I provide comprehensive worksheets to revise a particular topic (always with answers included) as well as extension materials, for pupils ranging from age about 11 to 16+.
All of my premium resources have a UK and US version.
I provide comprehensive worksheets to revise a particular topic (always with answers included) as well as extension materials, for pupils ranging from age about 11 to 16+.
All of my premium resources have a UK and US version.
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
Three Powerpoints with simple questions on
percentage change
finding a percentage
-percentage increase or decrease
with extension questions on reverse percentage
Edit: added another powerpoint of mixed questions, a summary sheet, and a worksheet
Four probability resources: Conditional Probability with tree diagrams, Conditional Probability with Venn diagrams, Conditional Probability with Set Notation, Deadly disease probability question
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 classic question on probability with a rare disease
Thirteen homeworks each with full solutions, covering the following areas of the course.
1 - Probability
2 - Probability, Sampling, Binomial
3 - Probability, Sampling, Binomial
4 - Binomial, Normal, Poisson #1
5 - Distributions
5a - Distributions and Regressions
6 - Hypothesis Test
7 - Normal Approximation
8 - Control charts, Confidence Interval, Fences
9 - Mean and Variance
10 - Binomial, Normal, Poisson #2
11 - Z and T tests
12 - More Distributions
13 - Wilcoxon and Mann Whitney
For some of the homeworks (2,3,5) I have made slightly different alternative versions and they are included too.
Update: homeworks 2,5,7 updated March 2023
A rare chance to see the first ever use of an equals sign "for what could be more equal than two parallel lines" and therefore the first ever equation.
Pupils can read the Olde English, translate it into modern equations, then solve them. The first two are linear, the remaining four quadratic.
Provided with full solutions.
A problem solving project where pupils use Pythagoras to find how far away the horizon is, depending on your height about sea level.
This is an open-ended project, where rather than being given all the information up front the pupils have to work in groups to explore the problem, then reflect on what techniques were effective.
It practices several useful skills such as Pythagoras, circle geometry, expanding brackets and rearranging formulas.
There is the scope for very good pupils to extend the project in interesting directions.
A collection of five nicely presented powerpoints each with 5-10 logic puzzles, taken from the books of Raymond Smullyan. For example:
Knights always tell the truth and Knaves always lie. You meet two people. The first says “At least one of us is telling the truth.” What can you say about the two people?
All provided with answers, and references from which Raymond Smullyan book they are taken from.
Three examples of how matrices can be used to solve real problems. Requires knowledge of
matrix multiplication
matrix inverses
simple probability
Aimed at Advanced Higher Maths but useful for anyone who wants to answer the question ‘what are matrices used for’.
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 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
This is a set of six puzzles presented as large scale Power Points. I used them as colour A3 posters for a monthly maths competition.
Although they are challenging, they can all be solved without using any advanced techniques.
Full solutions included.
Edit: Added two more puzzles
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.
15 numeracy questions of increasing difficulty.
Multiple copies should be printed out (one-sided) and each team starts on Q1. When they bring you the answer to that they get Q2, and so on.
Topics covered:
percentages
simple algebra
angles in a triangle/quadrilateral
time
Included with answers.
A fun lesson with shapes for pupils to cut out and reform. Everyone should have fun with this. Although even young children can understand dissection it hides complicated mathematics in geometry in proof.
The dissections to try here are:
- A rectangle into a square with one cut
- A vase into a square
- An equilateral triangle into a square
- A 8 by 8 square into a 13 by 5 rectangle (!)
- A couple of miscellaneous shapes
- An approximate dissection of a circle into a square
Worked examples and questions on these four topics:
Substitute values into expressions and evaluate
Multiply two brackets
Solve inequalities
Create and solve inequalities for problems in words
Solutions included
This is a set of six puzzles presented as large scale Power Points. I used them as colour A3 posters for a monthly maths competition.
These puzzles are challenging and give the scope for comprehensive answers.
Full solutions included.
This is Power Point and practice questions to get pupils comfortable with subtracting a negative number. Rather than just stating that “it’s the same as adding” they will learn to do this instinctively, by thinking about temperature.
Full solutions provided.
A Powerpoint with questions and answers, alongside video solutions.
The following binomial questions are solved:
finding exact probabilities using the formula
finding more than or equal probabilities using hte data booklet
solving large problems using the normal approximation
