ↦ f(x)SET016 Functions as mappings Classes 11–122D → p, qSET017 Propositions Classes 11–122D → ∧ ∨ ¬SET019 Logical AND/OR/NOT Classes 11–122D → ¬(p ∧ q)SET020 De Morgan laws Classes 11–122D →

SEQ002 Sequences and Series Classes 10–123D → a₁, a₂, a₃, …SEQ001 Sequence basics Classes 9–112D → aₙ = a + (n−1)dSEQ003 AP nth term Classes 10–112D → SₙSEQ004 AP sum Classes 10–112D → × rSEQ005 Geometric progression (GP) Classes 10–112D → arⁿ⁻¹SEQ006 GP nth term Classes 10–112D → Sₙ = a(rⁿ−1)/(r−1)SEQ007 GP sum Classes 10–112D → ½ + ¼ + ⅛ + …SEQ008 Infinite geometric series Classes 11–122D → 1, ½, ⅓, …SEQ009 Harmonic progression Classes 11–122D → 1, 1, 2, 3, 5, 8SEQ010 Fibonacci sequence Classes 8–122D → aₙ₊₁ = f(aₙ)SEQ011 Recursive sequences Classes 11–122D → ΣSEQ012 Sigma notation Classes 11–122D → Σ → ?SEQ013 Series convergence intuition Classes 11–12 + B.Tech2D → (a + b)/2SEQ014 Arithmetic mean Classes 9–112D → √(ab)SEQ015 Geometric mean Classes 10–122D → • •• •••SEQ016 Pattern recognition Classes 6–92D → (n, aₙ)SEQ017 Sequences from graphs Classes 9–11Graph → ₹ +d each yearSEQ018 Word problems on AP Classes 10–112D → × (1 + r)SEQ019 Word problems on GP Classes 10–122D → C(n, k)SEQ020 Binomial sequence Classes 11–122D →

FUN007 Parabola Graph Classes 9–12Graph → FUN020 Lissajous Curve Classes 11–12Graph → Extra Paraboloid Surface Class 123D → Extra Saddle Surface Class 123D → FUN008 Cubic Functions Classes 10–12Graph → FUN013 Polynomial Functions Classes 9–12Graph → Extra Graphs Classes 6–12Graph → FUN001 Functions Classes 11–122D → y = xFUN004 Identity Function Classes 9–12Graph → y = kFUN005 Constant Function Classes 9–12Graph → |x|FUN009 Absolute Value Function Classes 9–12Graph → 1/xFUN010 Reciprocal Function Classes 10–12Graph → √xFUN011 Square Root Function Classes 10–12Graph → aˣFUN015 Exponential Function Classes 10–12Graph → log_b xFUN016 Logarithmic Function Classes 11–12Graph → sin x·cos yExtra Surface z = sin x · cos y Classes 11–12 + B.Tech3D → dom / ranFUN002 Domain and range Classes 10–12Graph → | testFUN003 Vertical line test Classes 10–12Graph → y = mx + cFUN006 Linear function Classes 9–11Graph → { …FUN012 Piecewise function Classes 11–12Graph → (x + a)/(x − b)FUN014 Rational function Classes 11–12Graph → af(x − h) + kFUN017 Transformations of graphs Classes 11–12Graph → f⁻¹FUN018 Inverse functions Classes 11–12Graph → g ∘ fFUN019 Composite functions Classes 11–12Graph →

GEO001 Point Classes 1–123D → GEO002 Line Segment Classes 4–12Graph → Extra Ray Classes 5–122D → GEO003 Angle Classes 3–122D → GEO007 Triangle Classes 3–122D → GEO014 Regular Polygon Classes 6–122D → GEO004 Angle Relationships Classes 6–102D → Extra Geometry (2D) Classes 4–102D → ∥ + transversalGEO005 Parallel lines and transversal Classes 7–92D → ⊥GEO006 Perpendicular lines Classes 6–10Graph → A + B + C = 180°GEO008 Triangle angle sum Classes 6–92D → ext = A + BGEO009 Exterior angle theorem Classes 7–92D → ≅GEO010 Congruent triangles Classes 7–102D → ∼GEO011 Similar triangles Classes 8–102D → a² + b² = c²GEO012 Pythagorean theorem Classes 7–102D → (n − 2) × 180°GEO013 Polygon angle sums Classes 7–102D → ✶GEO015 Symmetry Classes 5–82D → ⇋GEO016 Reflection symmetry Classes 5–9Graph → ↻GEO017 Rotational symmetry Classes 6–92D → ⌒⌒GEO018 Geometric constructions Classes 6–92D → {P : PO = r}GEO019 Locus Classes 9–112D → ∠1 = ∠3GEO020 Euclidean proof basics Classes 8–102D →

