In short: Maharashtra SSC Class 10 Maths has two papers — Algebra (Paper I, 40 marks) and Geometry (Paper II, 40 marks). Together with 20 marks of internal assessment, the total is 100. The SSC board has moved to a more competency-based format with shorter questions and more objective items. This post lists every formula you need for both papers — organized by chapter, mapped to the new paper structure. Print this and keep it next to your notebook during revision.
Paper Structure — New Format
The Maharashtra Board SSC Maths exam follows this pattern for 2027:
Paper I: Algebra (40 marks)
| Section | Question Type | Marks |
|---|---|---|
| Q.1 | MCQs (4 × 1) | 4 |
| Q.2 | Very short answers (4 × 1) | 4 |
| Q.3 | Short answers (any 4 of 5) (4 × 2) | 8 |
| Q.4 | Short answers (any 3 of 4) (3 × 3) | 9 |
| Q.5 | Long answers (any 3 of 4) (3 × 4) | 12 |
| Q.6 | Activity-based (any 1 of 2) (1 × 3) | 3 |
| Total | 40 |
Paper II: Geometry (40 marks) — Same structure.
Your formula knowledge directly maps to Sections Q.3–Q.5, which carry 29 marks combined. The Maharashtra SSC model paper 2027 shows the exact question distribution.
Algebra Formulas (Paper I)
Chapter 1: Linear Equations in Two Variables
| Formula / Method | Expression |
|---|---|
| Standard form | a₁x + b₁y = c₁; a₂x + b₂y = c₂ |
| Elimination method | Multiply equations to make coefficients equal, subtract |
| Substitution method | Express one variable, substitute in other equation |
| Graphical method | Plot both lines; intersection = solution |
| Consistent (unique) | a₁/a₂ ≠ b₁/b₂ |
| Inconsistent (no solution) | a₁/a₂ = b₁/b₂ ≠ c₁/c₂ |
| Dependent (infinite) | a₁/a₂ = b₁/b₂ = c₁/c₂ |
| Cross-multiplication | x/(b₁c₂−b₂c₁) = y/(c₁a₂−c₂a₁) = 1/(a₁b₂−a₂b₁) |
Chapter 2: Quadratic Equations
| Formula | Expression |
|---|---|
| Standard form | ax² + bx + c = 0 (a ≠ 0) |
| Quadratic formula | x = [−b ± √(b²−4ac)] / 2a |
| Discriminant | D = b² − 4ac |
| Two distinct real roots | D > 0 |
| Two equal real roots | D = 0 |
| No real roots | D < 0 |
| Sum of roots | α + β = −b/a |
| Product of roots | αβ = c/a |
Chapter 3: Arithmetic Progression
| Formula | Expression |
|---|---|
| nth term | aₙ = a + (n−1)d |
| Sum of n terms | Sₙ = n/2 [2a + (n−1)d] or Sₙ = n/2 (a + l) |
| Common difference | d = aₙ₊₁ − aₙ |
| Arithmetic mean | AM = (a + b)/2 |
| Three in AP | a−d, a, a+d |
Chapter 4: Financial Planning
| Formula | Expression |
|---|---|
| Simple interest | SI = PNR/100 |
| Compound interest | A = P(1 + r/100)ⁿ |
| Amount | A = P + I |
| GST on selling price | GST amount = (rate/100) × selling price |
| Income tax (basic) | Tax = applicable rate × (income − deductions − exemptions) |
| Shares: dividend | Dividend = (face value × rate of dividend)/100 × number of shares |
| Shares: return on investment | (annual income / total investment) × 100 |
Chapter 5: Probability
| Formula | Expression |
|---|---|
| Probability of event | P(E) = n(E)/n(S) |
| Complement | P(E') = 1 − P(E) |
| Range | 0 ≤ P(E) ≤ 1 |
| Certain event | P(E) = 1 |
| Impossible event | P(E) = 0 |
| Two dice outcomes | Total = 36 |
| Cards: total | 52 cards; 4 suits × 13 each |
Chapter 6: Statistics
| Formula | Expression |
|---|---|
| Mean (direct) | x̄ = Σfᵢxᵢ / Σfᵢ |
| Mean (assumed mean) | x̄ = A + Σfᵢdᵢ/Σfᵢ |
| Mean (step deviation) | x̄ = A + h(Σfᵢuᵢ/Σfᵢ) |
| Median | Median = l + [(n/2 − cf)/f] × h |
| Mode | Mode = l + [(f₁ − f₀)/(2f₁ − f₀ − f₂)] × h |
| Standard deviation | σ = √[Σfᵢ(xᵢ − x̄)²/N] |
