Proofs of some of the key formulas in Advanced Higher Statistics. Not required for the course but some pupils (and teachers) may find it interesting. proof the two ways of writing the variance formula are equivalent proof that using the ‘divide by n-1’ formula gives the best estimate of a population variance proof of Bayes Theorem proof of laws of expectation and variance proof of the origin of the Poisson formula, and of the mean and variance proof of mean and variance for uniform discrete proof of mean and variance for uniform continuous proof that using proportions and the normal approximation to a binomial are equivalent proof a line of best fit goes through the average point proof the line of best fit gives the least squares proof of SSR formula proof in bivariate analysis DF=n-2 proof test slope parameter nonzero and coefficient of correlation nonzero are equivalent

A series of Pi Day resources aimed at GCSE / National 5 Level Homework is the easiest and features features: substitution, fractions, algebra, percentages, shapes, area Problems features: rearranging equations, simultaneous equations, volume of cuboids, Pythagoras. Revision is the hardest and features: radians, area, surds, area All with solutions included.

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.

A set of multi-part questions covering both chi-squared test for association and goodness of fit A set of questions building up to using chi-squared to work out whether a Binomial or Poisson distribution fits the data Both provided with full solutions.

A series of six questions on the Mann-Whitney test, including dealing with ties and the normal approximation (the data in these questions is not mine and is taken from various sources). A Wilcoxon and Mann-Whitney homework Both provided with full solutions

These are the course notes I have been using for the last few years to teach Advanced Higher Statistics. I wrote them myself, based on the SQA course description, and have included lots of examples. Included in this bundle AH Statistics Course Notes AH Statistics Formulas to Memorise (A list of all the important facts that need to be remembered for Advanced Higher Statistics, that are not in the formula sheet) AH Statistics 150 Quick Questions (A set of short questions covering all aspects of the Advanced Higher Statistics Course) AH Statistics 14 Tests (A revision resource giving a summary of the 14 hypothesis tests in the course:) AH Statistics Course Summary (Short questions on each aspect of the course and links to the place in the SQA Course Specification) All included with full solutions. If you spot any mistakes please let me know. Last update: March 2023

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 Edit June 2024: Added 19

Eleven fun questions based on the Scottish Advanced Higher Statistics course, also applicable to the English Statistics A level. Questions are on a Powerpoint and full solutions on a PDF. Topics covered include: conditional probability, regression analysis, confidence intervals, paired t-test, Poisson distribution, Binomial distribution, Chi-squared distribution, Continuous uniform distribution and Normal distribution. Edit: updated May 2023

A series of worksheets with practice questions on topics in the Advanced Higher Mechanics Course: - Centre of Mass, Energy, Freefall, Gravity, Momentum, Projectiles, Vectors, Work Energy & Power, Vectors Closest Approach, Circular Motion (including notes), SHM (including notes), mix of SUVAT/Kinetmatics/Vectors All with full solutions Updated Dec 2020

Many powerpoints, worksheets and a homework with mixed revision questions. Topic specific revision questions on the following topics, as both Powerpoints and PDFs. Circles Complete the Square Differentiation Functions Log Graphs M=tan theta Polynomials Straight Line Straight Line & Functions

A booklet for pupils to fill in with practice questions on curve sketching, of trig graphs and log graphs. Includes translating graphs. Q1 & Q2 are taken from past papers. Q7 and Q8 are left blank for extra questions. Full solutions at the end.

A worksheet of practice questions on everything to do with Higher Functions. domain and range max value of a function inverse functions tangent to a function showing a function is always positive sketch of a function differentiating a function quadratic inequalities

A write-on worksheet with 18 short questions revising exact values of trigonometry, Most questions simple e.g. sin(60) and also includes angles above 90 degrees, radians and a few questions on inverse trig. Solutions at the end.

Some revision questions on the topics my Higher Pupils found tricky this year log equations (e.g. cooling water, and algebra with logs) trig equations (algebra and wave equation) integration (polynomials and trig) There’s also a practice test which I took from somewhere and typed up solutions. I just used it as revision.

First homework covering Integration (polynomials and simple trig, area between curves) Revision (functions, circles, trig graphs, sequences) Edit: added second longer revision sheet covering polynomials trig calculus Full solutions included

A thorough test of differentiation skills. Covers differentiating polynomials and trig (chain rule but no product or quotient rule), tangents and stationary points. I’ve included the original homework, a version with hints (that my class needed) and full solutions.

Several revision Powerpoints and mixed revision worksheets. Many topics covered but in particular Binomial Theorem, Complex Numbers, Partial Fractions, Euclid and Proof. All with either short answers or full solutions Includes topic-specific revision material on the following topics, as Powerpoints and PDFs. Binomial Theorem Complex Numbers Binomial Theorem and Complex Numbers Loci of Complex Numbers Matrices Number Theory Partial Fractions Indices (revision of easier material to help with binomial theorem) Sequences

A set of revision questions involving bearings and then bearings with trigonometry - something pupils usually need a lot of practice on. Edit: added solutions October 2024

A bumper set of National 5 Maths resources grouped by topic. Five sets of Questions by Topic Four sets of Revision questions by Topic Whole Course Topic by Topic More Whole Course Topic by Topic Example Questions and Answers Covers everything in National 5: Fractions, Percentages, Inequalities, Straight Line, Brackets, Rearranging equations, Simultaneous equations, Area and perimeter, Function notation, Arcs and sectors, Volume, Pythagoras, Similarity, Quadratics, Trigonometry All provided with solutions

A two page Power Point with questions revising arcs and sectors.