← Applications of Mathematics syllabus

ScotlandApplications of Mathematics

Geometry and Measurement

6 dot points across 6 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you find the area of a composite shape including part of a circle, and the volume of a composite solid built from prisms, cylinders, cones, spheres or pyramids?

Solving a problem involving the area of a composite shape including part of a circle, and the volume of a composite solid made from standard solids such as cuboids, cylinders, cones, spheres and pyramids.
A focused answer to the SQA National 5 Applications of Mathematics geometry content on composite shapes, covering finding the area of a composite shape including part of a circle, and the volume of a composite solid built from cuboids, cylinders, cones, spheres and pyramids.
12 min answer →

How do you carry out efficient container packing, and use precedence tables to plan tasks and solve a time-management problem?

Carrying out efficient container packing to fit items into a space, and using precedence tables to plan tasks in order, find the minimum completion time and solve a time-management problem.
A focused answer to the SQA National 5 Applications of Mathematics measurement content on packing and planning, covering efficient container packing to fit items into a space, and using precedence tables to order tasks, find the minimum completion time and solve a time-management problem.
11 min answer →

How do you investigate a situation involving gradient, calculating the steepness of a slope or ramp as a ratio and relating it to vertical and horizontal distance?

Investigating a situation involving gradient, calculating gradient as vertical height divided by horizontal distance, and using it to find an unknown height or distance, including ramps and slopes.
A focused answer to the SQA National 5 Applications of Mathematics geometry content on gradient, covering calculating gradient as vertical height divided by horizontal distance, interpreting it as the steepness of a slope or ramp, and using it to find an unknown height or horizontal distance.
11 min answer →

How do you apply Pythagoras' theorem in a two-stage calculation, and use the properties of shapes to find an angle over at least two steps?

Using Pythagoras' theorem within a two-stage calculation to find a length, and applying the properties of shapes and angles to determine an angle in a calculation involving at least two steps.
A focused answer to the SQA National 5 Applications of Mathematics geometry content on Pythagoras and angles, covering using Pythagoras' theorem within a two-stage calculation to find a length, and applying the properties of shapes and angles to determine an angle over at least two steps.
12 min answer →

How do you construct a scale drawing and choose a sensible scale, and plan a navigation course using bearings and distances?

Constructing a scale drawing including choosing a suitable scale, converting between scaled and real distances, and planning a navigation course using three-figure bearings and distances.
A focused answer to the SQA National 5 Applications of Mathematics measurement content on scale drawings and navigation, covering choosing a sensible scale, converting between scaled and real distances, and planning a navigation course using three-figure bearings measured clockwise from north.
11 min answer →

How do you consider the effects of tolerance, finding the maximum and minimum acceptable values and deciding whether a measurement is within tolerance?

Considering the effects of tolerance, calculating the maximum and minimum acceptable values from a stated tolerance, and deciding whether a given measurement lies within the acceptable range.
A focused answer to the SQA National 5 Applications of Mathematics measurement content on tolerance, covering the meaning of tolerance, calculating the maximum and minimum acceptable values from a stated tolerance, and deciding whether a measurement lies within the acceptable range.
10 min answer →