| Variance | σ² = Σfᵢ(xᵢ − x̄)²/N |
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Geometry Formulas (Paper II)
Chapter 1: Similarity
| Formula | Expression |
|---|---|
| BPT (Thales theorem) | If DE ∥ BC in △ABC, then AD/DB = AE/EC |
| Similar triangles | Corresponding sides proportional, corresponding angles equal |
| Area ratio | Area(△₁)/Area(△₂) = (side₁/side₂)² |
| Pythagoras theorem | Hypotenuse² = Base² + Height² |
| 30-60-90 triangle | Sides in ratio 1 : √3 : 2 |
| 45-45-90 triangle | Sides in ratio 1 : 1 : √2 |
Chapter 2: Pythagoras Theorem
| Theorem / Application | Statement |
|---|---|
| Pythagoras | In right △, AC² = AB² + BC² |
| Converse | If AC² = AB² + BC², triangle is right-angled at B |
| Apollonius theorem | AB² + AC² = 2(AD² + BD²) where D is midpoint of BC |
| Geometric mean in right △ | BD² = AD × DC (altitude on hypotenuse) |
Chapter 3: Circle
| Formula | Expression |
|---|---|
| Tangent-radius | Tangent ⊥ radius at point of contact |
| Tangent lengths | PA = PB (tangents from external point P) |
| Tangent-secant | PA² = PB × PC |
| Secant-secant | PA × PB = PC × PD |
| Angle in semicircle | 90° |
| Cyclic quadrilateral | Opposite angles sum to 180° |
| Tangent-chord angle | = ½ × intercepted arc |
Chapter 4: Geometric Constructions
Construction-based (no formulas, but key methods):
- Division of line segment in given ratio
- Construction of triangle similar to given triangle (scale factor)
- Construction of tangent to circle from external point
Chapter 5: Coordinate Geometry
| Formula | Expression |
|---|---|
| Distance formula | d = √[(x₂−x₁)² + (y₂−y₁)²] |
| Section formula (internal) | P = [(mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n)] |
| Midpoint | M = [(x₁+x₂)/2, (y₁+y₂)/2] |
| Slope | m = (y₂−y₁)/(x₂−x₁) |
| Slope-intercept form | y = mx + c |
| Two-point form | (y−y₁)/(x−x₁) = (y₂−y₁)/(x₂−x₁) |
| Parallel lines | m₁ = m₂ |
| Perpendicular lines | m₁ × m₂ = −1 |
| Area of triangle | ½ |
Chapter 6: Trigonometry
| Identity / Ratio | Expression |
|---|---|
| sin θ | Opposite / Hypotenuse |
| cos θ | Adjacent / Hypotenuse |
| tan θ | Opposite / Adjacent = sin θ / cos θ |
| cosec θ | 1/sin θ |
| sec θ | 1/cos θ |
| cot θ | 1/tan θ = cos θ / sin θ |
| Pythagorean identity 1 | sin²θ + cos²θ = 1 |
| Pythagorean identity 2 | 1 + tan²θ = sec²θ |
| Pythagorean identity 3 | 1 + cot²θ = cosec²θ |
| Complementary angles | sin(90°−θ) = cosθ; tan(90°−θ) = cotθ |
Standard Angle Values:
| θ | 0° | 30° | 45° | 60° | 90° |
|---|---|---|---|---|---|
| sin | 0 | ½ | 1/√2 | √3/2 | 1 |
| cos | 1 | √3/2 | 1/√2 | ½ | 0 |
| tan | 0 | 1/√3 | 1 | √3 | ∞ |
Chapter 7: Mensuration
| Shape | Formula |
|---|---|
| Area of triangle | ½ × base × height; √[s(s−a)(s−b)(s−c)] (Heron's) |
| Area of circle | πr² |
| Circumference | 2πr |
| Area of sector | (θ/360) × πr² |
| Arc length | (θ/360) × 2πr |
| Area of segment | Area of sector − Area of triangle |
| CSA of cylinder | 2πrh |
| TSA of cylinder | 2πr(r + h) |
| Volume of cylinder | πr²h |
| CSA of cone | πrl (l = slant height = √(r²+h²)) |
| TSA of cone | πr(r + l) |
| Volume of cone | (1/3)πr²h |
| Surface area of sphere | 4πr² |
| Volume of sphere | (4/3)πr³ |
| CSA of frustum | π(r₁ + r₂)l |
| Volume of frustum | (πh/3)(r₁² + r₂² + r₁r₂) |
Formula-to-Paper Mapping
Here's which formulas map to which paper and approximate marks:
| Chapter Group | Paper | Approximate Marks | Key Formulas to Prioritize |
|---|---|---|---|
| Quadratic Equations | Algebra (I) | 6–8 | Quadratic formula, discriminant |