TRI004 Right Triangle Classes 6–122D → TRI001 Equilateral Triangle Classes 4–122D → TRI002 Isosceles Triangle Classes 4–122D → TRI003 Scalene Triangle Classes 4–122D → Extra Triangles Classes 6–102D → all < 90°TRI005 Acute triangle Classes 6–92D → > 90°TRI006 Obtuse triangle Classes 6–92D → a + b > c ?TRI007 Triangle inequality Classes 6–92D → ½ bhTRI008 Triangle area Classes 5–82D → √[s(s−a)(s−b)(s−c)]TRI009 Heron's formula Classes 9–102D → ⊥ heightTRI010 Altitude Classes 7–102D → → midpointTRI011 Median Classes 7–102D → ∠ ÷ 2TRI012 Angle bisector Classes 8–102D → ⊥ bisectorsTRI013 Perpendicular bisectors Classes 8–102D → GTRI014 Centroid Classes 8–102D → HTRI015 Orthocenter Classes 9–112D → ITRI016 Incenter Classes 9–112D → OTRI017 Circumcenter Classes 9–112D → O—G—HTRI018 Euler line Classes 11–12 + B.Tech2D → k : 1TRI019 Similarity ratios Classes 8–102D → SSS SAS ASA RHSTRI020 Congruence criteria Classes 8–102D →

POL001 Square Classes 2–122D → POL002 Rectangle Classes 2–122D → POL003 Parallelogram Classes 6–122D → POL004 Rhombus Classes 6–122D → POL005 Trapezium Classes 7–122D → POL006 Kite Classes 7–122D → 360°POL007 Quadrilateral angle sum Classes 6–92D → (n − 2)180°/nPOL008 Interior angles of polygons Classes 7–92D → Σ ext = 360°POL009 Exterior angles of polygons Classes 7–92D → ⬠POL010 Regular pentagon Classes 6–102D → ⬡POL011 Regular hexagon Classes 6–102D → ⯃POL012 Regular octagon Classes 7–102D → n(n − 3)/2POL013 Polygon diagonals Classes 7–102D → ⬡⬡⬡POL014 Tessellations Classes 6–102D → convexPOL015 Convex polygons Classes 7–102D → concavePOL016 Concave polygons Classes 7–102D → b × hPOL017 Area of parallelogram Classes 6–82D → ½(a + b)hPOL018 Area of trapezoid Classes 7–92D → ◇ ▭ ▱POL019 Quadrilateral properties Classes 7–92D → ⬡ mirrorsPOL020 Polygon symmetry Classes 6–92D →

CIR004 Circle Classes 4–122D → CIR016 Sector Classes 8–122D → CIR005 Arc Classes 8–122D → CIR015 Annulus Classes 8–122D → Extra Semicircle Classes 6–122D → Extra Quadrant Classes 7–122D → Extra Circles Classes 6–102D → (x−h)²+(y−k)²CIR018 Circle Equations Classes 10–12Graph → O, r, dCIR001 Circle parts Classes 5–82D → d = 2rCIR002 Radius and diameter Classes 5–82D → 2πrCIR003 Circumference Classes 6–92D → ∠AOBCIR006 Central angles Classes 7–92D → θ = ½ centralCIR007 Inscribed angles Classes 9–102D → ⊥ bisectsCIR008 Chord properties Classes 9–102D → ⊥ radiusCIR009 Tangent to a circle Classes 9–102D → PA · PBCIR010 Secant lines Classes 9–112D → ∠ tangent-chordCIR011 Tangent-chord theorem Classes 10–112D → A + C = 180°CIR012 Cyclic quadrilaterals Classes 9–102D → OP² − r²CIR013 Power of a point Classes 10–122D → AP·PB = CP·PDCIR014 Intersecting chords Classes 9–112D → rθCIR017 Arc length Classes 7–102D → x² + y² = r²CIR019 Coordinate circle Classes 10–12Graph → π ≈ 3.14CIR020 Pi approximation Classes 8–112D →

