
The curve C has polar coordinates satisfying the differential equation
d^{2}r/dθ^{2} + 4r = 5sin(3θ)
for π/5≤θ≤3π/5. When θ=π/2, we have r=1 and dr/dθ=−2. Show that C forms a closed loop whose area is
π/5+25(sin(π/5)sin(2π/5))/48.

This STEP preparation course, a joint effort between Sheffield's School of Mathematics and Statistics and the AMSP, will provide a systematic introduction to the advanced problem solving skills required for STEP examinations.
Classes will be delivered by staff with prior experience in delivering STEP preparation. Some sessions will introduce the additional syllabus material required for the STEP examinations. The course will have fifteen sessions (twelve pure mathematics and three applied). The pure mathematics sessions are on a Tuesday; the applied sessions will be scheduled by January. Also to be scheduled by January for the late Spring are mock examinations in the style of STEP 1, 2 and 3.
This course is free to all students holding university offers who can demonstrate the necessary commitment. Participating students are expected to solve problems in class on whiteboards or on paper. To request places on this course or for further enquiries contact Dr James Cranch at somasoutreach@sheffield.ac.uk: it would help if you give your school, and the universities you've applied to, and the dependence of your offers upon STEP.
Timetable 2019—2020
Subject 
Date and time 
Venue 
Division by Zero 
Tuesday 21st January, 1630—1830 
Arts Tower LT5 
Proof 
Tuesday 28th January, 1630—1830 
Arts Tower LT5 
Coordinate Geometry 
Tuesday 4th February, 1630—1830 
Arts Tower LT5 
Trigonometry 
Tuesday 11th February, 1630—1830 
Arts Tower LT5 
No session (industrial action) 
Tuesday 25th February, 1630—1830 
Arts Tower LT5 
No session (industrial action) 
Tuesday 3rd March, 1630—1830 
Arts Tower LT5 
No session (industrial action) 
Tuesday 10th March, 1630—1830 
Arts Tower LT5 
Vectors and Matrices 
Tuesday 17th March, 1630—1830 
Arts Tower LT5 
Hyperbolic functions 
Tuesday 24th March, 1630—1830 
Arts Tower LT5 
Complex numbers 
Tuesday 28th April, 1630—1830 
Arts Tower LT5 
Proof and series 
Tuesday 5th May, 1630—1830 
Arts Tower LT5 
Differential equations 
Tuesday 12th May, 1630—1830 
Arts Tower LT5 
Mechanics, Probability and Stats I 
TBA 
TBA 
Mechanics, Probability and Stats II 
TBA 
TBA 
Mechanics, Probability and Stats III 
TBA 
TBA 
Mechanics, Probability and Stats IV 
TBA 
TBA 
STEP 1: mock exam 
TBA 
TBA 
STEP 2: mock exam 
TBA 
TBA 
STEP 3: mock exam 
TBA 
TBA 
Click here to see the timetable from 2018—2019 
Timetable 2018—2019
Subject 
Date and time 
Venue 
Division by Zero 
Tuesday 22nd January, 1630—1830 
Hicks LT6 
Proof 
Tuesday 29th January, 1630—1830 
Hicks LT1 
Coordinate Geometry 
Tuesday 5th February, 1630—1830 
Arts Tower LT2 
Trigonometry 
Tuesday 12th February, 1630—1830 
Arts Tower LT2 
Inequalities 
Tuesday 26th February, 1630—1830 
Arts Tower LT1 
Calculus 
Tuesday 5th March, 1630—1830 
Arts Tower LT2 
Vectors 
Tuesday 12th March, 1630—1830 
Arts Tower LT2 
Numbers, sequences, series 
Tuesday 19th March, 1630—1830 
Arts Tower LT2 
Hyperbolic functions 
Tuesday 26th March, 1630—1830 
Arts Tower LT1 
Complex numbers 
Tuesday 30th April, 1630—1830 
Arts Tower LT1 
Proof and series 
Tuesday 7th May, 1630—1830 
Arts Tower LT2 
Mechanics, Probability and Stats I
(with Prof Alan Zinober) 
Wednesday 8th May, 1630—1830 
Hicks I12 
Differential equations 
Tuesday 14th May, 1630—1830 
Arts Tower LT2 
Mechanics, Probability and Stats II
(with Prof Alan Zinober) 
Thursday 9th May, 1630—1830 
Hicks I12 
Mechanics, Probability and Stats III (TBC)
(with Prof Alan Zinober) 
Thursday 16th May, 1630—1830 
Hicks I12 
Mechanics, Probability and Stats IV (TBC)
(with Prof Alan Zinober) 
Friday 17th May, 1630—1830 
Hicks I12 
STEP 1: mock exam 
Tuesday 28th May, 1300—1600 
Hicks F35 
STEP 2: mock exam 
Wednesday 29th May, 1300—1600 
Hicks F35 
STEP 3: mock exam 
Thursday 30th May, 1300—1600 
Hicks F35 

