General Mathematics 2014 HSC Formula Sheet, Cheat Sheet of Mathematics

Download General Mathematics 2014 HSC Formula Sheet and more Cheat Sheet Mathematics in PDF only on Docsity! x − x z = s standard deviation of y scores gradient = r × standard deviation of x scores FV n PV = FV = PV (1 + r ) (1 + r ) , n sum of scores x = number of scores 2014 HIGHER SCHOOL CERTIFICATE EXAMINATION Mathematics General 2 FORMULAE AND DATA SHEET Financial Mathematics Simple interest I = Prn P is initial amount r is interest rate per period, expressed as a decimal n is number of periods Compound interest n A P= (1 + r ) A is final amount P is initial amount r is interest rate per period, expressed as a decimal n is number of compounding periods Present value and future value r is interest rate per period, expressed as a decimal n is number of compounding periods Straight-line method of depreciation S = V − Dn0 S is salvage value of asset after n periods V is initial value of asset 0 D is amount of depreciation per period n is number of periods Declining-balance method of depreciation S V= 1 0 ( − r )n S is salvage value of asset after n periods V is initial value of asset 0 r is depreciation rate per period, expressed as a decimal n is number of periods Data Analysis Mean of a sample z-score For any score x, x is mean s is standard deviation Outlier(s) score(s) less than QL − 1.5 × IQR or score(s) more than QU + 1.5 × IQR Q is lower quartile L Q is upper quartile U IQR is interquartile range Least-squares line of best fit y = gradient × x + y-intercept y-intercept = −y (gradient × x ) r is correlation coefficient x is mean of x scores y is mean of y scores Normal distribution • approximately 68% of scores have z-scores between –1 and 1 • approximately 95% of scores have z-scores between –2 and 2 • approximately 99.7% of scores have z-scores between –3 and 3 1232 – 37 – θ l = 2πr 360 θ 2A = πr 360 h A = ( a b+ ) 2 1 V = Ah 3 h A ≈ ( d + 4d + d )f m l3 h V ≈ A + 4 A + A{ L M R }3 Spherical Geometry Circumference of a circle C = 2πr or C = πD r is radius D is diameter Arc length of a circle r is radius θ is number of degrees in central angle Radius of Earth (taken as) 6400 km Time differences For calculation of time differences using longitude: 15° = 1 hour time difference Area Circle A = πr2 r is radius Sector r is radius θ is number of degrees in central angle Annulus A = π ( R 2 − r 2 ) R is radius of outer circle r is radius of inner circle Trapezium h is perpendicular height a and b are the lengths of the parallel sides Area of land and catchment areas unit conversion: 1 ha = 10 000 m2 Surface Area Sphere A = 4πr2 r is radius Closed cylinder A = 2πr2 + 2πrh r is radius h is perpendicular height Volume Prism or cylinder V = Ah A is area of base h is perpendicular height Pyramid or cone A is area of base h is perpendicular height Volume and capacity unit conversion: 1 m3 = 1000 L Approximation Using Simpson’s Rule Area h is distance between successive measurements df is first measurement d is middle measurementm dl is last measurement Volume h is distance between successive measurements AL is area of left end AM is area of middle AR is area of right end – 38 –