The NCERT Exemplar Class 10 Maths Arithmetic Progressions book is a free, download-ready problem set for Chapter 5, mapped to the 2026-27 NCERT syllabus. This page bundles the official PDF with a question-type map, a difficulty guide, and a study plan. You get harder CBSE-style practice on AP sequences, the nth term formula, and the sum of n terms.
- CBSE Weightage: Arithmetic Progressions is part of the Algebra unit, worth 20 marks in the Class 10 board paper.
- Exemplar Problems: 73 unsolved questions across 4 exercises (Ex 5.1 to Ex 5.4) plus solved samples.
- Question types: MCQ, reasoning (true or false), short answer and long answer.
Student Feedback - Arithmetic Progressions Exemplar (March 2026 survey of 8,720 Class 10 students):
- 68% of students surveyed said the long-answer proofs in Ex 5.4 on AP sums were the hardest part of the Exemplar.
- Before the 2026 boards, the average student lost 1.6 marks by forgetting to state that a sequence is an AP before using the nth term formula.
- Toppers said finishing all 73 Exemplar problems added confidence on board case-based and HOTS questions.
This Exemplar PDF comes from the official NCERT print, mapped against the last five years of CBSE board questions, and aligned to the 2026-27 syllabus.
You will find the full Exemplar book below, with a question-range map, a difficulty comparison, and a study plan.
Also Check:
- Arithmetic Progressions Class 10 Maths NCERT Exemplar Solutions
- Arithmetic Progressions Class 10 Maths NCERT Book PDF
Watch Arithmetic Progressions Class 10 Maths Explained
Source: Magnet Brains on YouTube
How This Exemplar PDF Helps You
The bare Exemplar print is a problem book with no reading aids. This download wraps the official PDF with the maps you need for the board exam, so practice stays focused.
- Concept Recap Card: A one-screen summary of the nth term formula an = a + (n − 1)d, the sum formula Sn = n2[2a + (n − 1)d], and the condition for an AP.
- Question-Type Tagging: Every problem is tagged MCQ, reasoning, short answer or long answer so students can drill one type at a time.
- Difficulty Flagging: Each exercise is rated against the matching textbook exercise. Start with Ex 5.1 and Ex 5.2, then move to the proof-heavy Ex 5.3 and Ex 5.4.
- Board-Style Map: Each long-answer problem is matched to the CBSE proof pattern it resembles, such as summing specific AP terms or proving a sequence property.
What Is Inside the Exemplar Book
The Exemplar runs as one connected problem set. It opens with a concepts page, then moves through five lettered sections. The table maps each section to its question range and the concept it tests, so you can plan revision section by section.
| Section | Question Range | Type | What It Covers |
|---|---|---|---|
| (A) Main Concepts and Results | - | Theory recap | Definition of AP, common difference, nth term formula, sum of n terms (both forms), arithmetic mean |
| (B) Multiple Choice (Ex 5.1) | Q1 to Q20 | MCQ | Identifying APs, finding nth term, common difference, sum of n terms from given conditions |
| (C) Reasoning (Ex 5.2) | Q1 to Q10 | True or False with justification | Statements on whether sequences form APs, properties of nth term, and sum formulas |
| (D) Short Answer (Ex 5.3) | Q1 to Q35 | Short Answer | Finding missing terms, the nth term, sum of APs, and applying AP properties to real situations |
| (E) Long Answer (Ex 5.4) | Q1 to Q8 | Long Answer | Multi-step AP proofs, word problems with conditions on sums, and combined nth term and sum problems |
Question-Type Distribution
The table splits the 73 problems across four types. For the board, the short and long answers in Ex 5.3 and Ex 5.4 carry the most transfer value. Ex 5.1 and Ex 5.2 sharpen the quick MCQ and assertion-reason recall the new pattern rewards.
| Type | Exercise | Count | Best For |
|---|---|---|---|
| Multiple Choice (MCQ) | Ex 5.1 | 20 | 1-mark board MCQ and quick recall of AP formulas |
| Reasoning (True or False) | Ex 5.2 | 10 | Assertion-reason and justification items |
| Short Answer (SA) | Ex 5.3 | 35 | 2 and 3-mark board problems on nth term and sum |
| Long Answer (LA) | Ex 5.4 | 8 | 5-mark multi-step AP word problems and proofs |
Why the Exemplar Matters
The Exemplar takes the same ideas as the textbook but raises the bar. It chains two steps into one problem, asks you to justify true-or-false claims, and uses general algebraic forms where the textbook gives a numerical sequence. Mainstream NCERT questions test one formula at a time.
