Factorise the following quadratic x^2 - 8 + 16

Find two numbers that multiply together to equal the 3rd term and the product of the same two numbers also needs to equal the 2nd term. This is trial and error but in this case it will be,    (x - 4) (x - 4)

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Let Curve C be f(x)=(1/3)(x^2)+8 and line L be y=3x+k where k is a positive constant. Given that L is tangent to C, find the value of k. (6 marks approx)


A particle is moving in a straight line from A to B with constant acceleration 4m/s^2. The velocity of the particle at A is 3m/s in the direction AB. The velocity of the particle at B is 18m/s in the same direction/ Find the distance from A to B.


f'(x) = 3x^2 - 5cos(3x) + 90. Find f(x) and f''(x).


A curve is mapped by the equation y = 3x^3 + ax^2 + bx, where a is a constant. The value of dy/dx at x = 2 is double that of dy/dx at x = 1. A turning point occurs when x = -1. Find the values of a and b.


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