Vikas Mathematics Practical Book Std 10 Algebra answers explained chapter-wise with fully worked solutions for every activity type. Score full marks.
Vikas Mathematics Practical Book Std 10 Answers – Algebra (Part I): The Complete Worked-Solution Guide
If you’ve searched “Vikas Mathematics Practical Book Std 10 answers algebra,” you’re almost certainly staring at a practical file deadline with Linear Equations, Quadratic Equations, Arithmetic Progression, Financial Planning, Probability, or Statistics activities left half-done.
Here’s what actually works better than a copied PDF: knowing exactly which formula each activity is testing and having a fully worked example for that exact activity type in front of you. That’s what this guide gives you — a chapter-by-chapter map of the Algebra (Part I) practical book, plus a complete worked solution for one representative problem from every chapter, so you can mirror the method on your own activity numbers with full confidence.
Why This Book Matters for Your SSC Result
The Vikas Mathematics Practical Book for Std 10 (published by Vikas/Navneet) is built specifically around the Maharashtra SSC Board Class 10 syllabus. Class 10 Maths is split into two parts:
- Part I – Algebra: Linear Equations in Two Variables, Quadratic Equations, Arithmetic Progression, Financial Planning, Probability, Statistics
- Part II – Geometry: Similarity, Circles, Geometric Constructions, Coordinate Geometry, Trigonometry, Mensuration
The practical book mirrors this exact structure, chapter for chapter, so every activity you complete feeds directly into your internal assessment and semester exam marks — which is exactly why getting the method right (not just the final number) matters so much.
Chapter-Wise Breakdown: Algebra (Part I)
| Chapter | What the Activity Usually Tests |
|---|---|
| Linear Equations in Two Variables | Solving by graphical method, elimination, and substitution |
| Quadratic Equations | Factorisation, formula method, and nature of roots (discriminant) |
| Arithmetic Progression | Finding the nth term, sum of n terms, and common difference |
| Financial Planning | Simple/compound interest, GST, shares and dividends |
| Probability | Sample space, favourable outcomes, and basic event probability |
| Statistics | Mean, median, mode from grouped data, and cumulative frequency (ogive) |
A quick note before we go further: because this is a copyrighted textbook, we can’t reproduce the exact numbers printed in your specific edition’s answer key — those vary slightly between print runs anyway. What we can do, and what’s actually more useful, is walk through one fully solved example per chapter using the same method your activity expects, so you can apply it directly to your own numbers.
Detailed Worked Solutions – One Per Chapter
1. Linear Equations in Two Variables
Sample activity-style problem: Solve the pair of equations 2x + 3y = 12 and x − y = 1 using the elimination method.
Solution: From the second equation: x = y + 1
Substitute into the first equation: 2(y + 1) + 3y = 12 2y + 2 + 3y = 12 5y = 10 y = 2
Now substitute y = 2 back into x = y + 1: x = 3
Answer: x = 3, y = 2
Verification: 2(3) + 3(2) = 6 + 6 = 12 ✓ and 3 − 2 = 1 ✓
Method to remember: Isolate one variable from the simpler equation first, substitute it into the other, solve for the remaining variable, then back-substitute. Always verify by plugging both values into both original equations.
2. Quadratic Equations
Sample activity-style problem: Solve x² − 5x + 6 = 0 by factorisation, and state the nature of the roots using the discriminant.
Solution: Factorise: x² − 5x + 6 = (x − 2)(x − 3) = 0 So x = 2 or x = 3
Discriminant check: For ax² + bx + c = 0, D = b² − 4ac Here a = 1, b = −5, c = 6 D = (−5)² − 4(1)(6) = 25 − 24 = 1
Since D > 0 and is a perfect square, the roots are real, unequal, and rational.
Method to remember: Always find two numbers whose product equals a×c and whose sum equals b. If factorisation isn’t clean, switch to the quadratic formula x = [−b ± √D] / 2a — and always report the nature of the roots based on the sign of D.
3. Arithmetic Progression (AP)
Sample activity-style problem: Find the 15th term and the sum of the first 15 terms of the AP: 4, 9, 14, 19, …
Solution: First term a = 4, common difference d = 9 − 4 = 5
nth term formula: aₙ = a + (n − 1)d a₁₅ = 4 + (15 − 1)(5) = 4 + 70 = 74
Sum formula: Sₙ = n/2 [2a + (n − 1)d] S₁₅ = 15/2 [2(4) + (14)(5)] = 15/2 [8 + 70] = 15/2 (78) = 585
Method to remember: Always find a and d first before touching either formula — almost every AP activity fails at this step if d is calculated incorrectly.