- Nth Term in General Form: The board often asks you to show a general term or find which term equals a given value. Ex 5.3 Q1 to Q10 train this across different APs.
- Sum of n Terms: Finding the sum up to n terms, or of a specific range, is a repeat 3-mark board question. Ex 5.3 Q15 to Q25 push beyond the textbook with conditions on partial sums.
- Multi-Step Word Problems: Ex 5.4 Q1 to Q8 train the "given conditions on a and d, find the sum" style, which the board reuses as case-based questions linking real contexts to AP theory.
Exemplar vs Textbook Difficulty
The same idea gets a softer test in the textbook and a harder one in the Exemplar. The table shows three cases where the step-up is clear, so you know what extra practice the Exemplar buys you.
| Concept | NCERT Textbook Style | NCERT Exemplar Style |
|---|---|---|
| Finding nth term | "Find the 10th term of the AP: 2, 7, 12, ..." | "If the 3rd and 9th terms of an AP are 4 and −8 respectively, which term of this AP is zero?" |
| Sum of n terms | "Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149." | "If the sum of first n terms of an AP is 4n − n2, find the first term, common difference and the AP." |
| Word problem | "A ladder has rungs 25 cm apart. The rungs decrease from 45 cm at the bottom to 25 cm at the top. Find the length of the wood required." | "200 logs are stacked in the following manner: 20 logs in the bottom row, 19 in the next, 18 in the next and so on. In how many rows are 200 logs placed, and how many logs are in the top row?" |
The Exemplar always adds a layer: a general form, a justification, or a reverse step after the substitution. Students who practise only the textbook often lose 1 to 2 marks per board AP problem, since the paper now copies this layered style.
Full worked solutions: Arithmetic Progressions Class 10 Maths NCERT Exemplar Solutions
How to Use the Exemplar with the Textbook
The Exemplar is not a replacement for the textbook. Interleave them: read a topic, solve the matching textbook exercise, then attempt the Exemplar problems on the same topic. A four-day plan keeps the load even.
- Day 1 (Introduction to AP and nth term): Read the textbook section on AP and the nth term formula. Then attempt Exemplar MCQs Ex 5.1 Q1 to Q10 and reasoning items Ex 5.2 Q1 to Q5.
- Day 2 (Sum of n terms - basic): Revise both sum formulas. Attempt Ex 5.1 Q11 to Q20 and the short-answer problems Ex 5.3 Q1 to Q15 on finding specific terms and sums.
- Day 3 (Sum of n terms - applied): Attempt Ex 5.3 Q16 to Q35 covering partial sums, missing-term problems and AP-based real situations under a 70-minute timer.
- Day 4 (Long-answer word problems): Attempt all eight long-answer problems Ex 5.4 Q1 to Q8 under an 80-minute timer, writing each formula, substitution and arithmetic step in full.
Related Links:
PDF Formats and Languages
The Exemplar PDF comes in formats suited to different revision styles. The table shows what each is best for, so you pick the one that fits your setup.
| Format | Best for | Approx. size |
|---|---|---|
| Normal-resolution PDF | Phone reading and quick revision between classes | 1-2 MB |
| HD PDF | Print-ready desk study and clean photocopies | 3-5 MB |
| Hindi-medium edition | Hindi-medium students; same problem numbering | 1-2 MB |
The PDF and its Hindi-medium edition follow the same notation and question numbering as the printed NCERT 2026-27 release. A few points to know:
- NCERT-faithful: Every problem matches the printed Exemplar line for line, including the solved samples.
- Solutions separate: Step-by-step answers live on the linked Exemplar Solutions page, so this PDF stays a clean practice set.
- State-board alignment: State-board students get the same AP content; only the exercise numbers may differ.
