In short: The Karnataka SSLC Maths exam (KSEAB) is 80 marks theory + 20 marks internal assessment. The blueprint allocates highest weightage to Algebra (Quadratic Equations, AP) and Geometry (Similarity, Circles, Constructions), followed by Trigonometry and Mensuration. This post has every formula you need — organized by weightage (highest-marks chapters first). It is designed to be printable as a one-page quick-reference sheet. Revise this daily in the last 30 days.
Karnataka SSLC Maths Blueprint — Marks Distribution
| Chapter | Topic | Marks |
|---|---|---|
| 1 | Arithmetic Progressions | 10 |
| 2 | Triangles (Similarity) | 10 |
| 3 | Pair of Linear Equations in Two Variables | 8 |
| 4 | Circles | 8 |
| 5 | Areas Related to Circles | 6 |
| 6 | Quadratic Equations | 8 |
| 7 | Coordinate Geometry | 6 |
| 8 | Real Numbers | 4 |
| 9 | Polynomials | 4 |
| 10 | Introduction to Trigonometry | 6 |
| 11 | Some Applications of Trigonometry | 4 |
| 12 | Surface Areas and Volumes | 4 |
| 13 | Statistics | 6 |
| 14 | Probability | 4 |
| 15 | Constructions | 6 |
| Total | 80 (approx., some overlap with internal choices) |
For the full chapter-wise analysis, see the Karnataka SSLC Science chapter-wise weightage.
HIGH WEIGHTAGE: Arithmetic Progressions (10 marks)
| Formula | Expression |
|---|---|
| nth term | aₙ = a + (n−1)d |
| Sum of first n terms | Sₙ = n/2 [2a + (n−1)d] |
| Sum (when last term known) | Sₙ = n/2 (a + l) |
| Common difference | d = a₂ − a₁ |
| Arithmetic mean of a and b | AM = (a + b)/2 |
| Three numbers in AP | a − d, a, a + d |
| Four numbers in AP | a − 3d, a − d, a + d, a + 3d |
| nth term from sum | aₙ = Sₙ − Sₙ₋₁ |
HIGH WEIGHTAGE: Triangles — Similarity (10 marks)
| Theorem / Formula | Statement |
|---|---|
| Basic Proportionality Theorem (BPT) | If DE ∥ BC in △ABC, then AD/DB = AE/EC |
| Converse of BPT | If AD/DB = AE/EC, then DE ∥ BC |
| AAA Similarity | If all angles of two triangles are equal, triangles are similar |
| SAS Similarity | One angle equal + including sides proportional → similar |
| SSS Similarity | All three pairs of sides proportional → similar |
| Area ratio of similar triangles | (Area₁/Area₂) = (side₁/side₂)² = (altitude₁/altitude₂)² |
| Pythagoras Theorem | AC² = AB² + BC² (for right △ at B) |
| Converse of Pythagoras | If AC² = AB² + BC², then ∠B = 90° |
HIGH WEIGHTAGE: Quadratic Equations (8 marks)
| Formula | Expression |
|---|---|
| Standard form | ax² + bx + c = 0 (a ≠ 0) |
| Quadratic formula | x = [−b ± √(b²−4ac)] / 2a |
| Discriminant | D = b² − 4ac |
| D > 0 | Two distinct real roots |
| D = 0 | Two equal real roots |
| D < 0 | No real roots |
| Sum of roots | α + β = −b/a |
| Product of roots | αβ = c/a |
| Forming equation from roots | x² − (α+β)x + αβ = 0 |
HIGH WEIGHTAGE: Pair of Linear Equations (8 marks)
| Condition | Meaning | Graphical |
|---|---|---|
| a₁/a₂ ≠ b₁/b₂ | Unique solution (consistent) | Intersecting lines |
| a₁/a₂ = b₁/b₂ ≠ c₁/c₂ | No solution (inconsistent) | Parallel lines |
| a₁/a₂ = b₁/b₂ = c₁/c₂ | Infinite solutions (dependent) | Coincident lines |
Methods: Substitution, Elimination, Cross-multiplication, Graphical
HIGH WEIGHTAGE: Circles (8 marks)
| Property / Theorem | Statement |
|---|---|
| Tangent ⊥ Radius | Tangent at any point is perpendicular to the radius at that point |
| Equal tangent lengths | PA = PB (tangents from external point P to circle) |
| Number of tangents | From external point: 2; from on circle: 1; from inside: 0 |
| Angle in semicircle | Angle subtended by diameter = 90° |
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MEDIUM WEIGHTAGE: Trigonometry (6 + 4 = 10 marks combined)
Ratios
| Ratio | Definition |
|---|---|
| sin θ | Opposite / Hypotenuse |
| cos θ | Adjacent / Hypotenuse |
| tan θ | Opposite / Adjacent |
| cosec θ, sec θ, cot θ | Reciprocals of sin, cos, tan |
Standard Values
| θ | sin | cos | tan |
|---|---|---|---|
| 0° | 0 | 1 | 0 |
| 30° | ½ | √3/2 | 1/√3 |
| 45° | 1/√2 | 1/√2 | 1 |
| 60° | √3/2 | ½ | √3 |
| 90° | 1 | 0 | undefined |
Identities
- sin²θ + cos²θ = 1
- 1 + tan²θ = sec²θ
- 1 + cot²θ = cosec²θ
- sin(90°−θ) = cosθ; cos(90°−θ) = sinθ; tan(90°−θ) = cotθ
Applications (Heights and Distances)
- Angle of elevation: object above eye → look up
- Angle of depression: object below eye → look down
- tan θ = height/distance (most common setup)
- Two observation points: set up two equations, eliminate unknowns
MEDIUM WEIGHTAGE: Coordinate Geometry (6 marks)
| Formula | Expression |
|---|---|
| Distance | d = √[(x₂−x₁)² + (y₂−y₁)²] |