4. Financial Planning
Sample activity-style problem: Find the compound interest on ₹8,000 for 2 years at 10% per annum, compounded annually.
Solution: Amount formula: A = P(1 + r/100)ⁿ A = 8000 (1 + 10/100)² A = 8000 (1.1)² A = 8000 × 1.21 A = ₹9,680
Compound Interest = A − P = 9680 − 8000 = ₹1,680
Method to remember: Calculate the amount first using the compound interest formula, then subtract the principal — don’t try to add up year-by-year interest unless the activity specifically asks for a year-wise breakup.
5. Probability
Sample activity-style problem: A die is rolled once. Find the probability of getting a number greater than 4.
Solution: Sample space S = {1, 2, 3, 4, 5, 6}, so n(S) = 6
Favourable outcomes (numbers greater than 4) = {5, 6}, so n(A) = 2
P(A) = n(A) / n(S) = 2/6 = 1/3
Method to remember: Always write out the full sample space first, then carefully list only the outcomes that satisfy the condition — most marks are lost from miscounting favourable outcomes, not from the formula itself.
6. Statistics
Sample activity-style problem: Find the mean of the following grouped data using the assumed mean method.
| Class Interval | Frequency (f) |
|---|---|
| 0–10 | 5 |
| 10–20 | 8 |
| 20–30 | 12 |
| 30–40 | 7 |
Solution: Midpoints (x): 5, 15, 25, 35 Assumed mean (A) = 25 (midpoint of the class with highest frequency) Deviations (d = x − A): −20, −10, 0, 10
| x | f | d = x − A | f×d |
|---|---|---|---|
| 5 | 5 | −20 | −100 |
| 15 | 8 | −10 | −80 |
| 25 | 12 | 0 | 0 |
| 35 | 7 | 10 | 70 |
Σf = 32, Σfd = −110
Mean = A + (Σfd / Σf) = 25 + (−110/32) = 25 − 3.44 = 21.56 (approx.)
Method to remember: Choosing the class with the highest frequency as your assumed mean keeps the arithmetic small and reduces calculation errors — that’s exactly why examiners reward this approach with full marks even when the final decimal is slightly off due to rounding.
The 4-Step Method to Apply This to Your Own Activity Numbers
- Match the activity to its chapter using the table above.
- Copy the exact method from the matching worked example — same formula, same order of steps.
- Substitute your own given values carefully, keeping units and signs consistent.
- Verify your final answer the same way we did above (back-substitution, discriminant sign check, or a quick sanity check on magnitude).
Common Mistakes That Cost Marks in Algebra Practicals
- Forgetting to verify linear equation solutions in both original equations.
- Skipping the discriminant statement in quadratic equation activities — examiners specifically look for the “nature of roots” line.
- Mixing up simple and compound interest formulas in Financial Planning.
- Listing the wrong sample space in Probability — always write S explicitly before counting favourable outcomes.
- Choosing an inconvenient assumed mean in Statistics, which multiplies arithmetic errors.
Where to Verify Your Final Numbers
Once you’ve solved an activity using the method above, cross-check using this order:
- Your own class teacher — fastest, and accounts for any edition-specific variation.
- The answer key printed at the back of your copy of the book.
- Your textbook’s solved examples for the same chapter, since the practical book activities are built directly on them.
- A study group, comparing methods rather than only final numbers.
Relying on scanned answer-key PDFs circulating online is risky for two reasons: the numbers frequently don’t match your specific print edition, and even when they do, copying the final answer without the working typically loses more than half the marks assigned to that activity.
Quick FAQ
Is Financial Planning part of Algebra or a separate chapter? It’s part of Algebra (Part I) in the Maharashtra SSC Board syllabus, covering simple interest, compound interest, GST, and shares/dividends.
Which Algebra chapter carries the most weight in the SSC board exam? Quadratic Equations and Arithmetic Progression together typically carry significant weight, but all six Algebra chapters are examined, so practical file accuracy across every chapter matters for internal marks.
Can I use the quadratic formula even when factorisation works? Yes — the quadratic formula always works, but factorisation is faster when the equation factorises cleanly. Learn to recognise which method suits which equation to save time.
What’s the fastest way to complete the Financial Planning practicals correctly? Identify whether the question is asking for simple interest, compound interest, or a share/dividend calculation first — each has a distinct formula, and mixing them up is the single biggest source of errors in this chapter.
Final Word
The real goal of the Vikas Mathematics Practical Book isn’t just to fill in numbers — it’s to make sure you can walk into your SSC board exam and reproduce these same methods under time pressure, without a book in front of you. Work through the six worked examples above, apply the same steps to your own activity numbers, and verify carefully. That’s a stronger, more exam-ready result than any copied answer key could ever give you.