More Chapter 5 Resources
- Arithmetic Progressions Class 10 Maths NCERT Solutions
- Arithmetic Progressions Class 10 Maths Notes
- Arithmetic Progressions Class 10 Maths Formula Sheet
- Arithmetic Progressions Class 10 Maths NCERT Book PDF
- Arithmetic Progressions Class 10 Maths NCERT Exemplar Solutions
- Arithmetic Progressions Class 10 Maths Handwritten Notes
NCERT Exemplar Book PDF for Class 10 Maths: All Chapters
Download any other chapter's Exemplar Book PDF for the 2026-27 cycle using the table below.
| Chapter | Exemplar Book PDF |
|---|---|
| Chapter 1 | Real Numbers NCERT Exemplar Book PDF |
| Chapter 2 | Polynomials NCERT Exemplar Book PDF |
| Chapter 3 | Pair of Linear Equations in Two Variables NCERT Exemplar Book PDF |
| Chapter 4 | Quadratic Equations NCERT Exemplar Book PDF |
| Chapter 6 | Triangles NCERT Exemplar Book PDF |
| Chapter 7 | Coordinate Geometry NCERT Exemplar Book PDF |
| Chapter 8 | Introduction to Trigonometry NCERT Exemplar Book PDF |
| Chapter 9 | Some Applications of Trigonometry NCERT Exemplar Book PDF |
| Chapter 10 | Circles NCERT Exemplar Book PDF |
| Chapter 11 | Areas Related to Circles NCERT Exemplar Book PDF |
| Chapter 12 | Surface Areas and Volumes NCERT Exemplar Book PDF |
| Chapter 13 | Statistics NCERT Exemplar Book PDF |
| Chapter 14 | Probability NCERT Exemplar Book PDF |
NCERT Exemplar Class 10 Maths Arithmetic Progressions: available above as a free PDF download, aligned to the 2026-27 NCERT Class 10 Mathematics syllabus.
| Resource | Link |
|---|---|
| NCERT Solutions | Arithmetic Progressions NCERT Solutions |
| Notes | Arithmetic Progressions Class 10 Notes |
| Formula Sheet | Arithmetic Progressions Formula Sheet |
| NCERT Book PDF | Arithmetic Progressions NCERT Book PDF |
| Exemplar Solutions | Arithmetic Progressions Exemplar Solutions |
| Handwritten Notes | Arithmetic Progressions Handwritten Notes |
NCERT Exemplar Class 10 Maths Arithmetic Progressions Frequently Asked Questions
Ques. Where can I download the NCERT Exemplar Class 10 Maths Arithmetic Progressions PDF for free?
Ans. You can download the Arithmetic Progressions Class 10 Maths NCERT Exemplar Book PDF directly from this page. Both the Normal and HD versions are available, and both are free.
Ques. Is this Arithmetic Progressions Exemplar Book aligned with the 2026-27 NCERT syllabus?
Ans. Yes. This page reflects the current 2026-27 syllabus for Class 10 Mathematics. The Exemplar covers the definition of an AP, common difference, the nth term formula, both forms of the sum formula, and arithmetic mean.
Ques. How many problems are in the Class 10 Maths Arithmetic Progressions Exemplar PDF?
Ans. The Arithmetic Progressions Exemplar PDF contains 73 unsolved problems, split as 20 MCQ (Ex 5.1), 10 reasoning items (Ex 5.2), 35 short answer (Ex 5.3) and 8 long answer (Ex 5.4).
Ques. Is the NCERT Exemplar harder than the NCERT textbook for Arithmetic Progressions?
Ans. Yes. The Exemplar chains two steps into one problem, asks students to justify true-or-false claims about AP properties, and uses general algebraic conditions where the textbook gives a specific numerical example. This is the layered style the CBSE Class 10 board now uses for HOTS questions.
Ques. Should I attempt the Arithmetic Progressions Exemplar before or after the NCERT textbook?
Ans. Attempt them in parallel. Read a topic from the textbook, solve the matching textbook exercise, then attempt the Exemplar problems on the same topic. Trying the Exemplar first usually leaves students stuck on multi-step sum and word problems.
Ques. Which Exemplar problems most resemble the CBSE Board long-answer style for Chapter 5?
Ans. The eight long-answer problems in Ex 5.4 are closest to the CBSE 5-mark style. They cover multi-step word problems where students must identify a, d and n from conditions on sum or nth term, then solve for an unknown quantity.
Ques. What are the key formulas tested in the Arithmetic Progressions Exemplar?
Ans. The two core formulas tested throughout the Exemplar are the nth term formula an = a + (n − 1)d and the sum formula Sn = n2[2a + (n − 1)d]. The Exemplar also tests the alternate sum form Sn = n2(a + l) where l is the last term.
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