| Midpoint | M = [(x₁+x₂)/2, (y₁+y₂)/2] |
| Section formula | P = [(mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n)] |
| Area of triangle | **½ |
| Collinearity test | Area = 0 |
| Centroid | G = [(x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3] |
MEDIUM WEIGHTAGE: Areas Related to Circles (6 marks)
| Formula | Expression |
|---|---|
| Area of circle | πr² |
| Circumference | 2πr |
| Area of sector | (θ/360) × πr² |
| Length of arc | (θ/360) × 2πr |
| Area of segment | Area of sector − Area of triangle |
| Area of ring | π(R² − r²) |
MEDIUM WEIGHTAGE: Statistics (6 marks)
| Measure | Formula |
|---|---|
| Mean (direct) | x̄ = Σfᵢxᵢ / Σfᵢ |
| Mean (assumed mean) | x̄ = A + Σfᵢdᵢ/Σfᵢ |
| Median (grouped) | Median = l + [(n/2 − cf)/f] × h |
| Mode (grouped) | Mode = l + [(f₁−f₀)/(2f₁−f₀−f₂)] × h |
| Ogive | Plot cumulative frequency; median at n/2 on y-axis |
MEDIUM WEIGHTAGE: Constructions (6 marks)
No formulas — pure procedure. Key constructions to practice:
- Division of a line segment in given ratio (e.g., 3:2)
- Triangle similar to a given triangle with a given scale factor
- Pair of tangents to a circle from an external point
Each construction carries 3–4 marks. Draw with sharp pencil, show all arcs, label clearly.
LOWER WEIGHTAGE: Real Numbers (4 marks)
| Concept | Formula |
|---|---|
| HCF × LCM | HCF(a,b) × LCM(a,b) = a × b |
| Terminating decimal | Denominator = 2ᵐ × 5ⁿ only |
| Irrational proof | Contradiction method (standard format) |
| Euclid's division lemma | a = bq + r (0 ≤ r < b) |
LOWER WEIGHTAGE: Polynomials (4 marks)
| Relation | Formula |
|---|---|
| Sum of zeroes (quadratic) | α + β = −b/a |
| Product of zeroes (quadratic) | αβ = c/a |
| Forming polynomial | p(x) = k[x² − (sum)x + product] |
LOWER WEIGHTAGE: Surface Areas and Volumes (4 marks)
| Shape | Volume | Surface Area |
|---|---|---|
| Cylinder | πr²h | 2πr(r+h) |
| Cone | ⅓πr²h | πr(r+l); l=√(r²+h²) |
| Sphere | (4/3)πr³ | 4πr² |
| Hemisphere | (2/3)πr³ | 3πr² (total) |
| Frustum | (πh/3)(r₁²+r₂²+r₁r₂) | π(r₁+r₂)l + πr₁² + πr₂² |
LOWER WEIGHTAGE: Probability (4 marks)
| Formula | Expression |
|---|---|
| P(E) | n(E)/n(S) |
| P(not E) | 1 − P(E) |
| P(sure event) | 1 |
| P(impossible) | 0 |
Revision Strategy for Karnataka SSLC Maths
| Week | Focus Chapters | Total Marks Covered |
|---|---|---|
| 1 | AP + Quadratic Equations + Linear Equations | 26 |
| 2 | Triangles + Circles + Constructions | 24 |
| 3 | Trigonometry + Coordinate Geometry | 16 |
| 4 | Statistics + Mensuration + Probability + Real Numbers | 14 |
This ordering covers 100% of the blueprint. For Karnataka-specific preparation, check the Karnataka SSLC important questions 2027.
Frequently Asked Questions
Is the Karnataka SSLC Maths syllabus the same as CBSE?
About 85% of the topics overlap. SSLC uses the same NCERT textbook as CBSE. The key difference is in the blueprint (weightage distribution) and exam pattern. SSLC gives more marks to constructions and has a different question paper structure (Sections A through E).
Which chapters should I focus on for 60+ marks in SSLC Maths?
Focus on AP (10), Triangles (10), Quadratic Equations (8), Linear Equations (8), Circles (8), and Trigonometry (10 combined). These six topics alone cover 54 marks. Add Coordinate Geometry and Statistics for another 12. That's 66 marks from 8 topics.
Can I print this page for exam revision?
Yes, this page is designed to be printable. Use your browser's print function (Ctrl+P) and select "Save as PDF" for a clean reference sheet. Keep it next to your NCERT textbook during the last 15 days of revision.
How many marks are for Constructions in SSLC?
Constructions carry about 6 marks. There is typically one 3-mark construction question (tangent to circle or similar triangle) and sometimes construction elements appear in other questions. Practice with compass and ruler — neatness matters for full marks.
What is the passing mark for Karnataka SSLC Maths?
You need 35% (28 out of 80) in the theory exam to pass. For a first-class, you need 60% (48+). For distinction, 75% (60+). The formulas on this page, if mastered, can comfortably get you above 60 marks.
Is the Exam 1 and Exam 2 pattern the same for Karnataka SSLC?
Karnataka has introduced a two-exam system similar to CBSE. Both exams cover the full syllabus with identical weightage. The better score of the two counts. This formula sheet applies to both exams. See the Karnataka SSLC exam strategy for more.
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