Level 3 Mathematical Studies AQA
Full course content, a smart revision plan and instant past paper feedback for Level 3 Mathematical Studies AQA.
Start revising this course →Content Overview
78 topics in 12 modules
☑️ Analysis of Data 7 topics
- Appreciating the Difference between Qualitative and Quantitative Data
- Appreciating the Difference between Primary and Secondary Data
- Collecting Quantitative and Qualitative Primary and Secondary Data
- Inferring Properties of Populations or Distributions from a Sample
- Appreciating the Strengths and Limitations of Random, Cluster, Stratified and Quota Sampling Methods and Applying this Understanding when Designing Sampling Strategies
- Calculating/Identifying Mean, Median, Mode, Quartiles, Percentiles, Range, Interquartile Range, Standard Deviation
- Interpreting Numerical Measures and Reaching Conclusions
☑️ Maths for Personal Finance 18 topics
- Substituting Numerical Values into Formulae, Spreadsheets and Financial Expressions
- Using Conventional Notation for Priority of Operations
- Applying and Interpreting Limits of Accuracy, Specifying Simple Error Intervals due to Truncation or Rounding
- Finding Approximate Solutions to Problems in Financial Contexts
- Interpreting Percentages and Percentage Changes as a Fraction or a Decimal and Interpreting these Multiplicatively
- Expressing One Quantity as a Percentage of Another
- Comparing Two Quantities Using Percentages
- Working with Percentages Over 100%
- Solving Problems involving Percentage Change
- Simple and Compound Interest
- Savings and Investments
- Student Loans and Mortgages
- Graphical Representation
- Income Tax, National Insurance, Value Added Tax (VAT)
- The Effect of Inflation
- Setting Up, Solving and Interpreting the Solutions to Financial Problems
- Currency Exchange Rates including Commission
- Budgeting
☑️ Estimation 5 topics
- Representing a Situation Mathematically, Making Assumptions and Simplifications
- Selecting and Using Appropriate Mathematical Techniques for Problems and Situations
- Interpreting Results in the Context of a Given Problem
- Evaluating Methods and Solutions
- Making Fast, Rough Estimates of Quantities which are Either Difficult or Impossible to Measure Directly
☑️ Critical Analysis of Given Data and Models 4 topics
- Criticising the Arguments of Others
- Summarising and Report Writing
- Comparing Results from a Model with Real Data
- Critical Analysis of Data Quoted in Media, Political Campaigns, Marketing, etc.
☑️ The Normal Distribution 3 topics
- Knowledge that this is a Symmetrical Distribution and that the Area Underneath the Normal 'Bell' Shaped Curve Represents Probability
- Use of the Notation to Describe a Normal Distribution in Terms of Mean and Standard Deviation
- Using a Calculator or Tables to Find Probabilities for Normally Distributed Data with Known Mean and Standard Deviation
☑️ Probabilities and Estimation 15 topics
- Understanding what is Meant by the Term 'Population' in Statistical Terms
- Developing Ideas of Sampling to Include the Concept of a Simple Random Sample from a Population
- Knowing that the Mean of a Sample is Called a 'Point Estimate' for the Mean of the Population
- Confidence Intervals for the Mean of a Normally Distributed Population of Known Variance
- Recognising when Pairs of Data are Uncorrelated, Correlated, Strong, Positively and Negatively Correlated
- Appreciating that Correlation does not Necessarily Imply Causation
- Understanding the Idea of an Outlier
- Understanding that the Strength of Correlation is Given by the pmcc
- Understanding that pmcc Always has a Value in the Range from -1 to +1
- Appreciating the Significance of a Positive, Zero or Negative Value of pmcc in Terms of Correlation of Data
- The Plotting of Data Pairs on Scatter Diagrams and the Drawing, by Eye, of a Line of Best Fit through the Mean Point
- Understanding the Concept of a Regression Line
- Plotting a Regression Line from its Equation
- Using Interpolation with Regression Lines to Make Predictions
- Understanding the Potential Problems of Extrapolation
☑️ Critical Path Analysis 4 topics
- Representing Compound Projects by Activity Networks
- Activity-On-Node Representation will be Used
- Using Early Time and Late Time Algorithms to Identify Critical Activities and Find the Critical Path(s)
- Using Gantt Charts (Cascade Diagrams) to Present Project Activities
☑️ Expectation 5 topics
- Understanding that Uncertain Outcomes can be Modelled as Random Events with Estimated Probabilities
- Applying Ideas of Randomness, Fairness and Equally Likely Events to Calculate Expected Outcomes
- Understanding and Applying Venn Diagrams and Simple Tree Diagrams
- Calculating the Probability of Combined Events
