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
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