# 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 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.org, or contact us via twitter @stepsupportcam.

### STEP Support - Assignment 11

This module includes some functions defined in a way you may not have seen before, and several equations (most of which can be solved with carefully chosen substitutions). Previous assignments can be found here, but you can do this one without having done the others first.

### STEP Support - Assignment 12

This module includes proving divisibility of some expressions, probability and a puzzle which on first reading seems to be unsolvable. 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.

### 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 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 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 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 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 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 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.

Underground Mathematics: Selected worked STEP questions

STEP Question database

University of Cambridge Mathematics Faculty: What do we look for?

University of Cambridge Mathematics Faculty: Information about STEP