CHAPTER TEST - ICSE MATHEMATICS - Probability, Quadratic Equations, Factorisation, and Trigonometry:

 "TEST – ICSE MATHEMATICS - X", which covers topics in Probability, Quadratic Equations, Factorisation, and Trigonometry:

🧮 Topics Covered

• Probability:

  • Calculating probabilities based on card draws and coin tosses.
  • Real-life scenarios like games and playing cards used to frame questions.

• Quadratic Equations:

  • Solving quadratic equations.
  • Finding conditions for real and equal roots.
  • Application-based problems involving area and tile dimensions.

• Factorisation:

  • Using factor theorem to find unknown coefficients.
  • Polynomial division and complete factorisation.

• Trigonometry:

  • Proving identities involving cotangent, tangent, sine, cosine, secant, and cosecant.
  • Complex expressions simplified to standard trigonometric identities.

📝 Sample Questions

• Probability of winning different prizes based on number card properties.
• Proving trigonometric identities like: [ \frac{(\cot A + \tan A - 1)(\sin A + \cos A)}{\sin^3 A + \cos^3 A} = \sec A \cdot \csc A ]
• Solving and factorising polynomials such as: [ 2x^3 - 7x^2 + kx - 2 \quad \text{(given that } x - 2 \text{ is a factor)} ]
• Finding the value of ( x ) in a tile-based floor problem.
• Probability of drawing a specific card from a reduced deck.

⏱️ Format

• Total Marks: 40
• Duration: 1 hour 30 minutes
• Each question is marked individually, ranging from 1 to 4 marks.

HARDER PROBLEMS FOR CLASSES VIII- X Algebra

This collection is designed for secondary school students (Classes VIII–X) preparing for Math Olympiads and competitive exams. It brings together a variety of challenging algebra problems that go beyond routine textbook exercises and test deeper understanding, creativity, and problem-solving skills.

👉 Key Features of the Set

• Classical Identities – Problems based on famous results such as Sophie Germain’s identity.

• Equation Manipulation – Creative use of algebraic transformations and substitutions.

• Inequalities & Rationalization – Strengthening algebraic reasoning with proofs and simplifications.

• Number Theory Links – Problems connecting algebra with concepts of divisibility and composite numbers.

• Summations & Series – Telescoping series and rational number expansions.

• Olympiad Flavor – Each problem is selected to stimulate lateral thinking and develop advanced techniques.

This set not only sharpens algebraic manipulation but also trains students to recognize patterns, symmetry, and hidden structures in problems—an essential skill for Olympiads and higher-level mathematics.

CHAPTER TEST – ICSE Mathematics – Class X - Inequality, Ratio and Proportion, Section Formula, and Banking

Title: TEST – ICSE Mathematics – Class X

Chapters Covered: Inequality, Ratio and Proportion, Section Formula, and Banking
Full Marks: 40
Time: 1 hour 30 minutes

Structure:

• Total Questions: 15

• Marks Distribution:

  • Questions 1–6: Short answer, 1 mark each (concept recall and direct application).

  • Questions 7–8: Short problems, 3 marks each (multi-step reasoning).

  • Questions 9–15: Long problems, 4 marks each (detailed computation or proof).

Topics Tested:

• Solving and representing inequalities on a number line

• Ratios, continued proportion, fourth proportion

• Coordinate geometry: section formula, trisection points, centroid

• Proportion and algebraic identities (Componendo and Dividendo)

• Banking applications: recurring deposit calculations

• Determining numbers to make quantities proportional

Format:

• Mix of fill-in-the-blank, solve-and-show, and prove type questions

• Some require graphical representation of inequalities on a number line

• Involves both theoretical proofs and practical application problems