高中數(shù)學(xué)公式手匯總

1、TABLE OF CONTENTSPage4Core Mathematics C14Mensuration4Arithmetic series5Core Mathematics C25Cosine rule5Binomial series5Logarithms and exponentials5Geometric series5Numerical integration6Core Mathematics C36Logarithms and exponentials6Trigonometric identities6Differentiation7Core Mathematics C47Inte

2、gration 8 Further Pure Mathematics FP18 Summations8Numerical solution of equations 8Coordinate geometry8Conics8Matrix transformations9Further Pure Mathematics FP29Area of sector9Maclaurins and Taylors Series10Taylor polynomials11Further Pure Mathematics FP311Vectors13Hyperbolics14Integration14Arc le

3、ngth15Surface area of revolution16Mechanics M116There are no formulae given for M1 in addition to those candidates are expected to know. 16Mechanics M216Centres of mass 16Mechanics M316Motion in a circle16Centres of mass16Universal law of gravitation17Mechanics M417There are no formulae given for M4

4、 in addition to those candidates are expected to know.17Mechanics M517Moments of inertia17Moments as vectors18Statistics S118Probability18Discrete distributions18Continuous distributions19Correlation and regression20The Normal distribution function21Percentage points of the Normal distribution22Stat

5、istics S222Discrete distributions22Continuous distributions23Binomial cumulative distribution function28Poisson cumulative distribution function29Statistics S329Expectation algebra 29Sampling distributions 29Correlation and regression 29Non-parametric tests 30Percentage points of the 2 distribution

6、31Critical values for correlation coefficients 32Random numbers 33Statistics S4 33Sampling distributions 34Percentage points of Students t distribution35Percentage points of the F distributionThere are no formulae provided for Decision Mathematics units D1 and D2The formulae in this booklet have bee

7、n arranged according to the unit in which they are first introduced. Thus a candidate sitting a unit may be required to use the formulae that were introduced in a preceding unit (e.g. candidates sitting C3 might be expected to use formulae first introduced in C1 or C2). It may also be the case that

8、candidates sitting Mechanics and Statistics units need to use formulae introduced in appropriate Core Mathematics units, as outlined in the specificationCore Mathematics C1MensurationSurface area of sphere = 4 r 2 Area of curved surface of cone = r slant heightCore Mathematics C2Candidates sitting C

9、2 may also require those formulae listed under Core Mathematics C1.Cosine rulea2 = b2 + c2 2bc cos ABinomial series (n )where )Logarithms and exponentialsNumerical integrationThe trapezium rule: h(y0 + yn) + 2(y1 + y2 + . + yn 1), where Core Mathematics C3Candidates sitting C3 may also require those

10、 formulae listed under Core Mathematics C1 and C2.Logarithms and exponentialsTrigonometric identities Differentiationf(x)f(x)sec xsec x tan xcot xcosec2 xcosec xcosec x cot xCore Mathematics C4Candidates sitting C4 may also require those formulae listed under Core Mathematics C1, C2 and C3. Integrat

11、ion (+ constant)f(x)Further Pure Mathematics FP1Candidates sitting FP1 may also require those formulae listed under Core Mathematics C1 and C2.SummationsNumerical solution of equationsThe Newton-Raphson iteration for solving : Coordinate geometryThe perpendicular distance from (h, k) to is The acute

12、 angle between lines with gradients and is ConicsParabolaRectangularHyperbolaStandardFormxy = c2ParametricForm(at2, 2at) FociNot requiredDirectricesNot requiredMatrix transformationsAnticlockwise rotation through about O: Reflection in the line : Further Pure Mathematics FP2Candidates sitting FP2 ma

13、y also require those formulae listed under Further PureMathematics FP1 and Core Mathematics C1C4.Area of a sectorA = (polar coordinates)Complex numbersThe roots of are given by , for Maclaurins and Taylors SeriesTaylor polynomials Further Pure Mathematics FP3Candidates sitting FP3 may also require t

14、hose formulae listed under Further Pure Mathematics FP1, and Core Mathematics C1C4.VectorsThe resolved part of a in the direction of b is The point dividing AB in the ratio is Vector product: If A is the point with position vector and the direction vector b is given by , then the straight line throu

15、gh A with direction vector b has cartesian equationThe plane through A with normal vector has cartesian equationThe plane through non-collinear points A, B and C has vector equationThe plane through the point with position vector a and parallel to b and c has equation The perpendicular distance of from is .Hyperbolic functions ConicsEllipseParabolaHyperbolaRectangularHyperbolaStandardFormParametricForm(a sec , b ta