• Free-standing mathematics qualifications fsmq

TSR Wiki > Study Help > Exams and Qualifications > More Qualifications > Free-standing mathematics qualifications fsmq

The Free-Standing Mathematics Qualifications are a group of separate qualifications, that are neither a GCSE nor an A-level. They are meant to bridge the gap between GCSE Mathematics and AS level Mathematics, and are typically taken by students who take their GCSE Mathematics a year early, and study the syllabus for the FSMQ in year 11.



There are currently only two boards for the FSMQ, which are OCR and AQA. Edexcel used to have the FSMQ however they withdrew, with the last exam held in June 2004.


OCR offer two qualifications: 'Foundations of Advanced Mathematics' (which is jointly developed by OCR and MEI) and 'Additional Mathematics'.


AQA offer a much wider variety of qualifications:

  • At foundation level, there are three qualifications: 'Managing Money,' 'Working in 2 and 3 Dimensions' and 'Making Sense of Data'.
  • At intermediate level, there are again three qualifications: 'Calculation Finances,' 'Handling and Interpreting Data' and 'Using Algebra, Functions and Graphs'.
  • At Advanced level, there are four different qualifications: 'Using and Applying Statistics,' 'Modeling with Calculus,' 'Using and Applying Decision Mathematics' and 'Working with Algebraic and Graphical Techniques'.

AQA Specifications may be found here: http://www.aqa.org.uk/qual/pdf/AQA-6990-6991-6992-6994-W-SP-08.PDF


There are three levels, 1 to 3, which are foundation, intermediate and advanced. The intermediate qualification is roughly the equivalent to GCSE Mathematics, however the advanced qualification is a mixture of AS topics, and is about the same as one AS-module.

Some modules in both AQA and OCR FSMQ may be used towards the AS Use of Mathematics as well.


UCAS points are awarded on achievement in the FSMQ, with 20 points for an A, 17 points for a B, 13 for a C, 10 for a D and 7 for an E. Unlike GCSEs, it is impossible to gain the A* grade, with the highest grade being an A.


Unlike other examinations, for some FSMQs, formula sheets or booklets are not provided, and candidates are expected to recall all formulae in the syllabus.

Additional Maths - OCR - Some Key Formulae:

  • General Integration: \displaystyle\int {\dfrac{\mathrm{d}y}{\mathrm{d}x}} \, \mathrm{d}x = y
  • Indefinite Integration: \displaystyle\int kx^n \, \mathrm{d}x = \dfrac{kx^{n+1}}{n+1} +c
  • Definite Integration: \displaystyle\int^b_a f'(x) \, \mathrm{d}x = f(b) - f(a)
  • Differentiation:  \frac{\mathrm{d}}{\mathrm{d}x} \left(kx^n\right) = nkx^{n-1}
  • Binomial Theorem: \displaystyle\binom{n}{r} = ^n\mathrm{C}_r = \dfrac{n!}{r! (n-r)!}
  • Binomial Expansion: (a+b)^n = ^n\mathrm{C}_0 a^n + ^n\mathrm{C}_1 a^{n-1}b + ^n\mathrm{C}_2 a^{n-2}b^2 + ... + ^n\mathrm{C}_n b^n
  • Binomial Probability:  P(X = r) = ^n\mathrm{C}_r p^r q^{n-r}
  • Gradient Formula:  m = \dfrac{y_2 - y_1}{x_2 - x_1}
  • Alternate Gradient Formula:  m =\tan \theta
  • Midpoint Formula:  \left( \dfrac{x_1 + x_2}{2} , \dfrac{y_1 + y_2}{2} \right)
  • Distance Formula:  \sqrt{(x_1-x_2)^2 + (y_1-y_2)^2}
  • Circle, with centre = (0,0) and radius = r:  x^2 + y^2 = r^2
  • Circle, with centre = (a,b):  (x-a)^2 + (y-b)^2 = r^2
This may be rewritten:
 x^2 + y^2 + fx + gy + c = 0
Where  f = -2a and  g = -2b and  c = a^2 + b^2 - r^2
  • Trigonometric Identities:  \sin^2 \theta + \cos^2 \theta = 1 and  \tan \theta = \frac{\sin \theta}{\cos \theta}
  • SUVAT Equations:
 v = u + at
s = ut + \frac{1}{2} at^2
s = \left(\frac{v+u}{2}\right)t
v^2 = u^2 + 2as
where s = displacement; u = initial velocity; v = final velocity; a = acceleration; t = time.
  • Quadratic Formula: x = \dfrac{-b \pm \sqrt{b^2-4ac}}{2a}
  • Proof that two lines are perpendicular:  m_1 \times m_2 = -1
  • Proof that two lines are parallel:  m_1 = m_2
  • Remainder Theorem: For integer polynomials f(x), the remainder on division by ax+b is equal to  f(-b/a)

Internal Links

AS Use of Mathematics


FSMQ Integration Revision Wiki

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