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GCSE EDEXCEL MATHS HIGHER [GEOMETRY AND TRIGONOMETRY]
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area of a circle surface area of a sphere surface area of a cone πr x slanted length x πr^ volume of cone volume of a sphere area of trapezium 1/2(a+b) x height circumference of a circle π x d volume of a cuboid l x w x h volume of a cylinder volume of a pyramid 1/3 x area of base x h distance speed x time density mass/volume
pressure force/area Pythagoras' Theorem a^2 + b^2 = c^ Quadratic equation when ax^2 + bx + c = 0 Sine rule a/sinA = b/sinB = c/sinC Cosine rule Area of a triangle 1/2 x a x b x sinC area of a sector angle/360 x area of full circle segment area sector area - area of triangle x angles equal corresponding angles equal alternate angles equal co-interior angles add to 180 total of exterior angles
1 exterior angle 360/number of sides sum of interior angles (sides - 2) x 180 sin/cos/tan 45, lengths=
a^0 1 a^1 a (a^m)^n a^mxn (a/m)^n a^n/m^n a^-m 1/a^m a^1/m ^m√a a^m/n (^n√a)^m 3D Pythagoras' theorem a^2 + b^2 + c^2 = d^ when to use cosine rule 2 sides and an angle enclosed by them all 3 sides no angle when to use sine rule 2 angles any side 2 sides and an angle thats not enclosed by them inverse functions replace x's with y's and make everything equal to x make y the subject replace the y with f^-1(x) y=f(x)+a translation in the y-axis (move up or down by the amount of a eg. +2 = move up 2) y=f(x+a) translation in the x-axis (but if it says + move down 2 ITS OPPOSITE!!) y=f(xa) stretch in the x direction (leaving the y values unchanged) by a factor of 1/a y=f(x/a) stretch in the x direction (leaving the y values unchanged) by a factor of a y=-f(x) reflection in the x-axis y=f(-x) reflection in the y-axis ∉ not a member of a set ∈ (^) member of a set
ξ universal set (all the numbers in the Q) ∪ (^) union (combination of all members of each set in question) ∩ intersect^ (all^ numbers^ that^ are members of exclusively both sets in question) ' Everything NOT in the set √a x √b √a x b √a / √b √a/b √a + √b DO NOTHING a/ √b a/√b x √b/√b = a√b/b 'exact value' meaning surd form when to use quadratic formula if it wont factorise if the question mentions decimal places or significant figures dividing fractions KEEP TIMES SWITCH- KTS common denominator is also.... something both denominators divide into fibonacci sequence adding together the 2 previous terms how to know if 2 lines are perpendicular if gradient is m perpendicular will be - (1/m) cubic graph reciprocal graph (positive) exponential graph gradient vertical/horizontal or ycoord/xcoord estimated gradient tangent to curve (meets curve at point
tan 30 1 / √ 3 tan 45 1 tan 60 √ 3 tan 90 DOES NOT EXIST x^2 > a^ x > a x < - a x^2 < a^2 - a < x < a how to solve a simultaneous equation by plotting a line and circle graph the coordinates where the line meets the circle are the solutions 2:3 = 2/ y is proportional to x y is inversely proportional to x y is proportional to x squared exponential graph percentage change= (new value/original) x
