# Points from FP1 past papers, 28 April 2017, 5 May 2017, and 12 May 2017

Download pdf for issues arising from FP1 past papers on:

• How to explain a calculation of arg(z)
• How to indicate use of “sum of roots” and “product of roots”
• Symmetrical calculations in parabola and hyperbola questions
• Reading the word “hence”, in particular in questions using the Cayley-Hamilton theorem
• Why the sum for r=1 to n of n is…. n2
• Induction problems with divisibility

Download pdf (or odt file) for issues arising from FP1 past papers on:

• Induction problems with divisibility
• Simultaneous equations and matrices
• Square roots of complex numbers
• Problems like: “Find λ if λ is real, z= 5 + i√3, and arg (z + λ) = π/3”

Download pdf for issues arising from F1 IAL papers on:

• Solving cubics and quartics.
• Also note: If you say “call the other roots a±bi” and do the calculation from sum of roots and product of roots, you may get an imaginary value for b, say b2=−(49/4), so b=±(7i/2). That’s all right. It just means that those two other roots you are looking for are both real.

• “Prove that the approximate solution 0.642 is correct to three decimal places”.
• Finding the enlargement factor and the angle of rotation for a matrix which you know represents an enlargement combined with a rotation.
• Given a point on the axis of a parabola, to find the two points at which a circle centred at that point just touches the parabola.