MEA001 Perimeter and Area Classes 3–92D → MEA014 Surface Area Classes 8–123D → Extra Real-life Applications Classes 6–123D → cm²MEA002 Area units Classes 3–62D → m → cmMEA003 Unit conversion Classes 3–72D → a²MEA004 Area of square Classes 3–72D → l × wMEA005 Area of rectangle Classes 3–72D → ½ bhMEA006 Area of triangle Classes 5–82D → b × hMEA007 Area of parallelogram Classes 6–82D → ½(a + b)hMEA008 Area of trapezoid Classes 7–92D → ½ d₁d₂MEA009 Area of rhombus Classes 7–92D → ½ d₁d₂MEA010 Area of kite Classes 7–92D → L-shapeMEA011 Composite area Classes 6–92D → P of LMEA012 Perimeter of composite shapes Classes 6–92D → 1 : nMEA013 Scale drawings Classes 6–92D → kg → gMEA015 Metric conversions Classes 4–73D → in ↔ cmMEA016 Imperial-metric comparison Classes 6–92D → ≈ countMEA017 Area estimation Classes 5–82D → fenceMEA018 Boundary problems Classes 5–82D → ½ d(h₁ + h₂)MEA019 Land plot area Classes 8–102D → ± errorMEA020 Measurement error Classes 8–112D →

SOL003 Sphere Classes 8–123D → SOL004 Hemisphere Classes 9–123D → SOL005 Cylinder Classes 8–123D → SOL006 Cone Classes 9–123D → SOL007 Frustum Classes 10–123D → SOL001 Cube Classes 5–123D → SOL002 Cuboid Classes 5–123D → Extra Sphere Cross-section Classes 10–123D → SOL013 Torus Classes 11–123D → SOL011 Square Pyramid Classes 8–123D → SOL008 Prism Classes 7–123D → SOL012 Tetrahedron Classes 9–123D → Extra Octahedron Classes 9–123D → Extra Dodecahedron Classes 10–123D → Extra Icosahedron Classes 10–123D → Extra 3D Solids Classes 5–123D → Extra Nets of 3D Shapes Classes 5–93D → Extra Volume Classes 5–123D → SOL020 Mensuration Classes 8–123D → Extra Geometry (3D) Classes 8–123D → ½bh × LSOL009 Triangular prism Classes 7–103D → ⅓ BhSOL010 Pyramid Classes 8–103D → 4/3 πabcSOL014 Ellipsoid Classes 11–12 + B.Tech3D → a³SOL015 Volume of cube Classes 5–83D → l × w × hSOL016 Volume of cuboid Classes 5–83D → πr²hSOL017 Volume of cylinder Classes 8–103D → ⅓ πr²hSOL018 Volume of cone Classes 8–103D → 4πr²SOL019 Sphere surface area Classes 9–103D →

COO008 Line Classes 5–12Graph → COO020 Plane Classes 6–123D → COO004 Coordinate Geometry Classes 9–123D → COO001 Cartesian Plane Classes 6–12Graph → (x, y)COO002 Ordered pairs Classes 6–9Graph → I II III IVCOO003 Quadrants Classes 6–9Graph → MCOO005 Midpoint formula Classes 9–10Graph → m : nCOO006 Section formula Classes 10–11Graph → Δy/ΔxCOO007 Slope of a line Classes 9–10Graph → y − y₁ = m(x − x₁)COO009 Line equation: point-slope Classes 10–11Graph → x/a + y/b = 1COO010 Intercept form Classes 10–11Graph → ∥COO011 Parallel lines Classes 9–11Graph → m₁m₂ = −1COO012 Perpendicular lines Classes 9–11Graph → (x−h)² + (y−k)²COO013 Circle in coordinate plane Classes 10–12Graph → |ax₀+by₀+c|/√(a²+b²)COO014 Distance from point to line Classes 11–12Graph → ½|…|COO015 Area of triangle coordinates Classes 10–11Graph → • • •COO016 Collinearity Classes 10–11Graph → PA = PBCOO017 Locus on coordinate plane Classes 11–12Graph → T, RCOO018 Transformations coordinates Classes 9–12Graph → (x, y, z)COO019 3D coordinate axes Classes 11–123D →

TRG012 Sine Wave Classes 10–12Graph → TRG013 Cosine Wave Classes 10–12Graph → TRG014 Tangent Function Classes 10–12Graph → TRG002 Trigonometry Classes 10–123D → ° ↔ radTRG001 Degree and radian measure Classes 10–122D → sin θTRG003 Sine Classes 10–112D → cos θTRG004 Cosine Classes 10–112D → tan θTRG005 Tangent Classes 10–112D → cosec θTRG006 Cosecant Classes 10–112D → sec θTRG007 Secant Classes 10–112D → cot θTRG008 Cotangent Classes 10–112D → 30° 45° 60°TRG009 Special angles Classes 10–112D → (cos θ, sin θ)TRG010 Unit circle Classes 11–122D → All · Sin · Tan · CosTRG011 Trigonometric signs by quadrant Classes 11–122D → tan = sin/cosTRG015 Trigonometric identities Classes 10–122D → sin² + cos² = 1TRG016 Pythagorean identity Classes 10–122D → a/sin A = b/sin BTRG017 Sine rule Classes 11–122D → a² = b² + c² − 2bc cos ATRG018 Cosine rule Classes 11–122D → h = d tan θTRG019 Heights and distances Classes 10–113D → sin⁻¹ xTRG020 Inverse trigonometric functions Class 12 + B.TechGraph →