Click here to see the timetable from 2017—2018 
Timetable 2017—2018
Subject 
Date and time 
Venue 
Proof 
Tuesday 23rd January, 1630—1830 
Hicks G34a 
Division by Zero
(with Dr Sam Marsh) 
Tuesday 30th January, 1630—1830 
Dainton GRC Seminar Room 
Coordinate Geometry 
Tuesday 6th February, 1630—1830 
Hicks G34a 
Trigonometry 
Tuesday 13th February, 1630—1830 
Hicks G34a 
Inequalities Cancelled (strike) 
Tuesday 27th February, 1630—1830 
Hicks G34a 
Calculus Cancelled (strike) 
Tuesday 6th March, 1630—1830 
Hicks G34a 
Vectors Cancelled (strike) 
Tuesday 13th March, 1630—1830 
Hicks G34a 
Numbers, sequences, series
(with Dr Evgeny Shinder) 
Tuesday 20th March, 1630—1830 
Hicks G34a 
Hyperbolic functions Inequalities 
Tuesday 17th April, 1630—1830 
Hicks G34a 
Complex numbers
(with Dr Fionntan Roukema) 
Tuesday 24th April, 1630—1830 
Hicks G34a

Proof and series Calculus 
Tuesday 1st May, 1630—1830 
Hicks G34a 
Differential equations Vectors 
Tuesday 8th May, 1630—1830 
Hicks G34a 
Mechanics, Probability and Stats I 
Monday 14th May, 1630—1830 
Hicks G34a 
Mechanics, Probability and Stats II 
Tuesday 15th May, 1630—1830 
Hicks G34a 
STEP 1: mock exam 
Tuesday 29th May, 1300—1600 
Hicks LT9 
STEP 2: mock exam 
Wednesday 30th May, 1300—1600 
Hicks LT9 
STEP 3: mock exam 
Thursday 31st May, 1300—1600 
Hicks LT9 

Click here to see the timetable from 2016—2017 
Timetable 2016—2017
Subject 
Date and time 
Venue 
Proof 
Tuesday 24th January 2017 (1600–1800) 
Hicks E36 
Division by zero 
Tuesday 31st January 2017 (1600–1800) 
Hicks E36 
Coordinate geometry 
Tuesday 7th February 2017 (1600–1800) 
Hicks E36 
Trigonometry 
Tuesday 14th February 2017 (1600–1800) 
Hicks E36 
Half term in Sheffield: no class 


Inequalities 
Tuesday 28th February 2017 (1600–1800) 
Hicks E36 
Calculus 
Tuesday 7th March 2017 (1600–1800) 
Hicks E36 
Vectors 
Tuesday 14th March 2017 (1600–1800) 
Hicks E36 
Numbers, sequences, series
(with Dr Evgeny Shinder) 
Tuesday 21st March 2017 (1600–1800) 
Hicks E36 
Applied mathematics
(with Prof Alan Zinober) 
Monday 27th March 2017 (1600–1800) 
Hicks G7 
(STEP 3) Hyperbolic functions 
Tuesday 28th March 2017 (1600–1800) 
Hicks E36 
Easter holidays: no classes 


Applied and probability 1
(with Prof Alan Zinober) 
Monday 24th April 2017 (1600–1800) 
Hicks G7 
(STEP 3) Complex numbers
(with Dr Fionntan Roukema) 
Tuesday 25th April 2017 (1600–1800) 
Hicks E36 
(STEP 3) Proof, series, trigonometry 
Tuesday 2nd May 2017 (1600–1800) 
Hicks E36 
Applied and probability 2
(with Prof Alan Zinober) 
Wednesday 3rd May 2017 (1600–1800) 
Hicks G7 
(STEP 3) Differential equations 
Tuesday 9th May 2017 (1600–1800) 
Hicks E36 
Mock exam (STEP 1) 
Tuesday 23rd May 2017 (13301630) 
Hicks LT 11 
Mock exam (STEP 2) 
Wednesday 24th May 2017 (13301630) 
Hicks LT 11 
Mock exam (STEP 3) 
Thursday 25th May 2017 (13301630) 
Hicks LT 11 