| AP | Algebra (I) | 5–6 | nth term, sum of n terms |
| Statistics | Algebra (I) | 5–6 | Mean, median, mode |
| Probability | Algebra (I) | 3–4 | P(E) = n(E)/n(S) |
| Similarity + Pythagoras | Geometry (II) | 8–10 | BPT, area ratio, Pythagoras |
| Circle | Geometry (II) | 6–8 | Tangent properties |
| Coordinate Geometry | Geometry (II) | 6–8 | Distance, section, slope |
| Trigonometry | Geometry (II) | 6–8 | Identities, standard values |
| Mensuration | Geometry (II) | 6–8 | Volume, surface area combinations |
For more on the Maharashtra SSC paper structure and strategy, see the Maharashtra SSC model paper 2027 analysis.
Common Mistakes in Maharashtra SSC Maths
| Mistake | Impact |
|---|---|
| Forgetting to write "units" in final answer (cm², m³, etc.) | 0.5 marks lost per question |
| Using wrong section formula (internal vs external) | Full marks lost |
| Not drawing construction lines in Geometry Paper II | Activity questions need clear construction marks |
| Mixing up radius and diameter in mensuration | Double or half the answer — full marks lost |
| Not simplifying discriminant before concluding root type | Common in MCQs |
For answer writing tips, see the board exam answer sheet guide.
Frequently Asked Questions
How is Maharashtra SSC Maths different from CBSE Class 10 Maths?
Maharashtra SSC has two separate papers (Algebra and Geometry) of 40 marks each, while CBSE has one combined paper of 80 marks. SSC includes Financial Planning (GST, shares, income tax) which CBSE does not. SSC Geometry has more emphasis on circle theorems and constructions. The formula set overlaps about 70%.
Which chapters carry the most marks in the SSC Maths exam?
In Algebra: Quadratic Equations (6–8 marks) and Statistics (5–6 marks). In Geometry: Similarity + Pythagoras (8–10 marks) and Trigonometry (6–8 marks). Together, these four topics carry over half the total marks.
Do I need to memorize the cross-multiplication formula for linear equations?
Yes. Maharashtra SSC specifically tests cross-multiplication as a method. While substitution and elimination also work, cross-multiplication is the preferred method in the marking scheme for certain question types. It appears as a 3-mark question regularly.
Is the mensuration chapter in Algebra or Geometry paper?
Mensuration (surface areas and volumes) is in the Geometry paper (Paper II). It includes combined solids questions (cone on cylinder, hemisphere on cone, etc.) which carry 3–4 marks.
How should I prepare for the activity-based question (3 marks)?
The activity question requires you to complete a partially solved problem with specific steps. It tests procedural understanding. Practice all textbook activities — especially graphic constructions, statistical calculations, and algebraic manipulations. These are the easiest 3 marks if you know the procedure.
Are the formulas different for Marathi medium students?
The formulas are identical. Only the language of questions differs. All symbols, notation, and mathematical expressions are the same in English and Marathi medium papers.
Related Guides
- Maharashtra SSC Class 10 Model Paper 2027 New Pattern
- Maharashtra Board Class 10 Maths Chapter Wise Marks Weightage 2027
- CBSE Class 10 Maths Chapter Wise Marks Weightage 2027
- Board Exam Answer Sheet — Write for Maximum Marks 2027
- Board Exam Time Management — 3 Hour Strategy 2027
- How to Study Smart Not Hard — Indian Students
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