Four challenging problems as extension material. The first is to make the number 2021 from the numbers 10,9,8,…,3,2,1 in order. The other three are tough too! Solutions at the bottom of each slide.

Explanations and examples of the key statistical concepts for the Cambridge STEP Mathematics entrance exam. Covers Basic probability Combinatorics Mean and variance Continuous probability distributions Uniform, binomial and normal distributions Hypothesis testing All with solutions to my questions and references for the past paper questions

Practice question on topics that pupils might come across when sitting extra maths tests for admission to Cambridge, Oxford, or some other universities. The topics covered are: Worksheet 1 - Trapezium Rule, Fixed Point Iterations Worksheet 2 - Equations, Proportion, Probaility, Riddles Worksheet 3 - Graphs, Logarithms Worksheet 4 - Inequalities, Necessary and Sufficient, Proof, Logic Worksheet 5 - Sine and Cosine Rule, Trig Identities All with full solutions. (See my other resource for all the STEP Statisitc questions)

A Powerpoint / PDF giving the Indices Rules with some examples - I have printed these two-sided and laminated these for lots of pupils Also a few practice questions on Surds and Indices to diagnose what they need to practice.

A Powerpoint of revision and a Worksheet of practice questions. Covers: mean standard deviation median interquartile range statements

A series of ten questions asking pupils to prove Trig Identities. For example Show that 3 tan⁡x cos⁡x=3 sin⁡x All included with full solutions.

A set of 13 practice tests covering all aspects of the National 5 Course. Each one is laid out with space for write-on answers, and provided with solutions.

A set of nine revision homeworks, including one for calculator and one non-calculator. Covers all areas of the National 5 Mathematics syllabus. All provided with solutions.

A fun challenge to try and work out the maths behind the fact that a dog will take the optimal path into a river to get a ball. Needs knowledge of visualising 2D motion distance speed time finding the minimum of a quadratic Provided with solutions

Questions on the following topics: Direct and Inverse Proportion Reciprocal Graphs Nth term of linear or quadratic sequences Circle Theorems Probability Trigonometry Modulus function These are particularly aimed at Scottish pupils as these topics aren’t included in the Scottish syllabus.

Four worksheets with questions covering the maths required for Advanced Higher Mechanics (partial fractions, differentiation, integration). These topics are also included in Advanced Higher Maths so could be useful for that too. Update - added 2022 practice questions and a practice test. All with solutions.

Two resources about the Poisson Distribution A Powerpoint that contains everything you need for the Poisson distribution recap of the properties of the Normal and Binomial distributions (to avoid getting them mixed up) examples of situations with Poisson distributions solving small problems using the Poisson formula solving medium problems using a data booklet solving large problems using a normal approximation analysis of the assumptions involved in a Poisson distribution summary of the properties of the Poisson distribution An extra page of questions with solutions at the end

Three probability resources: Conditional Probability with tree diagrams, Conditional Probability with Venn diagrams, and Conditional Probability with Set Notation. A short video explaining how to solve a conditional probability problem using tree diagrams. A video using a Venn Diagram to determine if the events are independent, mutually exclusive, and calculate some conditional probabilities. This is done alongside calculating with a table. Practice questions with solutions using Set Notation

A Powerpoint with questions and answers, alongside video solutions. The following questions are solved for a normally distributed population: probability of being above a certain value probability of being below a certain value probability of being between two values Final answers are found using a data booklet (specifically the one for Advanced Higher Statistics in Scotland) Also included ‘AH Statistics Normal Distributions with Phi Notation’ which shows how the number of standard deviations above or below the mean leads to a probability. Normal distribution short questions

Three resources: A Powerpoint with questions and answers, alongside video solutions. The following questions are solved: finding the mean of a sample finding the variance of a sample estimating population mean from a sample estimating population variance from a sample Mean and Varirance questions by P Benson for which I’ve written out solutions Expectation Algebra questions

A one page summary of the four different types of two sample tests: Mann Whitney Wilcoxon Z-test T-test Also extra questions on two sample z-tests for proportions

Questions and solutions on linear regression: AH Statistics Linear Regression Questions - estimating the value of r, then calculating all of the information by hand from the table of values. Full solutions included. AH Statistics Regression.pdf - harder questions testing some theoretical topics AH Statistics Confidence and Prediction Intervals for Regression - questions AH Statistics Hypothesis Testing in Regression Analysis - longer explanation and questions on the beta and rho tests AH Statistics Linear Regression Running Times - a Paper 1 style practice question AH Statistics Regression FlowChart - a suggested order in which to approach bivariate data (data with two variables), starting with approximate methods and checking the validity of the model as you go.

An example of using Venn Diagrams to categorise the numbers from 1 to 20 as either even or prime. Included is Powerpoint Video explanation

A variety of resources for pupils to master Excel. Starts with a simple introduction then moves on to using it to run statistical tests. Although this isn’t part of the syllabus it’s useful for pupils to be able to check their answers, and learn some useful skills. AH Statistics - Simple Activities to learn Excel AH Statistics - How to draw a graph in Excel AH Statistics - Excel AH Statistics - Excel (solutions) AH Statistics - More Excel

Practice questions covering Western Electric Rules Determining if a system is in statistical control Calculating upper and lower control limits Working backwards from limits to finding standard deviation or sample size Finding the probability of a rule being broken Provided with solutions