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Trapezium Rule

Trapezium Rule. Formula given 5 ordinates means n=4 strips. Trig Equations 1. Sin -1 0.5 Bow ties to get 2 angles As its 3x goes round the bow tie 2 more times Take away 15, divide by 3 Its only x between 0 and 180. Trig Equations II. Subs sin 2 x = 1 – cos 2 x or vice versa

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Trapezium Rule

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  1. Trapezium Rule • Formula given • 5 ordinates means n=4 strips

  2. Trig Equations 1 • Sin-1 0.5 • Bow ties to get 2 angles • As its 3x goes round the bow tie 2 more times • Take away 15, divide by 3 • Its only x between 0 and 180

  3. Trig Equations II • Subs sin 2 x = 1 – cos2 x or vice versa • Set up quadratic equation • Solve • Don’t forget bow ties Stays the same

  4. Integration • Rearrange to get powers of x • Cube root is 1/3 • Write powers on the bottom as negative powers

  5. Area under the curve • Solve curve = line to find A and B • Integrate between these x values • Integration is area under curve • Here shaded area = area under curve - trapezium

  6. APs • Use nth term = a + (n-1)d • Expect simultaneous equations to find a and d • Learn proof

  7. GPs • 3 formula to learn: • Nth term = a x r n-1 • Only if r is a between -1 and 1, • Set up equations • Expect quadratic equation, or to divide equations • Learn proof

  8. Radians • 3 formula to set up and solve equation • Arc length = rθ • Sector area = ½ r2θ • Triangle area = ½ r2 sin θ • Don’t forget area of circle = π r2 • Circumference of circle = πd

  9. Circles • C1 complete the square • Find the number in front of x • Halve and square • Repeat for y • Centre and radius can be written down • Radius and tangent meet at 90°, so grads x to -1 • If 2 circles touch, distance between centres is the 2 radius added

  10. Logs • Adopt a log eg log 10 100 = 2, as 10 2 = 100 • Log x + log y = log xy • Log x – log y = log (x/y) • Log x n = n log x • Use to write as a single log • Solve equation with x as a power

  11. Triangles • Also • Sin 30 = cos 60 = ½ • Sin 60 = cos 30 = √3 • 2

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