ගණිත සම්පත් & ක්‍රීඩා

(+) × (+) = (+) (−) × (−) = (+) (+) × (−) = (−) |a| = a if a ≥ 0, −a if a < 0

HCF × LCM = a × b HCF: ලොකුම ෙ‍ ‍පොදු ගාණකය LCM: කුඩාම ෙ‍ ‍පොදු ගුණිතය

ax + b = c x = (c − b) / a ax + b = cx + d x = (d − b) / (a − c)

A ∪ B = A හෝ B හෝ දෙකෙහිම ඇති A ∩ B = A සහ B දෙකෙහිම ඇති n(A ∪ B) = n(A) + n(B) − n(A ∩ B)

Line symmetry: රූපය 접어 ගත් විට දෙකොටස ගළපෙයි Rotational symmetry: n-fold 360° / n = rotation angle

Prime: ගාණකයෝ 1 සහ ස්වයං පමණි. Composite: ගාණකයෝ > 2 ඇත. 1 → prime හෝ composite නොවේ.

aᵐ × aⁿ = aᵐ⁺ⁿ aᵐ ÷ aⁿ = aᵐ⁻ⁿ (aᵐ)ⁿ = aᵐⁿ a⁰ = 1 (a ≠ 0) a⁻ⁿ = 1/aⁿ

√(a×b) = √a × √b √(a/b) = √a / √b (√a)² = a a² + b² = c² (Pythagoras)

(a+b)² = a²+2ab+b² (a−b)² = a²−2ab+b² (a+b)(a−b) = a²−b²

y = mx + c m = (y₂−y₁)/(x₂−x₁) (slope) c = y-intercept

Circumference = 2πr = πd Area = πr² Arc length = (θ/360) × 2πr Sector area = (θ/360) × πr²

Mean = Σx / n Median = මැද අගය (sorted data) Mode = වඩාත් නිතර ඇති අගය Range = max − min

Elimination method: ලකුන සමාන කර + හෝ − කරන්න Substitution method: x = ... ලෙස 2 වැනියෙහි replace කරන්න

sin θ = opposite / hypotenuse cos θ = adjacent / hypotenuse tan θ = opposite / adjacent SOH-CAH-TOA

P(A) = n(A) / n(S) 0 ≤ P(A) ≤ 1 P(A') = 1 − P(A) P(A∪B) = P(A)+P(B)−P(A∩B)

√a × √b = √(ab) √a / √b = √(a/b) (a + √b)(a − √b) = a² − b Rationalize: × conjugate

ax² + bx + c = a(x−p)(x−q) Factor theorem: p root → (x−p) factor Common factor first, then grouping

Angle at centre = 2 × angle at circumference Angles in same segment are equal Opposite angles in cyclic quad = 180°

ax² + bx + c = 0 x = (−b ± √(b²−4ac)) / 2a Discriminant: Δ = b²−4ac Δ>0: 2 real roots Δ=0: 1 repeated root Δ<0: no real roots

Distance = √((x₂−x₁)²+(y₂−y₁)²) Midpoint = ((x₁+x₂)/2, (y₁+y₂)/2) Gradient = (y₂−y₁)/(x₂−x₁) Parallel: m₁ = m₂ Perpendicular: m₁×m₂ = −1

[a b] + [e f] = [a+e b+f] [c d] [g h] [c+g d+h] det(A) = ad − bc A⁻¹ = (1/det) × [d −b; −c a]

σ = √(Σ(x−x̄)²/n) Variance = σ² z-score = (x − x̄) / σ IQR = Q₃ − Q₁

Sine Rule: a/sinA = b/sinB = c/sinC Cosine Rule: a² = b²+c²−2bc·cosA Area = ½ ab sinC

P(A and B) = P(A) × P(B) [independent] P(A and B) = P(A) × P(B|A) [dependent] P(A|B) = P(A∩B) / P(B)

(a+b)² = a²+2ab+b² (a−b)² = a²−2ab+b² (a+b)(a−b) = a²−b² (a+b)³ = a³+3a²b+3ab²+b³

Triangle: sum of angles = 180° Exterior angle = sum of 2 interior opp. Parallel lines: co-int = 180°, alt = equal Similar triangles: ratios equal

sin²θ + cos²θ = 1 tan θ = sin θ / cos θ sin(90°−θ) = cosθ Area = ½ ab sinC

Mean (grouped) = Σfx / Σf Median class: n/2 th value σ = √(Σf(x−x̄)² / Σf) P(A∪B) = P(A)+P(B)−P(A∩B)

Reflection in x-axis: [1 0; 0 −1] Reflection in y-axis: [−1 0; 0 1] Rotation 90° CCW: [0 −1; 1 0] Enlargement k: [k 0; 0 k]

Paper: 2 hours 30 minutes Section A: 25 × 2 marks = 50 Section B: 5 × 10 marks = 50 Total: 100 marks