In short: Algebra and Trigonometry together carry 35 to 40 marks in the CBSE Class 10 Maths paper, making them the most important topics for scoring well. Master the standard question types in Quadratic Equations and Trigonometric Identities, practice Arithmetic Progressions until the formulas are automatic, and solve at least 50 problems from each chapter to build speed and accuracy.
If you want to score high in CBSE Class 10 Maths, Algebra and Trigonometry are where you win or lose. These two areas account for nearly half the paper, and unlike some other topics, they reward practice directly. The more problems you solve, the faster and more accurate you become.
This guide covers every chapter in these two areas with specific strategies, common mistakes, and practice tips.
Marks Distribution: Why These Chapters Matter
Based on the CBSE Class 10 Maths paper pattern, here is the typical marks distribution:
Algebra chapters:
- Polynomials (Chapter 2): 5 to 7 marks
- Pair of Linear Equations in Two Variables (Chapter 3): 7 to 8 marks
- Quadratic Equations (Chapter 4): 7 to 8 marks
- Arithmetic Progressions (Chapter 5): 7 to 8 marks
Trigonometry chapters:
- Introduction to Trigonometry (Chapter 8): 7 to 8 marks
- Some Applications of Trigonometry (Chapter 9): 5 to 6 marks
Combined, these chapters carry approximately 38 to 45 marks out of 80. Getting strong in these areas alone can take your Maths score from average to excellent.
Chapter 2: Polynomials
Polynomials sets the foundation for Quadratic Equations. The board exam typically asks 1 to 2 questions on the relationship between zeroes and coefficients.
Practice Strategy
The question format is predictable: given a quadratic polynomial, find the zeroes and verify the relationship.
- Factorize the polynomial to find zeroes
- Calculate sum of zeroes and product of zeroes
- Verify using the formulas: sum = -b/a, product = c/a
Practice 15 to 20 problems of this type. Once you have the pattern down, these questions take under 3 minutes each.
Common Mistakes
- Forgetting to verify the relationship after finding the zeroes (verification carries marks)
- Sign errors when calculating -b/a
Chapter 3: Pair of Linear Equations in Two Variables
This chapter tests your ability to solve two equations simultaneously.
Practice Strategy
The board paper almost always includes one word problem, typically in the 3-mark or 5-mark section. The trick is converting the word problem into equations.
Practice these word problem types:
- Age-related problems
- Fraction problems
- Speed, distance, and time problems
- Number problems
For each type, solve at least 10 problems. After 40 problems, you will recognize the pattern instantly.
Common Mistakes
- Choosing the wrong method (use elimination for most exam questions since it is faster)
- Errors in forming equations from word problems
Chapter 4: Quadratic Equations
Quadratic Equations is one of the highest-weightage chapters and appears in every board paper without exception.
What to Master
- Standard form of quadratic equation (ax² + bx + c = 0)
- Solving by factorization (splitting the middle term)
- Solving using the quadratic formula
- Nature of roots using discriminant (D = b² - 4ac)
- Word problems leading to quadratic equations
Practice Strategy
Factorization (splitting the middle term): This is the most frequently tested skill. Practice 30 problems minimum. The key is finding two numbers that multiply to give a×c and add up to b.
Quadratic formula: Memorize it perfectly: x = (-b ± √(b² - 4ac)) / 2a. Practice applying it to at least 15 problems where factorization is not straightforward.
Nature of roots: Three cases based on discriminant:
- D > 0: Two distinct real roots
- D = 0: Two equal real roots
- D < 0: No real roots
Board questions often ask: "For what value of k does the equation have equal roots?" To solve, set D = 0 and solve for k.
Word problems: Common types include area problems, consecutive number problems, and speed-time problems. Solve 15 to 20 word problems from NCERT and previous year papers.
Keep all your formulas organized with our CBSE Class 10 Maths formulas complete list for quick revision.
Common Mistakes
- Forgetting to check if the root satisfies the original context (negative lengths or speeds are not valid)
- Sign errors when substituting into the quadratic formula
- Not writing the equation in standard form before solving
Chapter 5: Arithmetic Progressions
AP is a very scoring chapter because the question types are limited and predictable.
What to Master
- nth term formula: an = a + (n-1)d
- Sum of first n terms: Sn = n/2 × [2a + (n-1)d] or Sn = n/2 × (a + l)
- Finding a, d, n, or Sn when other values are given
- Word problems involving AP patterns
Practice Strategy
Master the two formulas first. Write them 10 times from memory. Then solve 5 problems using each formula.
Common board question types:
- Find the nth term of a given AP
- Find the number of terms in an AP
- Find the sum of first n terms
- Find the value of k if three terms are in AP
- Word problems: seating arrangements, savings patterns, distance patterns
The "find the value of k" question appears in almost every paper. If a, b, c are in AP, then 2b = a + c. This simple relationship solves many problems quickly.
