Class 10 Maths Half-Yearly Exam: Chapter-Wise Preparation Guide
This article covers the important chapters, key concepts, and exam-focused questions to help students prepare effectively. A quick revision of the high-weightage chapters is recommended.
CBSE does not conduct half-yearly exams. The syllabus and chapters can differ from school to school. So, confirm with your school or class teacher which chapters are coming up. You might already know this. The chapters listed below are commonly included in most schools.
Chapter 1: Real Numbers
This is one of the initial chapters and is very important for scoring marks.
From previous year analysis:
1- to 2-mark questions come consistently from this chapter every year.
Types of questions:
1-mark MCQs
2-mark very short answer questions
What you need to prepare (only these two things):
Fundamental Theorem of Arithmetic
You should know how to find HCF and LCM using the prime factorization method.
Proof of Irrational Numbers
Questions like “Prove that √2 is irrational, √3 is irrational, √5 is irrational, √8 is irrational, etc.”
This type of question comes in both half-yearly and board exams.
Note: Euclid’s Division Lemma is no longer in the syllabus, so you don’t need to study it.
Chapter 2: Polynomials (Bahupad)
From analysis of previous half-yearly papers:
3- to 5-mark questions come consistently from this chapter.
This chapter is the base of algebra. Chapter 4 (Quadratic Equations) is also based on this. If you understand polynomials well, quadratic equations will become easy.
What you need to prepare:
Relationship between Zeroes and Coefficients
Sum of zeroes = –b/a
Product of zeroes = c/a
Division Algorithm
One zero is given; find the other zero(s).
Prepare only these two things properly.
Chapter 3: Pair of Linear Equations in Two Variables
Weightage: 3 to 5 marks consistently.
This chapter is especially important because case-based/application-based questions (real-life situations) mostly come from here (ticket prices, ages, time-speed-distance, cost problems, etc.).
What you must prepare:
Substitution Method and Elimination Method
(The cross-multiplication method is no longer in the syllabus.)
Graphical Method
(Plotting the lines on graph paper)
Consistency of equations
(Conditions for unique solution, no solution, and infinitely many solutions using a1/a2, b1/b2, and c1/c2)
Word problems and case-based questions are very common from this chapter.
Chapter 4: Quadratic Equations (Highest Weightage Chapter)
This is the highest weightage chapter.
Up to 8-mark questions have come from this single chapter in previous papers.
Questions can come as:
Case-based questions
Long answer questions (Section E)
MCQs and short answers
What you must prepare:
Factorization Method
Quadratic Formula (and Discriminant D = b² – 4ac)
Nature of Roots
(Based on discriminant: two distinct real roots, equal roots, or no real roots)
Application-based questions like
Age problems
Train problems
Aeroplane problems
Boat and stream
Time and work
All these come from this chapter. Prepare this chapter very thoroughly.
Chapter 5: Arithmetic Progression (AP)
Weightage: 5 to 6 marks consistently.
Most questions are case-based/application-based.
Examples: Stadium seats, salary increment, savings in a piggy bank, etc.
Two most important formulas (backbone of the chapter):
nth term:
\( a_n = a + (n-1)d \)
Sum of n terms:
\( S_n = \frac{n}{2} [2a + (n-1)d] \)
or
\( S_n = \frac{n}{2} (a + l) \)
Practice as many questions as possible on these two formulas.
Chapter 6: Triangles (High Weightage – Geometry)
This also falls under high-weightage chapters (the geometry section carries good marks).
Up to 8-mark questions have appeared.
Most questions are proof-writing / “show that” type.
What you must prepare:
Similarity Criteria of Triangles (AAA, SSS, SAS, etc.)
Basic Proportionality Theorem (BPT / Thales’ Theorem)
– You must know how to write the complete proof properly.
Pythagoras’ Theorem
– Full proof writing (Given, Construction, To Prove, Proof—step by step).
In proof questions, marks are given for every step (Given, Construction, Statements, Proof). So learn the proper format of writing theorems.
Quick Summary / Strategy for Half-Yearly
Highest Weightage Chapters (Prepare these first):
Quadratic Equations
Triangles
Arithmetic Progression
Pair of Linear Equations
Then prepare:
Polynomials
Real Numbers
Priority Order for Maximum Marks:
Quadratic Equations
Triangles
Arithmetic Progression
Pair of Linear Equations
Polynomials
Real Numbers
Confirm the exact chapters with your school teacher, as the portion can vary slightly from school to school.
Frequently Asked Questions (FAQs)
1. How many marks can come from quadratic equations in the half-year?
Up to 8-mark questions have come from the Quadratic Equations chapter alone in previous years’ papers.
2. Is Real Numbers an important chapter for Half Yearly?
Yes, 1–2-mark questions come consistently every year from Real Numbers, mainly HCF-LCM and proof of irrational numbers.
3. What are the most important topics in Polynomials for Half Yearly?
Relationship between zeroes and coefficients, and the division algorithm (finding other zeroes when one is given).
4. Which methods should I prepare in Pair of Linear Equations?
You should prepare the substitution method, elimination method, and graphical method and check consistency of equations.
5. Are case-based questions important in Class 10 Maths Half Yearly?
Yes, case-based and application-based questions are very common, especially from pairs of linear equations, quadratic equations, and arithmetic progression.
6. What are the most important formulas in arithmetic progression?
The two most important formulas are
- nth term: \( a_n = a + (n-1)d \)
- Sum of n terms: \( S_n = \frac{n}{2}[2a + (n-1)d] \)
7. Which theorems are most important in the Triangles chapter?
Basic Proportionality Theorem (BPT/Thales’ Theorem), Similarity Criteria, and Pythagoras Theorem (with full proof writing).
8. Is Euclid’s Division Lemma still in the Class 10 syllabus?
No, Euclid’s Division Lemma has been removed from the syllabus. You don’t need to study it.
9. In what order should I prepare chapters for maximum marks?
Recommended priority order:
- Quadratic Equations
- Triangles
- Arithmetic Progression
- Pair of Linear Equations
- Polynomials
- Real Numbers
10. Do half-yearly chapters remain the same in every school?
No. Half-yearly exams are conducted by schools, so the portion can vary. Always confirm the exact chapters with your class teacher.
