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ScotlandMaths

Applications

7 dot points across 7 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you apply trigonometry to bearings, angles of elevation and depression, and problems in three dimensions?

Applying trigonometry, the sine and cosine rules and the area formula to practical problems involving bearings, angles of elevation and depression, and three-dimensional shapes.
A focused answer to the SQA National 5 Mathematics applications of trigonometry content, covering bearings, angles of elevation and depression, and using the sine rule, cosine rule and area formula in practical and three-dimensional problems.
10 min answer →

How do you summarise and compare data sets using the five-figure summary, quartiles, the interquartile range and a boxplot?

Calculating the five-figure summary (minimum, lower quartile, median, upper quartile, maximum), the range and interquartile range, drawing boxplots, and comparing two data sets.
A focused answer to the SQA National 5 Mathematics statistics content, covering the five-figure summary, the median and quartiles, the range and interquartile range, drawing and reading boxplots, and comparing two data sets by their average and spread.
9 min answer →

How do you add, subtract, multiply and divide fractions, including mixed numbers, without a calculator?

Calculating with fractions: adding, subtracting, multiplying and dividing fractions and mixed numbers, and finding a fraction of a quantity.
A focused answer to the SQA National 5 Mathematics fractions content, covering adding and subtracting fractions with a common denominator, multiplying and dividing fractions, working with mixed numbers, and finding a fraction of a quantity, all for non-calculator work.
9 min answer →

How do you work with percentage increase and decrease, reverse percentages, and repeated percentage change such as compound interest and appreciation?

Calculating percentage increase and decrease, finding the original amount in reverse percentage problems, and using a multiplier for repeated percentage change including appreciation, depreciation and compound interest.
A focused answer to the SQA National 5 Mathematics percentages content, covering percentage increase and decrease using a multiplier, reverse percentage problems to find an original amount, and repeated percentage change such as compound interest, appreciation and depreciation.
10 min answer →

How do you use a scattergraph and a line of best fit to describe correlation and make predictions?

Drawing and interpreting scattergraphs, describing correlation, drawing a line of best fit, finding its equation and using it to estimate values.
A focused answer to the SQA National 5 Mathematics scattergraph content, covering plotting and interpreting scattergraphs, describing positive, negative and no correlation, drawing a line of best fit, finding its equation, and using it to estimate values.
9 min answer →

How do you calculate the standard deviation of a data set and use it to compare the spread of two data sets?

Calculating the standard deviation of a data set using the standard formula, and using the mean and standard deviation to compare two data sets.
A focused answer to the SQA National 5 Mathematics standard deviation content, covering how to calculate the standard deviation with the National 5 formula, what it measures, and how to compare two data sets using the mean and standard deviation together.
10 min answer →

How do you add, subtract and scale vectors, and find the magnitude of a vector in two and three dimensions?

Working with vectors in two and three dimensions: vector components, adding and subtracting vectors, multiplying by a scalar, and calculating the magnitude of a vector.
A focused answer to the SQA National 5 Mathematics vectors content, covering vectors in component form, adding and subtracting vectors, multiplying a vector by a scalar, and finding the magnitude of a vector in two and three dimensions.
9 min answer →