Common Mistakes
- Confusing the nth term formula with the sum formula
- Using the wrong value of n (the number of terms, not the last term)
- Not checking whether the sequence given is actually an AP before applying the formula
Chapter 8: Introduction to Trigonometry
Trigonometry is where many students panic, but the chapter is actually very structured and formula-driven.
What to Master
- Trigonometric ratios: sin, cos, tan, cosec, sec, cot
- Values at standard angles: 0°, 30°, 45°, 60°, 90°
- Trigonometric identities:
- sin²θ + cos²θ = 1
- 1 + tan²θ = sec²θ
- 1 + cot²θ = cosec²θ
- Proving trigonometric identities
Practice Strategy
Step 1: Memorize the value table for sin, cos, and tan at 0°, 30°, 45°, 60°, and 90°. For sin, the values follow the pattern: √0/2, √1/2, √2/2, √3/2, √4/2. Simplify these.
Step 2: For proving identities, always start from the more complex side. Convert everything into sin and cos, then simplify.
Step 3: Practice at least 25 identity proofs. Common strategies include converting tan to sin/cos, using sin²θ + cos²θ = 1 to substitute, and taking LCM when fractions are involved.
Common Mistakes
- Assuming sin(A+B) = sinA + sinB (this is wrong)
- Not starting from the correct side in proofs
- Forgetting to write the standard angle values correctly (especially for cos, which decreases from 1 to 0)
Chapter 9: Some Applications of Trigonometry
This chapter applies trigonometric ratios to real-world problems involving heights and distances.
What to Master
- Angle of elevation and angle of depression
- Problems involving one triangle (single observation point)
- Problems involving two triangles (two observation points)
- Applications with buildings, towers, and poles
Practice Strategy
For every problem, draw the diagram first. This is non-negotiable. A clear diagram shows you which trigonometric ratio to use.
Standard problem types: finding the height of a tower given the angle and distance, finding the distance from the base given height and angle, problems with two observation points, and problems involving angle of depression.
Practice 20 problems with diagrams. After 20 problems, the patterns become obvious.
Common Mistakes
- Not drawing the diagram (this leads to using the wrong ratio)
- Confusing angle of elevation with angle of depression
- Not rationalizing the denominator when the answer involves surds
- Forgetting to add the height of the observer when stated in the problem
Revision and Practice Plan
8 weeks before the exam:
- Weeks 1 to 2: Complete Polynomials and Linear Equations. Solve all NCERT exercises.
- Weeks 3 to 4: Complete Quadratic Equations and AP. Focus on word problems.
- Weeks 5 to 6: Complete both Trigonometry chapters. Practice 50 problems total.
- Weeks 7 to 8: Solve previous year question papers and CBSE sample papers. Focus on Algebra and Trigonometry questions specifically.
Last week: Revise formulas daily. Solve 10 mixed problems per day from all chapters. Do not attempt new types of problems; focus on speed and accuracy with familiar patterns.
For revision techniques that help with formula retention, read about science-backed study techniques for students, including spaced repetition and active recall methods.
Practice Maths with Padhaao
Padhaao provides chapter-wise practice for every CBSE Class 10 Maths topic. Use the Quiz mode for quick concept checks, Exam Practice for board-style problems with step-by-step solutions, and Important Questions for the most frequently asked problems. Three chapters are free every day, giving you focused daily practice in the areas that matter most.
Frequently Asked Questions
How many problems should I solve daily in Algebra and Trigonometry?
Aim for 10 to 15 problems per day, taking about 60 to 90 minutes. Quality matters more than quantity. Over 8 weeks, this adds up to over 500 problems, which is more than enough for board exam mastery.
Is the quadratic formula or factorization better for board exams?
Use factorization when the middle term splits easily. Use the quadratic formula when factorization is not obvious. For "nature of roots" questions, you must use the discriminant. Practice both methods.
How do I remember trigonometric values for all standard angles?
Use the pattern trick: for sin 0° to sin 90°, the values are √0/2, √1/2, √2/2, √3/2, √4/2 (which simplify to 0, 1/2, √2/2, √3/2, 1). For cos, reverse the order. For tan, divide sin values by cos values. Practice writing the complete table from memory every day for 2 weeks, and it will become automatic.
What type of trigonometry questions carry the most marks?
Proving trigonometric identities and height-and-distance application problems carry the most marks (typically 3 to 5 marks each). These two question types appear in almost every board paper. Master identity proofs by practicing the techniques of converting to sin/cos and using standard identities. For application problems, always draw the diagram first.
How do I avoid silly mistakes in Algebra during the exam?
Three habits help: re-read the question after solving to check you answered what was asked, substitute your answer back into the original equation to verify, and write each step clearly instead of calculating mentally.
Good luck with your preparation.
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