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What is STEP?

STEP (Sixth Term Examination Paper) is a maths admissions test used primarily by the University of Cambridge and the University of Warwick. Other UK universities sometimes ask for STEP as part of their offer. STEP questions are designed to reflect the difficulty of undergraduate maths.

If you’re applying to a university other than Cambridge or Warwick, you can tell the admissions tutors in advance that you’re doing STEP, and they may adjust your offer to include a STEP grade. 

How does STEP work?

STEP is graded on a scale of S to U: 

  • S (outstanding) 
  • 1 (very good)
  • 2 (good)
  • 3 (satisfactory)
  • U (unclassified)

It consists of up to three 3-hour exams: STEP 1, STEP 2 and STEP 3. Universities usually ask applicants to sit either one or two of the examinations. 

  • Cambridge offers A*A*A (A* Maths and Further Maths), and then asks you to sit STEP 2 and STEP 3. The grades they will ask for in these papers vary between colleges, but generally they ask for a 1 in both STEP 2 and STEP 3
  • Warwick have a wide variety of different offers for their Mathematics course: 
    • A*A*A (A* Maths and Further Maths), and grade 1 in STEP. This grade 1 can be in any of the three STEP Papers.  
    • A*A*A* (Including Maths and Further Maths) 
    • A*A*AA (A* Maths and Further Maths) 
    • Also, if you have achieved a good scored in MAT or TMUA, you may receive the reduced offer of A*A*A (A* Maths and Further Maths).

How are the papers structured?


A 3-hour paper divided into two parts: 

  • Section A (Pure Mathematics) (8 questions)
  • Section B (Mechanics and Probability/Statistics) (3 questions, with at least one on Probability/Statistics, and one on Mechanics).

STEP 2 and STEP 3

These are also 3-hour papers, but they are divided into three sections:

  • Each paper will consist of 12 questions:
    • Section A (Pure Mathematics) (8 questions
    • Section B (Mechanics) (2 questions)
    • Section C (Probability/Statistics) (2 questions)

In all three papers, each question will have a maximum mark of 20. You will be assessed on the six best answers given in all of the papers, but there is no restriction on the number you can try. There is also no restriction on where these sections may come from. For example, you could answer six questions from Section A and none from B or C.

You cannot have a formulae book or a calculator in the STEP exams. On their website, STEP specifies the formulae you should know, as some are beyond the A-Level syllabus. 

What’s the STEP syllabus?

STEP is mostly based on the A-Level syllabus, but there are some sections that will require knowledge beyond the scope of your A-Level Maths and Further Maths. 


STEP 1 tests the Pure, Mechanics and Probability/Statistics content of A-Level Maths.

It also tests the following non-A-level content

  • Proof: induction, necessary and sufficient conditions
  • Inequalities involving any function
  • Relating roots and coefficients of quadratics
  • Limits
  • Log change of base formula
  • Derivatives of sec, cosec, cot
  • Non-perpendicular moments
  • Use of binomial coefficients, and their applications to probability 


STEP 2 relies on the content from Pure AS Further Maths, and the additional Mechanics and Probability/Statistics content listed below:

  • Method of differences for series
  • Series expression for ex 
  • Hyperbolae and Ellipses
  • Derivatives of inverse trig functions and trig substitutions for integrals
  • Integration using partial fractions and reduction formulae 
  • Cartesian and vector equations of lines in 2D or 3D
  • Dot product
  • Use of energy in Mechanics
  • Collisions, including coefficient of restitution
  • Hooke’s Law and Elastic Potential Energy
  • Poisson distribution (including as an approximation of the binomial distribution)
  • Arbitrary continuous distributions


STEP 3 requires the content from the Pure Further Maths A-Level, and the additional topics below:

  • Arc length (finding lengths of curves)
  • Vector (cross) product, including in equations of lines
  • Transforming differential equations by substitution
  • Impulse (in mechanics) 
  • Mechanics of oblique impacts 
  • Finding centres of mass by integration 
  • Circular motion, including variable speed
  • Differential equations in mechanics, including derivatives with respect to displacement, rather than time
  • Identities for expectations and variances of sums and scalar multiples of variables 


Now that you’re familiar with everything you need to know about STEP, start preparing with our ultimate STEP guide or our free STEP guidebook.