- Calculating the Expected Value of Quantities Such as Financial Loss or Gain
☑️ Cost Benefit Analysis 4 topics
- Understanding that Many Decisions have to be Made when Outcomes Cannot be Predicted with Certainty
- Understanding that the Actions that can be Taken to Reduce or Prevent Specific Risks may have their Own Costs
- Using Probabilities to Calculate Expected Values of Costs and Benefits of Decisions
- Understanding that Calculating an Expected Value is an Important Part of Such Decision Making
☑️ Graphical Methods 3 topics
- Sketching and Plotting Curves Defined by Simple equations
- Plotting and Interpreting Graphs (Including Exponential Graphs) in Real Contexts, to Find Approximate Solutions to Problems
- Interpreting the Solutions of Equations as the Intersection Points of Graphs and Vice Versa
☑️ Rates of Change 5 topics
- Interpreting the Gradient of a Straight Line Graph as a Rate of Change
- Interpreting the Gradient at a Point on a Curve as an Instantaneous Rate of Change
- Estimating Rates of Change for Functions from their Graphs
- Knowing that the Average Speed of an Object During a Particular Period of Time
- Knowing that the Gradient of a Distance–Time Graph Represents Speed and that the Gradient of a Velocity–Time Graph Represents Acceleration
☑️ Exponential Functions 5 topics
- Using a Calculator to Find Values of Such a Function
- Using a Calculator Log Function to Solve Equations of the Form
- Understanding that e has been Chosen as the Standard Base for Exponential Functions
- Formulating and Using Equations of the Form y = Cax and y=Cekx
- Using Exponential Functions to Model Growth and Decay in Various Contexts
Level 3 Mathematical Studies AQA Revision Content
Take a look at the written content available for this course. Practice-question availability may vary.
Level 3 Mathematical Studies AQA - Analysis of Data - Appreciating the Difference between Qualitative and Quantitative Data Content Preview
Analysis of Data
Appreciating the Difference between Qualitative and Quantitative Data
Defining and Distinguishing
- Qualitative Data refers to data that is not numerical and typically relates to concepts, opinions or experiences.
- On the other hand, Quantitative Data is numerical and can be measured or quantified.
- Qualitative data is often described as unstructured because it cannot be neatly fit into stats or mathematical models.
- Conversely, quantitative data is structured; it can be organised and analysed using statistical methods.
Gathering Data
- Gathering qualitative data often involves methods such as interviews, focus groups, and participant observation, which aim to gain a detailed understanding of a topic.
- Quantitative data is commonly collected through methods such as surveys or experiments which produce numerical results.
- While collecting qualitative data, the main aim is to get an in-depth comprehension of human behaviour and the reasons behind such behaviour.
- While collecting quantitative data, the objective is to generate numerical data that can be transformed into usable statistics.
Analysing and Interpreting Data
- Qualitative data analysis is frequently interpretive and seeks to explain the 'why' and 'how' of human behaviour.
- Quantitative data analysis, however, often involves focusing on the measurable, using methods such as statistical analysis or computational techniques.
- Qualitative data lends itself to detailed, narrative descriptions, while quantitative data results in numerical summaries, charts, or graphs.
- Interpretations of qualitative data are based on observed patterns or themes, while quantitative data interpretations rely on statistical significance or differences in measurement.
Strengths and Weaknesses
- Qualitative data can provide rich, detailed information but may be difficult to generalise and time-consuming to collect and analyse.
- Quantitative data, however, is relatively quick to collect and analyse and can be easily generalised but may not provide the same depth or complexity of information.
- It's worth noting that combining both qualitative and quantitative data, a method known as 'mixed methods' approach, can leverage the strengths of both, helping to build a more complete and nuanced understanding of the study area.
Question: What type of research method, qualitative or quantitative, would be more appropriate for a study aiming to understand the reasons behind overseas students choosing to attend a specific university and why?
Unlock instant, personalised feedback
Sign up to Adapt to practise the exam questions available for this course with instant, personalised feedback.
Start revising this course →Try Adapt now
Add this exact course and build your personalised revision plan.