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GCSE Maths
17/06/2023
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Median from arouped frequency table intervals freq cumu freq 3 3 6 9 6 0322210 104x420 20<x<30 304x440 40<x<50 Total: total frequency 2 = 12 8 15 23 1 24 24 additional Column 12 Cumulative frequency median interval median interval = 20 ≤ x² 30 Means from grouped frequency table intervals freq midpoint_mid x freq 05 5210 8 40 1055420 2045430 30≤5440 40.45450 Total : 10 7 30 mean = 19 3 e.g. 570= 19 30 S 15 25 35 total midx frequency total frequency 45 70 135 additional 570 columns 150 = mean 175 CORRESPONDING ANGLES → equal CO-INTERIOR ANGLES ALTERNATE ANGLES equal 180-x X VERTICALLY OPPOSITE → equal X 180-X 180-x X 180-X → Complete the square of the quadratic E=0. 1 +4% +7 = 2 +2) - 4 + 7 = น 2 +3 (-2,3) → minimum point → factorise the quadratic into two brackets e.g. x² - 2x - 15 (x - 5)(x+3) x = 5 x=-3 (5,0) and (-3,0)→ roots Ⓒ-15 2 y = f (x - 2) y = 3f (x) y coodingte x3 2 2 in x direction | y=f(-x) y = f (x) - - in y direction Y = f (2x) 1/1/2 x co-ordinate * co-ordinate becomes minus Y = -f(x) y co-ordinate becomes minus 90° 60° 45° انکا 30° امد اكرام الی ام ۔ ام اكوام -۲۱ 3 13 00 ه sin O 8502 tang I (x-a)² + (y - b)² = p² (a, b) → centre of circle r² → radius Circle Theorems Alternate segment theorem B Angles in the same segment theorem A 0 X- C. Chord of a circle A X- Bo B The angle that lies between a tangent cand a chord is equal to the angle subtended by the same chord in the alternate segment. D B A Angles in the same segment are equal. Tangent of a circle Diagram A The perpendicular from the centre of a E circle to a chord bisects the chord (splits the chord into two equal parts). Diagram B D A Angle at the centre theorem D I 2x D Angles in a semicircle I The angle...
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Alternative transcript:
at the centre is twice the B angle at the 180-a B circumference. Cyclic quadrilateral A The angle in a semicircle is 90 degrees. The opposite angles in a cyclic B quadrilateral total 180°. A. The angle between a tangent and radius is 90 degrees. B. Tangents which meet at the same point are equal in length. y=sin(x) graph Y 2 1 -360 -270 -180 -90 0 -2 90 180 270 y = sin x → starts at (0,0) → every 90° it cycles 1,0,-1,0 360 y = cos(x) graph 2 M -360 -270 -180 -90 a -2 90 180 2/70 360 y = cos x → starts at (0,1) → every 90° it cycles 0,-1, 0, 1 y = tan (x) graph YA 2 -360 -270 -180 -9D 9D 180 270 y = tan x asymptotes. → starts at (0,0) → every 90° it is either O or an asymptote 360 Asymptote - line that a graph gets close to, without ever touching or crossing it.