STEP Support - Assignment 13
This STEP support 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 questions are difficult, they are supposed to be and you should expect to get stuck. However, as you tackle more and more STEP questions you will develop a range of problem solving skills (and spend less time "being stuck").
About this assignment
The assignment is published as a pdf file below. Each STEP Support assignment module starts with a warm-up exercise, followed by preparatory work leading to a STEP question. Finally, there is a warm-down exercise. The warm up for this assignment introduces the definitions of convex and concave graphs, and also discusses points of inflection. The main STEP question (2012 STEP 1 Question 2) uses some of these ideas to help sketch some quartics, and use these to determine how many solutions there are of some related equations. The final question is a problem where all the solutions have to be integers, i.e. a Diophantine equation.
Further reading
For more advice on tackling problems involving differentiation, try this NRICH Advanced Problem Solving module. This website describes an algorithm which can be used to solve linear Diophantine equations of the form $ax + by = c$.
Hints, support and self evaluation
The “Hints and partial solutions for Assignment 13” file gives suggestions on how you can tackle the questions, and some common pitfalls to avoid, as well as some partial solutions and answers.
