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.

A worksheet for F angles and a worksheet for Z angles. Now with answers included.

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.

When a pupil asked “what do we need to know for the exam” this is what I wrote. It covers every topic in National 5 maths, with examples of the formulas then ones for you to try (reading isn’t enough in maths, you need to do the problems yourself). The formulas that are in grey are the ones that you are given in the exam, but I included here anyway. Edit: Jan 2022 fixed two mistakes with indices

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

Some resources to help understand the normal approximation to a binomial distribution. A Powerpoint investigating when a Binomial distribution is close to a normal distribution, and also a video commentary of the Powerpoint. We find that if the sample size is too small (or too skewed) then the normal approximation is good. Specifically, we want np>5 and nq>5. A couple of worked solutions to example problems, in video form

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

Three standard questions testing pupils can correctly use the Wilxocon test, for determining if there is a difference between two sets of data. There are also two extension questions. Provided with full solutions.

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

Two worksheets, testing basic probability with dice, coloured balls and letters. The second worksheet is more difficult and introduces sampling with and without replacement. Full solutions included. Edit: May 2023 fixed question numbering

18 revision sheets all provided with full solutions. Some cover the whole course some a few areas only. Edit March 2023: Updated Sheets 1-6, 9, 14-16 Edit Dec 2023: Added 17-18

Practice Questions on one-sample and two-sample versions of the following tests • z-test for a difference in population means • t-test for a difference in population means (including paired) • z-test for a difference in population proportions

Three sets of questions revising: - Trig Graphs - Sine Rule, Cosine Rule and Area of Triangle (everything except trig identities) Plus an extra couple of questions as a Homework Edit: added some Powerpoint slides for revision Provided with full worked solutions