Class 10 Mathematics Master Hub
Complete Syllabus Coverage: Every Chapter, Every Activity & Proof Across All 14 Chapters (Zero Exclusion)
Chapter 1: Real Numbers
Activity 1.1: Fundamental Theorem of Arithmetic (HCF & LCM)
Compute prime factorisation products and verify HCF × LCM = Product of two numbers.
Activity 1.2: Irrationality Proof Demonstrator (Proof that sqrt(2) is irrational)
Step-by-step logical contradiction walkthrough.
Assuming sqrt(2) = a/b leads to co-prime factor contradiction. Proven irrational!
Chapter 2: Polynomials
Activity 2.1: Parabolic Zeroes Visualizer
Observe parabolic curves intersecting the x-axis for quadratic polynomials.
Discriminant Status:
Parabola intersects x-axis at 2 distinct points.
Activity 2.2: Relationship Between Zeroes and Coefficients
Verify sum of zeroes (-b/a) and product of zeroes (c/a).
Sum = -b/a and Product = c/a verified successfully.
Chapter 3: Pair of Linear Equations in Two Variables
Activity 3.1: Graphical Consistency & Ratio Analyzer
Check ratios a1/a2, b1/b2, c1/c2 for intersecting, parallel, or coincident lines.
Consistent / Unique Solution (Intersecting Lines)
Activity 3.2: Algebraic Methods (Substitution & Elimination Solvers)
Solve simultaneous linear equations step by step.
Solution found: x = 2, y = 3
Chapter 4: Quadratic Equations
Activity 4.1: Discriminant & Nature of Roots Visualizer
Determine root types based on D = b^2 - 4ac.
Activity 4.2: Completing the Square Method Explorer
Transform quadratic expressions into square binomial form.
Expressed in (x - p)^2 = q form successfully.
Chapter 5: Arithmetic Progressions
Activity 5.1: AP Term & Sum Formula Generator
Compute nth term and sum of first n terms.
Chapter 6: Triangles
Activity 6.1: Basic Proportionality Theorem (Thales Theorem Proof)
Verify that if a line is drawn parallel to one side of a triangle, it divides the other two sides in the same ratio.
AD/DB = AE/EC (Proportions verified)
Activity 6.2: Similarity Criteria Verification (AAA, SSS, SAS)
Check angle and side proportionality for similar triangles.
Corresponding angles equal & proportional sides verified!
Chapter 7: Coordinate Geometry
Activity 7.1: Distance Formula & Section Formula Calculator
Compute distances and internal division coordinates.
Distance = sqrt((5-2)^2 + (7-3)^2) = 5 units
Activity 7.2: Area of Triangle in Cartesian Plane
Calculate polygon areas using coordinate formula vertices.
Area = 0.5 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)| calculated successfully.
Chapter 8: Introduction to Trigonometry
Activity 8.1: Trig Ratios & Standard Angle Table
Explore sine, cosine, and tangent ratios across 0°, 30°, 45°, 60°, 90°.
Angle:
sin(45°) = 0.707 (1/sqrt(2)) | cos(45°) = 0.707 | tan(45°) = 1.0
Activity 8.2: Trigonometric Identities Verifier (sin^2 θ + cos^2 θ = 1)
Check fundamental trigonometric identities.
sin^2(θ) + cos^2(θ) = 1 verified for all angles!
Chapter 9: Some Applications of Trigonometry
Activity 9.1: Heights and Distances (Angle of Elevation & Depression)
Solve tower height and shadow problems using right triangle trigonometry.
Height = 30 × tan(30°) = 17.32 meters
Chapter 10: Circles
Activity 10.1: Tangent Theorem Proof (Tangent is perpendicular to radius)
Verify tangent properties and length equality from external points.
Lengths of tangents drawn from an external point to a circle are equal.
Chapter 11: Areas Related to Circles
Activity 11.1: Sector Area & Segment Area Calculator
Compute sector area and arc lengths from central angle theta.
Chapter 12: Surface Areas and Volumes
Activity 12.1: Combined Solid Combinations (Cone on Hemisphere, Frustum)
Calculate surface areas and volumes of combined 3D shapes.
Total Volume = Volume of Cone + Volume of Hemisphere computed accurately.
Chapter 13: Statistics
Activity 13.1: Mean, Median, and Mode for Grouped Data
Apply empirical relationship: 3 Median = Mode + 2 Mean.
3(Median) = Mode + 2(Mean) relation verified successfully.
Chapter 14: Probability
Activity 14.1: Theoretical Probability Experiments (Cards, Dice, Coins)
Compute P(E) = Number of favorable outcomes / Total outcomes.
P(Face Card) = 12 / 52 = 3 / 13