CON006 Ellipse Classes 11–122D → CON002 Conic Section: Circle Classes 11–123D → CON012 Conic Section: Ellipse Classes 11–123D → CON003 Conic Section: Parabola Classes 11–123D → CON009 Conic Section: Hyperbola Classes 11–123D → CON010 Hyperbola Graph Classes 11–12Graph → ◯ ⬭ ∪ )(CON001 Conic section overview Classes 11–123D → PF = PDCON004 Parabola focus and directrix Classes 11–12Graph → y² = 4axCON005 Parabola standard equations Classes 11–12Graph → F₁ F₂CON007 Ellipse foci Classes 11–12Graph → e = c/aCON008 Ellipse eccentricity Classes 11–122D → e > 1CON011 Hyperbola eccentricity Classes 11–12Graph → LRCON013 Latus rectum Classes 11–12Graph → B² − 4ACCON014 Conic equation parameters Classes 11–12 + B.TechGraph → xy termCON015 Rotated conics Class 12 + B.TechGraph → ∩CON016 Conic intersections Classes 11–12Graph → r(θ)CON017 Polar conics Class 12 + B.TechGraph → ✕CON018 Degenerate conics Class 12 + B.TechGraph → → FCON019 Reflective property of parabola Classes 11–12Graph → ☀ ellipseCON020 Orbit interpretation Classes 11–12 + B.Tech2D →

VEC005 Vectors Classes 11–12Graph → 5 vs 5→VEC001 Scalar and vector Classes 11–12Graph → 2i − 3jVEC002 Vector notation Classes 11–12Graph → |v|VEC003 Magnitude Classes 11–12Graph → v̂VEC004 Unit vector Classes 11–12Graph → u − vVEC006 Vector subtraction Classes 11–12Graph → kvVEC007 Scalar multiplication Classes 11–12Graph → (r cos θ, r sin θ)VEC008 Vector components Classes 11–12Graph → AB = b − aVEC009 Position vector Classes 11–12Graph → u · vVEC010 Dot product Classes 11–12Graph → cos θVEC011 Angle between vectors Classes 11–12Graph → u × vVEC012 Cross product Class 12 + B.Tech3D → projVEC013 Vector projection Class 12 + B.TechGraph → u ∥ vVEC014 Parallel vectors Class 12 + B.TechGraph → u ⊥ vVEC015 Perpendicular vectors Class 12 + B.TechGraph → r = a + tdVEC016 3D vector line Class 12 + B.Tech3D → n · r = dVEC017 3D vector plane Class 12 + B.Tech3D → u · (v × w)VEC018 Triple product Class 12 + B.Tech3D → RVEC019 Vector applications Classes 11–12Graph → → → →VEC020 Vector field introduction Class 12 + B.TechGraph →

MAT020 Matrices Class 12Graph → aᵢⱼMAT001 Matrix notation Classes 11–122D → m × nMAT002 Matrix order Classes 11–122D → A + BMAT003 Matrix addition Classes 11–122D → A − BMAT004 Matrix subtraction Classes 11–122D → kAMAT005 Scalar multiplication Classes 11–122D → ABMAT006 Matrix multiplication Classes 11–122D → AᵀMAT007 Transpose Classes 11–122D → IMAT008 Identity matrix Classes 11–122D → OMAT009 Zero matrix Classes 11–122D → ad − bcMAT010 Determinant 2x2 Classes 11–12Graph → |3×3|MAT011 Determinant 3x3 Classes 11–122D → Mᵢⱼ, CᵢⱼMAT012 Minor and cofactor Classes 11–122D → A⁻¹MAT013 Inverse matrix Classes 11–122D → det = 0MAT014 Singular matrix Classes 11–12Graph → rankMAT015 Rank intuition Class 12 + B.Tech2D → AX = BMAT016 Systems using matrices Classes 11–12Graph → x = Dₓ/DMAT017 Cramer's rule Classes 11–12Graph → λMAT018 Eigenvalues introduction Class 12 + B.TechGraph → Av = λvMAT019 Eigenvectors introduction Class 12 + B.TechGraph →

