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Straight Lines

Straight Lines. Draw a diagram Y – y coordinate = gradient ( x – x coordinate) Gradient of Perpendicular lines x to -1 Intersect lines = solve the 2 lines as simultaneous equations. Surds. Rationalise by x top and bottom by √11 – 2 Treat like eyebrows and smiley face. 25x2.

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Straight Lines

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  1. Straight Lines • Draw a diagram • Y – y coordinate = gradient ( x – x coordinate) • Gradient of Perpendicular lines x to -1 • Intersect lines = solve the 2 lines as simultaneous equations

  2. Surds • Rationalise by x top and bottom by √11 – 2 • Treat like eyebrows and smiley face 25x2 • X top and bottom by √2

  3. Differentiation I Move power up to top as a negative Square root is power 1/2

  4. Differentiation II Get dy/dx This gives tangent gradient Turn upside down and change sign for normal gradient Equation of line y – y coord = gradient (x – x coord)

  5. Differentiation III Get dy/dx Solve dy/dx=0 to get stationary points Use x values in y= formula to get y values Use d2y/dx2 to decide max or min

  6. Binomial Expansion Use formula booklet for ( a + b ) n if you know n Use to find n Watch out for powers of eg 3x So 6 x (3X)2 = 6 x 9X2 = 54 X2

  7. Factor and Remainder Theorem Use x = -3, put equal to -39 If x = -3 gives zero, x + 3 would be a factor Get one factor, then use long division

  8. Roots of a quadratic Write down a, b and c then use the above facts Solve inequalities like quadratic equations

  9. Completing the square Half and square

  10. Transforming graphs

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