F1 exam technique

The paper

• One written paper: 1 hour 30 minutes, 75 marks, answer every question.
• A calculator is allowed, and the Mathematical Formulae and Statistical Tables booklet is provided.
• F1 is worth one third of the International AS in Further Mathematics and one sixth of the full International A level.
• Knowledge of P1 and P2 is assumed.

Show the method

• Complex numbers: when told to find roots "showing your working" or "without a calculator", show the factorising, division or completing the square.
• Roots of quadratics: "without solving" means use α + β and αβ.
• Numerical methods: state f(a) and f(b) with signs, and write a conclusion about the sign change and continuity. Show the substitution in Newton-Raphson.
• Induction: write all four parts, including the conclusion.

Common slips

• Wrong quadrant for an argument: always sketch.
• Matrix products in the wrong order, especially for combined transformations.
• Forgetting that Σ_(r=1)ⁿ c = cn.
• Losing marks for rounding: keep full calculator values and round only at the end, to the accuracy asked.
• Describing a transformation without its centre, angle, direction, mirror line or scale factor.

Worked example

A question says: "Show that f(x) = x³ + 8x - 19 has a root between 1 and 2." What does a full-mark answer look like?

1. f(1) = -10 < 0 and f(2) = 5 > 0.
2. There is a change of sign and f is continuous.

Answer: So there is a root between x = 1 and x = 2

Check yourself

1. The F1 paper has 75 marks in 90 minutes. About how many minutes should you spend per mark?
   Show answer

   1.2. 90/75 = 1.2 minutes per mark, so a 10-mark question deserves about 12 minutes.

2. Which conclusion earns the final mark for locating a root of a continuous function f in [1, 2]?
   • f(1) < 0 and f(2) > 0, sign change and f continuous, so a root lies in [1, 2]
   • f(1) = -10 and f(2) = 5
   • The root is 1.5
   • f is a cubic, so it has a root
   Show answer

   f(1) < 0 and f(2) > 0, sign change and f continuous, so a root lies in [1, 2]. Values alone are not enough; you need the sign change, continuity and a conclusion.

3. A question says "without solving the equation, find α² + β²". What should you do?
   • Solve with the formula and square the roots
   • Use a calculator's equation solver and add the squares
   • Use α² + β² = (α + β)² - 2αβ with the sum and product
   • Guess α and β
   Show answer

   Use α² + β² = (α + β)² - 2αβ with the sum and product. "Without solving" means use the symmetric function method; solving gets no method marks.

4. Which part of an induction proof do students most often lose a mark for leaving out?
   • Writing n = 1
   • The concluding statement
   • Using a pen
   • Writing the formula
   Show answer

   The concluding statement. The conclusion that links the basis and the inductive step carries a mark.

5. What is the best first step when finding arg(-3 + 2i)?
   • Type tan^-1(2/-3) into a calculator and use the answer
   • Use degrees
   • Find the conjugate
   • Sketch the point on an Argand diagram to see its quadrant
   Show answer

   Sketch the point on an Argand diagram to see its quadrant. The calculator gives a fourth quadrant angle, but -3 + 2i is in the second quadrant.

Practise with instant feedback Print this lesson

Sources

• Pearson Edexcel International Advanced Level in Mathematics, Further Mathematics and Pure Mathematics specification (issue 3), Unit FP1
• Pearson Edexcel IAL Further Pure Mathematics 1 scheme of work

Last updated 8 November 2026. Spotted a mistake? Tell us.