# One week to improve...

## One week to improve...

I'm currently helping a number of students in their final week before their A-Level pure maths papers.

As part of my tuition services, I am running daily zoom sessions discussing questions set on individual topics. I thought I would share the questions and answers that I am sharing with my students.

So if you check this article each day, you will find pdf copies of the questions and hopefully answers later the same day along with any commentary I find an appropriate addition!

My students are of course doing a substantial number of past papers too; the questions I am setting are designed to ensure we've not overlooked any particular techniques and if we have give us chance to discuss and repair the problems!

**Question set 1**

The first set of questions is on functions (and a little, related, trigonometry). Finding the range and inverses often proves to be problematic so it seemed a good first choice. Of particular interest is the trick for solving equations of the form $f(x) = f^{-1}(x)$ and this appears in a couple of places in these questions. (link at the bottom to "functions and trig 3")

**Question set 2**

The second set of questions are predominantly sequences and series (with a couple of functions and trig questions thrown in for fun). Of particular interest and importance is the geometric sequence, expressed in terms of an unknown value k. These give rise to polynomials equations which again add an extra level of difficulty to a question (link at the bottom to "sequences, series and some functions")

**Question set 3**

The third set of questions contains a series of useful integrals, any one of which is likely to feature on an exam. Mainly however, they're designed to remind students of some of the key integration techniques.

**Question set 4**

Trig, integration and functions with some parametric thrown in!

**Question set 5**

Theres a bit of a theme developing within these questions, clearly there is a series of topics that students find particularly difficult and this will help inform the site development!

**Question set 6**

More questions on a theme, with some interesting sequence questions and thrown into the mix.