FMPRFurther Maths, Maths & Physics Revision
Further Maths, Maths & Physics Revision

About FMPR

One place to learn and revise A level content, written to the exact specification you sit.

Specifications

Further MathematicsPearson Edexcel9FM0 Further MathematicsAQA7367 MathematicsPearson Edexcel9MA0 MathematicsAQA7357 PhysicsPearson Edexcel9PH0 PhysicsAQA7408

Section and topic headings use each specification's own wording, and every point keeps the specification's reference, so you can find it in the official document. Year 12 means the content is also in the AS specification; Year 13 means A level only.

What FMPR has

TopicsEvery specification point, with a plain-English summary of each topic. FormulaeWhat you must remember, for Year 12 and Year 13. PracticeEasy, medium and hard exam-style questions with full worked answers and marks.
LessonsComing next: a lesson for each topic, explained from what you already know.

How answers look

Core Pure · section 2.1 · Year 12

1. f(z)=z3−3z2+z+5\mathrm{f}(z) = z^3 - 3z^2 + z + 5

Given that 2−i2 - \mathrm{i} is a root of the equation f(z)=0\mathrm{f}(z) = 0, solve f(z)=0\mathrm{f}(z) = 0 completely.

(5)
  1. Real coefficients, so the complex roots are a conjugate pair: 2+i2 + \mathrm{i} is also a root.B1
  2. (z−(2−i))(z−(2+i))=(z−2)2−i2\bigl(z-(2-\mathrm{i})\bigr)\bigl(z-(2+\mathrm{i})\bigr) = (z-2)^2 - \mathrm{i}^2M1
  3. =z2−4z+5= z^2 - 4z + 5A1
  4. z3−3z2+z+5=(z2−4z+5)(z+1)z^3 - 3z^2 + z + 5 = (z^2 - 4z + 5)(z + 1)constant terms: 5×1=55 \times 1 = 5 ✓M1
  5. z=−1,  z=2+i,  z=2−iz = -1,\; z = 2 + \mathrm{i},\; z = 2 - \mathrm{i}A1

Total5

The question as printed, the working as a student would write it, and the marks each line earns.

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