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 STEP I papers, with some STEP II questions appearing in later modules. The assignments also introduce mathematical ideas beyond the syllabus with lots of opportunities for extra reading.

Even if you are not intending to sit STEP I we strongly recommend that you work through these resources to develop your problem solving skills before attempting the STEP II (and later STEP III) modules. If your university offer only includes a STEP I paper then you should concentrate your efforts on the Foundation modules.

The modules are ordered so that the most recent one is at the top.

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### STEP Support - Assignment 22

This module derives some more differentiation results and asks you to sketch some graphs. Previous assignments can be found here, but you can do this one without having done the others first.

### STEP Support - Assignment 21

This module introduces a couple of functions that might look familiar, and asks you to sketch some regions involving the modulus function. Previous assignments can be found here, but you can do this one without having done the others first.

### STEP Support - Assignment 20

This module includes some differentiation by first principles and an introduction to induction. Previous assignments can be found here, but you can do this one without having done the others first.

### STEP Support - Assignment 19

This module introduces the small angle approximations for $\sin \theta$, $\cos \theta$ and $\tan \theta$ and asks some questions about coordinate geometry. Previous assignments can be found here, but you can do this one without having done the others first.

### STEP Support - Assignment 18

This module includes some curve sketching, equation solving and an introduction to fractals. Previous assignments can be found here, but you can do this one without having done the others first.

### STEP Support - Assignment 17

This module includes some work with summations, and an introduction to Modular Arithmetic. Previous assignments can be found here, but you can do this one without having done the others first.

### STEP Support - Assignment 16

This module includes some work on trigonometric inequalities and using them to solve equations, and a "proof" that all triangles are isosceles. Previous assignments can be found here, but you can do this one without having done the others first.

### STEP Support - Assignment 15

This module includes some work on sequences, some notation which you may not have seen before and a problem about crossing the desert. Previous assignments can be found here, but you can do this one without having done the others first.

### STEP Support - Assignment 14

This module includes some useful factorisation results, and some work with Fibonacci numbers. Previous assignments can be found here, but you can do this one without having done the others first.

### STEP Support - Assignment 13

This module practises sketching graphs including consideration of whether they are convex or concave, and using these to determine how many roots of an equation there are. Previous assignments can be found here, but you can do this one without having done the others first.