CAL001 Calculus: Limits Classes 11–12Graph → CAL004 Calculus: Derivatives Classes 11–12Graph → CAL018 Calculus: Integrals Class 12Graph → ∫π(ln x)²Extra Solid of Revolution: y = ln x Class 12 + B.Tech3D → x → 1⁻ / 1⁺CAL002 One-sided limits Classes 11–12Graph → no gapCAL003 Continuity Classes 11–12Graph → nxⁿ⁻¹CAL005 Power rule Classes 11–12Graph → (uv)′CAL006 Product rule Classes 11–12Graph → (u/v)′CAL007 Quotient rule Classes 11–12Graph → f(g(x))′CAL008 Chain rule Classes 11–12Graph → dy/dx = −x/yCAL009 Implicit differentiation Class 12 + B.TechGraph → sin′ = cosCAL010 Derivative of trigonometric functions Classes 11–12Graph → (aˣ)′CAL011 Derivative of exponential functions Classes 11–12Graph → (ln x)′ = 1/xCAL012 Derivative of logarithms Classes 11–12Graph → y = mx + cCAL013 Tangent line Classes 11–12Graph → Δs/Δt → ds/dtCAL014 Rate of change Classes 11–12Graph → f′ > 0 ↗CAL015 Increasing and decreasing functions Classes 11–12Graph → max areaCAL016 Maxima and minima Classes 11–12Graph → ∫ f dxCAL017 Antiderivatives Classes 11–12Graph → F(b) − F(a)CAL019 Fundamental theorem of calculus Class 12 + B.TechGraph → Σ f ΔxCAL020 Area under curve Classes 11–12Graph →

STA009 Gaussian (Normal) Curve Classes 11–12Graph → STA018 Probability Classes 8–123D → STA002 Statistics Classes 6–123D → 🔤 🔢STA001 Data types Classes 6–102D → middleSTA003 Median Classes 6–102D → most oftenSTA004 Mode Classes 6–102D → max − minSTA005 Range Classes 6–102D → Q₁ Q₂ Q₃STA006 Quartiles Classes 9–112D → Q₃ − Q₁STA007 Interquartile range Classes 9–112D → σ²STA008 Variance Classes 11–122D → tallySTA010 Frequency tables Classes 8–102D → ▁▃▅▇STA011 Histogram Classes 8–102D → ⊢▭⊣STA012 Box plot Classes 9–112D → • ⋰STA013 Scatter plot Classes 9–12Graph → rSTA014 Correlation Classes 11–12Graph → ŷ = mx + cSTA015 Regression line Classes 11–12Graph → 6 × 6STA016 Sample space Classes 9–112D → HHTSTA017 Events Classes 9–112D → P(A ∪ B)STA019 Addition rule of probability Classes 10–122D → P(A | B)STA020 Conditional probability Classes 11–122D →

Extra Elliptic Curve Class 12Graph → Extra Rose Curve Classes 11–12Graph → Extra Lemniscate Class 12Graph → Extra Archimedean Spiral Classes 11–12Graph → Extra Cycloid Class 12Graph → Extra Cardioid Class 12Graph → ADV002 Combinatorics Classes 11–123D → ⁿPᵣADV001 Permutations Classes 11–12 + B.Tech3D → (a + b)ⁿADV003 Binomial theorem Classes 11–12 + B.Tech2D → P(k) ⇒ P(k+1)ADV004 Mathematical induction Classes 11–122D → T(n) = 2T(n−1) + 1ADV005 Recurrence relations Classes 11–12 + B.Tech3D → Re + ImADV006 Complex plane Classes 11–12Graph → |z|ADV007 Complex number modulus Classes 11–12Graph → arg zADV008 Complex number argument Classes 11–12Graph → z₁ z₂ADV009 Complex number operations Classes 11–12Graph → zⁿADV010 De Moivre theorem Class 12 + B.TechGraph → r∠θADV011 Polar form of complex numbers Classes 11–12Graph → dy/dx = f(x, y)ADV012 Differential equations Class 12 + B.TechGraph → dy/dt = −kyADV013 First-order differential equations Class 12 + B.TechGraph → y″ + ω²y = 0ADV014 Second-order differential equations Class 12 + B.TechGraph → L{f}(s)ADV015 Laplace transform introduction B.TechGraph → Σ sinADV016 Fourier series introduction B.TechGraph → ≈ ∫ADV017 Numerical approximation Class 12 + B.TechGraph → xₙ₊₁ = xₙ − f/f′ADV018 Newton-Raphson method Class 12 + B.TechGraph → KₙADV019 Graph theory vertices and edges Classes 11–12 + B.Tech2D → KönigsbergADV020 Euler and Hamilton paths Classes 11–12 + B.Tech2D →