TSR question packs

Really need somewhere to put these. Every pack starts with 5 questions, though I will add more questions over time. (at the moment, I'm trying for breadth as opposed to depth) I plan on making written solutions but I doubt I'd have them all done by exams, so I'll only be doing them for the questions without markschemes first.

Most of the questions are either from the 2000-2008 spec (rarely, the IAL spec) or different exam boards, particularly OCR, MEI and CIE, though AQA FP4 comes in handy for vectors/matrices. Included are the markschemes and the examiner reports. (where available) The questions are largely included verbatim except in the case of notational differences (for example, MEI prefers using j to mean the imaginary unit) and differences in terminology/convention. I try to include a mix of standard and extension questions. I am not sure how good the questions I wrote myself are, they definitely differ in style. Let me know if they are too hard or too easy.

[D] indicates a pack that is done, sitting on my Google Drive, but that I'm yet to check through.

[P] indicates a pack I'm currently making.

I've started putting headers with the relevant spec points on the sheets. Let me know what you think about these on TSR or in comments here.

Note: Where it says [Markscheme pg xx] [Examiner report pg xx] below a question - these are links. In newer sheets these will be made blue to make this clear. The links should take you straight to the relevant page, the page numbers are provided if it doesn't. 

Packs

Core Pure 1

• Basic complex numbers (arithmetic, solving polynomials, modulus and argument)
• Complex loci (Solutions)
• Sums of simple finite series
• Roots of polynomials (Solutions)
• Volumes of revolution
• 2x2 Matrix Algebra
• 3x3 Matrix Algebra
• New matrices (invariant lines/points, solving sim equations)
• Induction (Solutions) - updated 14/04/19 adding 5 more questions
• Vectors (worked solution to Q2)

Core Pure 2

• De Moivre's Theorem
• Solving geometric problems with complex numbers
• Sums of series with complex numbers (Solutions)
• Method of differences
• Maclaurin series [D]
• Improper Integrals
• Mean value of functions
• Mixed integrals [D]
• Volumes of revolution
• Polar Coordinates (Solutions)
• Hyperbolic Functions (Solutions)
• Modelling with differential equations

Further Pure 1

• Vectors
• Parabolas/rectangular hyperbolas
• Ellipses/hyperbolas
• Inequalities [D]
• T-formulae
• Finding Taylor Series
• Mixed limits
• Limits by Series Expansion
• Series solution of differential equations
• Leibniz's Theorem
• Weierstrass Substitution for Integrals
• L'Hopital's Rule
• Numerical Methods (Solutions)
• Reducible Differential Equations

Further Pure 2

To come.

• Group Theory
• Further Integration - Reduction Formulae
• Further Integration - Arc Length and Area of Surface of Revolution
• Further Matrix Algebra
• Further Complex Loci
• Number Theory
• Recurrence relations

Further Mechanics 1

• Momentum and impulse
• Work energy and power
• Elastic strings and springs
• Elastic collisions in one dimension
• Elastic collisions in two dimensions

Further Statistics 1

• Discrete Random Variables
• Poisson Distribution
• Geometric and Negative Binomial distributions
• Hypothesis Testing [P]
• Central Limit Theorem
• Chi-Square Testing - updated 24/04/19 adding 5 more questions
• Probability Generating Functions - updated 15/04/19 adding 5 more questions
• Quality of tests

Further Statistics 2

• Linear Regression and Correlation
• Continuous Probability Distributions
• Combinations of Random Variables
• Estimation and Hypothesis Testing with the Normal Distribution
• Further Hypothesis Testing
• Testing with the t-distribution.

Single maths

Statistics Year 1

• Sampling
• Measures of location and spread/representation of data
• Correlation
• Probability
• Binomial Distribution

Statistics Year 2

• Correlation [P]
• Conditional Probability
• Normal Distribution

Mechanics Year 1

• Constant Acceleration
• Forces and Motion
• Variable Acceleration in One Dimension

Mechanics Year 2

• Moments
• Projectile Motion
• Applications of Forces
• Variable Acceleration in Two Dimensions

Some advice

A major complaint that appeared in several examiner reports for the 2018 series was that students didn't know the new stuff or were unprepared for the new style, so having a good understanding of the topics, not just memorising the procedures for common questions, will give you the upper hand. Doing questions from other sources should help with this.

You should be prepared for an increase in contextual/synoptic questions (questions that combine aspects of various topics, which happens a fair amount in maths) and questions with unseen aspects. Do note that they can assume single maths knowledge. The AS specimen paper mixed SM1 binomial distributions with CP1 volumes of revolution, and the 2019 AS Core Pure paper had a question on standard deviation. I will try to include these types of questions in these packs. This was not the case with the old specification since everyone had done different applied options. (you could forego mechanics or stats completely)

Option papers assume knowledge in Core Pure. FP2/FS2/FM2/D2 can assume knowledge from FP1/FS1/FM1/D1 respectively.

If you use Pearson's textbooks - do note that a considerable number of "challenge" questions are not extension work and are realistic exam questions and should not really be skipped. (though there are exceptions) As an example, see SM2 Mixed Exercise 7 (where a standard M2 moments question, similar to one seen in the specimen, is labelled "challenge") or FP1 Chapter 6 [will check which exercise]. (the spec says you may have to use substitution for limits) Some of the textbooks really aren't great and would gladly point people to third party textbooks here.

About

The packs are made using LaTeX with the exam document class. PGFPlots in TikZ is used for any graphs not from exam papers. Can give the source .tex to any pack if anyone wants it for some reason.

A good amount of the packs should be accessible to someone with only AS knowledge, but the year 1 packs do include synoptic questions involving year 2 topics. (I think, for example, induction should either come at the end of the course so as to draw upon any topic, as it used to or be more properly integrated.)

I'm going to prioritise packs for Core Pure, FS1 and FP1 as those are the options I'm taking. I was asked to do FM1 so I'll do those if I have time. I haven't studied FM1 properly so I don't think I'll be able to make up interesting/challenging questions. They will be mostly past paper questions and I'll probably have to guesstimate difficulty based off examiner reports. After this, FS2 and FP2 will follow. (I know a decent proportion of these options so will be able to make up questions as well as collate past paper questions) If there's any demand I'll do FM2/D1/D2 too. (but I haven't studied FM2/D2 at all)