Higher Applications of Maths formula sheet: there is no list, but there is a data booklet
Higher Applications of Maths
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Formula sheet
The nearest thing to a formula sheet is the R commands page of the data booklet. The card below opens today's paper with those commands in the drawer. The commands follow, grouped as in the 2026 booklet, with our own notes on what each does. The 2026 booklet was dated 30 March 2026, and the booklet for 2027 will be issued to schools before the exam. Check yours against the 2026 data booklet.
Higher Applications of Maths
Entering data
| Command | What it does |
|---|---|
| mydata<-read.csv("excel_data.csv") | Reads a CSV file from your working directory into R Studio and calls it mydata |
| attach(mydata) | Lets you use the column names as variables. Use detach(mydata) when you have finished |
Graphics
| Command | What it does |
|---|---|
| hist(X, main="Title", xlab="x", ylab="Frequency") | Histogram of a numeric variable X, with a title and axis labels |
| boxplot(Y, main="Title", ylab="y") | Box plot of a numeric variable Y |
| boxplot(X, Y, names=c("X","Y")) | Comparative box plots of X and Y side by side |
| plot(X, Y, main="Scatterplot", xlab="x", ylab="y") | Scatter diagram of Y against X |
| table(X) | Counts the observations in each category of X |
| pie(table(X), main="Title") | Pie chart of a categorical variable |
| barplot(table(X), main="Title") | Bar chart of a categorical variable |
Descriptive statistics
| Command | What it does |
|---|---|
| mean(X) | Mean of X |
| sd(X) | Standard deviation of X |
| summary(X) | Mean, median, minimum, maximum and the two quartiles of X |
| IQR(X) | Interquartile range of X |
| prop.table(table(X)) | Proportion of observations in each category |
| prop.table(table(X))*100 | The same as percentages |
| table(X, Y) | Cross-tabulation of two categorical variables |
Correlation and regression
| Command | What it does |
|---|---|
| cor.test(X, Y) | Correlation between X and Y, and a test of whether it is zero |
| lm(Y~X) | Fits the least squares regression line of Y on X |
| abline(lm(Y~X)) | Adds that line to a scatter diagram you have already drawn |
| summary(lm(Y~X)) | Shows the fitted model, including R-squared |
| predict(lm(Y~X), newdata=data.frame(X=C), interval="pred") | Predicts Y when X = C, with a 95% prediction interval |
Hypothesis testing
| Command | What it does |
|---|---|
| t.test(X, Y) | Two-sample t-test comparing X and Y |
| t.test(X, Y, paired=TRUE) | Paired t-test |
| prop.test(x=c(a, b), n=c(n1, n2)) | Test for equality of two proportions |
What the data booklet is and what is not in it
The 2026 data booklet was pre-release material: it was issued to schools in advance so that you could get to know the contexts. You get a clean copy in the exam, and an electronic copy is available during it. You may not take your own copy in. It had four documents:
- Deductions from salaries: the 2025/26 Scottish tax bands and National Insurance rates.
- Mortgage products and affordability: loan-to-value and the 28/36 rule.
- Honeybees: facts about beehives and colonies.
- Some helpful R commands: the page in the drawer above.
The booklet says that some examination questions will be based on this material, so read it before the exam. What is not in the 2026 booklet:
- Formulae. There are none: no compound interest, no standard deviation formula and no regression formulae. The spreadsheet and R do the calculation, and you decide what to ask them for.
- Spreadsheet functions. You need to know how to build a formula in a spreadsheet and how to use its functions.
- Interpretation. The commands print numbers. The marks are for explaining what they mean in context.
How the paper uses the booklet
The course specification gives the question paper 65 marks, scaled to 80, and 2 hours 5 minutes. The project is 30 marks over 8 hours, so the course is 110 marks in all. The paper is on a computer: the specimen paper lists spreadsheet and word processing files and says some answers must be completed on software and printed. In the 2027 timetable it is on Monday 26 April from 13:00 to 15:05 (Exam Timetable 2027, version 02). Our Higher Applications of Maths guide covers the whole course.
Using the R commands under exam pressure
Suppose a question gives two columns, hours revised and test mark, and asks for a scatter diagram, the correlation and a line of best fit. The commands you would use come straight from the page:
| Step | Command | What you do with the result |
|---|---|---|
| 1 | plot(hours, mark, main="Revision and marks", xlab="Hours", ylab="Mark") | Print the scatter diagram |
| 2 | cor.test(hours, mark) | Quote the correlation and say how strong it is |
| 3 | lm(mark~hours) | Read off the intercept and the slope |
| 4 | abline(lm(mark~hours)) | Draw the line on the scatter diagram |
Then write the interpretation. A slope of 3.2, for example, means each extra hour of revision goes with about 3.2 more marks, and you should say that the relationship is an association, not proof of cause.
Exam answers
The answers and a worked mark scheme come with today's paper once it is marked. Sit the paper with the sheet open beside you, mark it, and the worked answers show which line each question wanted. We do not publish official or past paper answers.
Use the sheet with today's paper
Uni-Sine publishes a free daily paper for Higher Applications of Maths. It is a short timed paper of 8 questions worth 25 to 35 marks, not a full SQA paper and not set by SQA. Many schools set a longer prelim in winter: see our prelims guide. Open the sheet, set a timer, and write the line you use at the start of each answer.
Common mistakes
- Looking for a formula sheet. There is not one. Read the data booklet instead.
- Not reading the booklet before the exam. Some questions are based on its contexts.
- Typing a command from memory. The names are in the booklet, so copy them exactly.
- Giving a number without a meaning. State what the result shows in the context of the question.
- Forgetting the printouts. Name, candidate number and centre must be on each one.
Common questions
Do you get a formula sheet in Higher Applications of Maths?
What is in the Higher Applications of Maths data booklet?
Can I take my own copy of the data booklet into the exam?
Is the Higher Applications of Maths exam on a computer?
When is the Higher Applications of Maths exam in 2027?
Revision cards
Say the answer first, then flip the card to check it.
Where to go next
- Solve it
Linear Regression Calculator
Fit a line of best fit and measure the correlation
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Probability
Distributions, expected values and the maths behind uncertainty
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Scotland · HigherHigher Applications of Maths grade boundaries 2025Higher Applications of Maths grade boundaries 2025 from the SQA: A needed 75 of 110, B 64, C 53 and D 42, with the question paper and project explained.