Formulae for maths GCSE - Higher tier 0.0 / 5 ? MathematicsVolume and surface areaGCSEAQA Created by: 20rkaneCreated on: 25-04-24 14:18 Area of a square/rectangle A = bh 1 of 60 Area of a triangle A = bh/2 2 of 60 Area of a parallelogram A = bh 3 of 60 Area of a trapezium A = 1/2 (a+b) h 4 of 60 Circumference of a circle C = πD or C = 2πr 5 of 60 Area of a circle A = πr² 6 of 60 Surface area of a cylinder 2πr² + πdh 7 of 60 Surface area of a sphere 4πr² 8 of 60 Surface area of a cone πr² + πrl 9 of 60 Surface area of a frustum πr² + πR² + π(R+r)l 10 of 60 Volume of a cube/cuboid V = bhl 11 of 60 Volume of a triangular prism V = (bh/2) x l 12 of 60 Volume of a cylinder V = πr²h 13 of 60 Volume of a prism V = area of cross section x l 14 of 60 Volume of a pyramid V = 1/3(base area x h) 15 of 60 Volume of a cone V = 1/3 x πr²h 16 of 60 Volume of a sphere V = 4/3 x πr³ 17 of 60 Arc length θ/360 x πd 18 of 60 Sector area θ/360 x πr² 19 of 60 Area of a segment area of sector - area of triangle 20 of 60 Enlarged perimeter original perimeter x scale factor 21 of 60 Enlarged area original area x (scale factor)² 22 of 60 Enlarged volume original volume x (scale factor)³ 23 of 60 Compound interest original amount x (1 ± %/100)^n 24 of 60 Original amount (reverse percentage) new amount / (1 ± %/100) 25 of 60 Percentage change difference/original x 100 26 of 60 Percentage score score/total available x 100 27 of 60 Sum of interior angles of a polygon 180 x (n - 2) 28 of 60 Relationship between interior and exterior angles in a polygon interior + exterior = 180° 29 of 60 Exterior angle of a polygon 360°/n 30 of 60 Number of sides of a polygon 360°/exterior angle 31 of 60 Pythagoras' theorem a² + b² = c² 32 of 60 Trigonometry: Mnemonic to help choose the correct ratio SOH CAH TOA 33 of 60 Sin0 Sin30 Sin45 Sin60 Sin90 Sin0 = 0 Sin30 = 1/2 Sin45 = (√2)/2 Sin60 = (√3)/2 Sin90 = 1 34 of 60 Cos0 Cos30 Cos45 Cos60 Cos90 Cos0 = 1 Cos30 = (√3)/2 Cos45 = (√2)/2 Cos60 = 1/2 Cos90 = 0 35 of 60 Tan0 Tan30 Tan45 Tan60 Tan90 Tan0 = 0 Tan30 = 1/(√3) Tan45 = 1 Tan60 = (√3)/1 Tan90 = 1/0 (undefined) 36 of 60 The angle for 1 person or thing 360°/Σfrequency 37 of 60 Position of the median value Odd -> (n+1)/2 Even -> n/2, (n/2)+1 38 of 60 Frequency density (histogram) frequency/class width 39 of 60 Interquartile range upper quartile - lower quartile UQ - LQ 40 of 60 Speed speed = distance / time https://www.youtube.com/watch?v=K_kzgW_OYX0 41 of 60 Pressure pressure = force / area 42 of 60 Density density = mass / volume 43 of 60 Multiplying a^(m) x a^(n) = a^(m+n) 44 of 60 Dividing a^(m)/a^(n) = a^(m-n) 45 of 60 Raising to another power (a^m)^n = a^(mn) 46 of 60 Anything to the power of zero n^(0) = 1 47 of 60 Negative index a^(-m) = 1/a^m 48 of 60 Unit fractional index a^(1/n) = (n)√a 49 of 60 Any fractional index a^(m/n) = ( (n)√a )^m 50 of 60 Nth term: Linea sequence U˅(n) = dn + (a-d) a = first term, d = difference 51 of 60 Nth term: Geometric sequence U˅(n) = ar^(n-1) a = first term, r = common ratio 52 of 60 Converting between lengths: cm and m cm / 100 = m m x 100 = cm 53 of 60 Converting between areas: cm² and m² cm² / 10,000 = m² m² x 10,000 = cm² 54 of 60 Converting between volumes: cm³ and m³ cm³ / 1,000,000 = m³ m³ x 1,000,000 = cm³ 55 of 60 Equation of a straight line y = mx + c 56 of 60 Gradient difference in y / difference in x 57 of 60 Midpoint of a line (between 2 points) ( (x˅(1) + x˅(2)) , (x˅(1) + x˅(2)) /2 /2 58 of 60 Equation of a circle x² + y² = r² 59 of 60 Quadratic formula x = (-b ± √(b² - 4ac)) /2 60 of 60
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