SPM · Matematik 1449
Senarai rumus
Rumus yang boleh digunakan semasa menjawab Kertas 1 dan Kertas 2.
Nombor dan OperasiNumbers and Operations
- Hukum indeksLaws of indices
- aᵐ × aⁿ = aᵐ⁺ⁿaᵐ ÷ aⁿ = aᵐ⁻ⁿ(aᵐ)ⁿ = aᵐⁿ
- Indeks negatif dan sifarNegative and zero indices
- a⁻ⁿ = 1 ÷ aⁿa⁰ = 1
- Indeks pecahanFractional indices
- a¹ᐟⁿ = ⁿ√aaᵐᐟⁿ = (ⁿ√a)ᵐ = ⁿ√(aᵐ)
- Faedah mudahSimple interest
- I = Prt
- Faedah kompaunCompound interest
- MV = P(1 + r ÷ n)ⁿᵗ
Perkaitan dan AlgebraRelationship and Algebra
- Jarak antara dua titikDistance between two points
- √((x₂ − x₁)² + (y₂ − y₁)²)
- Titik tengahMidpoint
- (x, y) = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2)
- KecerunanGradient
- m = (y₂ − y₁) ÷ (x₂ − x₁)m = −(pintasan-y) ÷ (pintasan-x)m = −(y-intercept) ÷ (x-intercept)
- Persamaan garis lurusEquation of a straight line
- y = mx + c
- Songsangan matriksInverse matrix
- A = abcdA⁻¹ = 1 ÷ (ad − bc) × d−b−ca
- Laju purataAverage speed
- laju purata = jumlah jarak ÷ jumlah masaaverage speed = total distance ÷ total time
- PecutanAcceleration
- a = (v − u) ÷ t
Sukatan dan GeometriMeasurement and Geometry
- Teorem PythagorasPythagoras' theorem
- c² = a² + b²
- Luas segi tigaArea of a triangle
- ½ × tapak × tinggi½ × base × height
- Luas trapeziumArea of a trapezium
- ½ × hasil tambah sisi selari × tinggi½ × sum of parallel sides × height
- BulatanCircle
- lilitan = 2πjcircumference = 2πrluas = πj²area = πr²
- Panjang lengkokArc length
- (θ ÷ 360°) × 2πj(θ ÷ 360°) × 2πr
- Luas sektorArea of a sector
- (θ ÷ 360°) × πj²(θ ÷ 360°) × πr²
- Isi padu prismaVolume of a prism
- luas keratan rentas × panjangarea of cross section × length
- Isi padu silinderVolume of a cylinder
- πj²tπr²h
- Isi padu konVolume of a cone
- ⅓πj²t⅓πr²h
- Isi padu sferaVolume of a sphere
- ⁴⁄₃πj³⁴⁄₃πr³
- Isi padu piramidVolume of a pyramid
- ⅓ × luas tapak × tinggi⅓ × base area × height
- Luas permukaan silinderSurface area of a cylinder
- 2πj² + 2πjt2πr² + 2πrh
- Luas permukaan konSurface area of a cone
- πj² + πjsπr² + πrl
- Luas permukaan sferaSurface area of a sphere
- 4πj²4πr²
- Nisbah trigonometriTrigonometric ratios
- sin θ = sisi bertentangan ÷ hipotenussin θ = opposite side ÷ hypotenusekos θ = sisi bersebelahan ÷ hipotenuscos θ = adjacent side ÷ hypotenusetan θ = sisi bertentangan ÷ sisi bersebelahantan θ = opposite side ÷ adjacent side
- PembesaranEnlargement
- k = PA′ ÷ PAluas imej = k² × luas objekarea of image = k² × area of object
Statistik dan KebarangkalianStatistics and Probability
- MinMean
- x̄ = Σx ÷ Nx̄ = Σfx ÷ Σf
- VariansVariance
- σ² = Σx² ÷ N − x̄²σ² = Σfx² ÷ Σf − x̄²
- Sisihan piawaiStandard deviation
- σ = √variansσ = √variance
- KebarangkalianProbability
- P(A) = n(A) ÷ n(S)P(A′) = 1 − P(A)
- Peristiwa bergabungCombined events
- P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
- Peristiwa tak bersandarIndependent events
- P(A ∩ B) = P(A) × P(B)