# STEP Support Foundation modules

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.

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 II or STEP III 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.

### STEP Support - Assignment 1

This module involves some algebraic manipulation and some work on quadratic equations. It also has a puzzle which at first glance seems to be unsolvable.

### STEP Support - Assignment 2

This module involves some more algebra, graph sketching and finding the maximum and minimum values of some functions. There is also a geometry question with a surprising result.

### 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 include 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.

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.