These Foundation modules are designed to develop your problem solving skills and provide an introduction to solving STEP (and STEP-like) problems. Most of the questions are taken from old STEP 1 papers, with some STEP 2 questions appearing in later modules. The assignments also introduce mathematical ideas beyond the syllabus with lots of opportunities for extra reading.

**Please note that STEP 1 has now been discontinued, and the last STEP 1 paper was in 2019.**

A lot of these assignments only require GCSE or AS knowledge (though they will ask you to use it in unusual ways!), and the first 10 to 15 Assignments are aimed at year 12 students. If you think there is a possibility that you will be sitting STEP 2 or STEP 3 in the summer of year 13 then we **strongly advise** that you start working on these assignments in year 12, or in the summer before you start year 13.

There are 25 Foundation modules, and the intention is that you work through them in order. There are also three collections of STEP questions (one each for pure, mechanics and statistics) which can be found after Assignment 25. Once you feel ready, you can move onto the 21 STEP 2 and STEP 3 modules.

If you have any questions about the assignments, or STEP in general, or feedback about our resources you can email us at step@maths.cam.ac.uk, or contact us via twitter @stepsupportcam.

There is more information about the different module types here.

### STEP Support - Assignment 1

This module involves some algebraic manipulation and some work on quadratic equations. There is also a geometry question with a surprising result.

### STEP Support - Assignment 2

This module involves some more algebra, graph sketching and finding the maximum and minimum values of some functions.

### STEP Support - Assignment 3

This module involves some series work, an introduction to the "floor" function and a linear Diophantine equation.

### STEP Support - Assignment 4

This module includes a proof of a circle theorem, sketching inequalities in 2 variables and a couple of logic puzzles. Previous assignments can be found here, but you can do this one without having done the others first.

### STEP Support - Assignment 5

This module involves some trigonometry and a question about a tetrahedron (and a question about socks!). Previous assignments can be found here, but you can do this one without having done the others first.

### STEP Support - Assignment 6

This module covers arrangements and some problems with probability. Previous assignments can be found here, but you can do this one without having done the others first.

### STEP Support - Assignment 7

This module involves some graph sketching and work on the roots of equations. Previous assignments can be found here, but you can do this one without having done the others first.

### STEP Support - Assignment 8

This module introduces the AM-GM inequality and the intersections of circles and ellipses. Previous assignments can be found here, but you can do this one without having done the others first.

### STEP Support - Assignment 9

This module includes some proofs involving triangles and sketching cubics. Previous assignments can be found here, but you can do this one without having done the others first.

### STEP Support - Assignment 10

This module derives some of the compound trigonometry formula ($\sin(\alpha + \beta)$ etc.) and introduces a new function. Previous assignments can be found here, but you can do this one without having done the others first.