公式表

SPM 数学公式表(1449)

学生整理实用的 SPM 数学公式参考

这是 SPM 数学考试提供给你的 39 条公式,就印在试卷上,按官方格式的分组方式排列。这里没有的,就是要你记住的,因此本页也标明哪些需要背。

Number and Operations

Law of indices (product)
am × an = am+n
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Law of indices (quotient)
am ÷ an = am−n
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Law of indices (power)
(am)n = amn
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Fractional index
am/n = (n-th root of am)
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Simple interest
I = Prt
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Maturity value (compound)
MV = P(1 + r/n)nt
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Total repayment
A = P + Prt
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Relationship and Algebra

Distance between two points
Distance = √(x2−x1)2 + (y2−y1)2
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Midpoint
(x, y) = ((x1+x2)/2, (y1+y2)/2)
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Average speed
Average speed = Total distance / Total time
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Gradient (two points)
m = (y2−y1)/(x2−x1)
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Gradient (intercepts)
m = −(y-intercept)/(x-intercept)
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Inverse of a 2x2 matrix
A-1 = 1/(ad−bc) × [[d, −b], [−c, a]]
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Measurement and Geometry

Pythagoras theorem
c2 = a2 + b2
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Sum of interior angles of a polygon
(n − 2) × 180°
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Circumference of circle
πd = 2πr
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Area of circle
πr2
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Arc length
(θ/360°) × 2πr
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Area of sector
(θ/360°) × πr2
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Area of kite
(1/2) × product of two diagonals
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Area of trapezium
(1/2) × sum of two parallel sides × height
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Surface area of cylinder
2πr2 + 2πrh
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Surface area of cone
πr2 + πrs
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Surface area of sphere
4πr2
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Volume of prism
area of cross section × height
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Volume of cylinder
πr2 h
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Volume of cone
(1/3)πr2 h
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Volume of sphere
(4/3)πr3
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Volume of pyramid
(1/3) × base area × height
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Scale factor
k = PA'/PA
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Area of image
area of image = k2 × area of object
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Statistics and Probability

Mean (ungrouped)
x̄ = Σx / N
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Mean (grouped)
x̄ = Σfx / Σf
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Variance (ungrouped)
σ2 = Σ(x−x̄)2 / N = Σx2/N − x̄2
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Variance (grouped)
σ2 = Σf(x−x̄)2 / Σf = Σfx2/Σf − x̄2
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Standard deviation (ungrouped)
σ = √Σ(x−x̄)2 / N = √Σx2/N − x̄2
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Standard deviation (grouped)
σ = √Σf(x−x̄)2 / Σf = √Σfx2/Σf − x̄2
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Probability of an event
P(A) = n(A) / n(S)
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Complement of an event
P(A') = 1 − P(A)
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资料来源:SPM: Format Pentaksiran mulai 2021, Matematik (1449)

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