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Maths

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AQA AS Core Maths Paper 1 Revision Notes PDF - Easy Study Guide

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AQA AS Core Maths Paper 1 Revision Notes PDF - Easy Study Guide

danica

@danica_n

14 Followers

Core Maths Paper 1 Revision Notes: A Comprehensive Guide for AQA Level 3 Mathematical Studies

This document provides essential revision notes for the AQA Level 3 Mathematical Studies (Core Maths) Paper 1. It covers key topics including:

Numerical Data Analysis
Estimation
Graphical Data Analysis
Personal Finance (excluding Tax and National Insurance)

The notes are designed to help students prepare for the AQA Certificate Level 3 Mathematical Studies (1350) examination, which has been taught since September 2014 with exams from June 2016.

Key features of these revision notes include:

Detailed explanations of data types and analysis methods
Step-by-step guides for creating and interpreting various graphs and charts
Formulas and techniques for statistical calculations
Practical examples and applications of core mathematical concepts

These AQA AS Core Maths Paper 1 revision notes are an invaluable resource for students looking to excel in their Core Maths Paper 1 examination.

28/05/2023

1114

Paper 1 Core Maths
Notes
AQA
Realising potential
*/ Subjects / Mathematics / AQA Certificate / Level 3 Mathematical Studies (1350)
AQA Certi

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Outliers and Data Distribution in Box Plots

This page focuses on identifying outliers and interpreting data distribution using box plots. Key topics covered include:

Definition and identification of outliers
Formula for calculating outlier boundaries
Interpreting box plot shapes (positive skew, negative skew, symmetrical distribution)
Comparing multiple box plots

The page explains that outliers are values that fall more than 1.5 times the interquartile range (IQR) below the lower quartile or above the upper quartile.

Definition: An outlier is a data point that differs significantly from other observations in a dataset.

Example: If the IQR is 11 and the upper quartile is 72.5, any value above 89 (72.5 + 1.5 * 11) would be considered an outlier.

Highlight: Understanding outliers and data distribution is crucial for accurate data interpretation in AQA Core Maths examinations.

The page also discusses how to interpret the shape of box plots, explaining concepts like positive skew (median closer to lower quartile) and negative skew (median closer to upper quartile).

This information is vital for students preparing for Core Maths Paper 1 topics related to data analysis and interpretation. Mastering these concepts will help students excel in AQA Level 3 Mathematical Studies Past papers and future examinations.

View

Percentiles: Understanding Data Distribution

This page introduces the concept of percentiles, a crucial statistical measure for understanding data distribution. Key points covered include:

Definition of percentiles
Relationship between percentiles and quartiles
Examples of common percentiles and their interpretations

The page explains that a percentile indicates the value below which a given percentage of observations in a group of observations falls. For instance, the 70th percentile (P70) is the value below which 70% of the observations may be found.

Definition: A percentile is a measure used in statistics indicating the value below which a given percentage of observations in a group of observations falls.

Example: The median (50th percentile or P50) has 50% of the data before it.

Highlight: Understanding percentiles is crucial for interpreting data distribution and making comparisons between different datasets.

This page is particularly important for students studying Level 3 mathematical studies AQA numerical data analysis. Mastering percentiles is essential for success in Core Maths Paper 1 Past papers and future examinations.

View

Stem and Leaf Diagrams: Organizing and Visualizing Data

This page focuses on stem and leaf diagrams, a powerful tool for organizing and visualizing numerical data. The key points covered include:

Structure of stem and leaf diagrams
How to create a stem and leaf diagram
Interpreting stem and leaf diagrams
Using back-to-back stem and leaf diagrams for data comparison

The page explains that in a stem and leaf diagram, the stem represents the first digit(s) of the data values, while the leaf represents the last digit. This method allows for a quick visual representation of data distribution.

Example: In a stem and leaf diagram with the stem "2" and leaves "3, 4, 5", this represents the values 23, 24, and 25.

Highlight: Stem and leaf diagrams are particularly useful for finding the median and identifying patterns in the data distribution.

Vocabulary: Back-to-back stem and leaf diagrams allow for the comparison of two sets of data side by side.

This page is essential for students preparing for Core Maths Paper 1 topics related to data representation and analysis. Understanding stem and leaf diagrams is crucial for effective data visualization and interpretation in the AQA Core Maths curriculum.

View

Graphical Data Analysis: Overview of Key Techniques

This page provides an overview of various graphical data analysis techniques crucial for the AQA Core Maths curriculum. The main topics covered include:

Box Plots
Cumulative Frequency Graphs
Histograms
Comparing Graphs and Charts

The page emphasizes the importance of these techniques in visualizing and interpreting data distributions, making comparisons, and identifying patterns.

Highlight: Graphical data analysis is a fundamental skill in Core Maths Revision AQA, essential for interpreting complex datasets and drawing meaningful conclusions.

Vocabulary: Box plots, also known as box-and-whisker plots, provide a visual summary of the distribution of a dataset.

The page also introduces key formulas for calculating quartiles and the interquartile range (IQR), which are essential for creating box plots and identifying outliers.

This overview sets the stage for more detailed explanations of each graphical technique in the subsequent pages, preparing students for Core Maths Paper 1 Past papers and examinations.

View

Numerical Data Analysis: Understanding Data Types and Collection Methods

This page introduces the fundamental concepts of numerical data analysis, focusing on different types of data and their characteristics.

The main types of data discussed are:

Primary Data: Original data collected specifically for the current investigation.
Secondary Data: Data originally collected for other purposes but used for the current investigation.
Quantitative Data: Numerical data, further divided into discrete and continuous.
Qualitative Data: Non-numerical data capturing attitudes or qualities.

Each data type is explained with its pros and cons, helping students understand when to use each type in their analyses.

Definition: Primary data is data collected specifically for the current investigation, while secondary data is obtained from existing sources.

Highlight: Understanding the differences between data types is crucial for selecting appropriate analysis methods and interpreting results accurately.

Example: Quantitative discrete data might include the number of students in a class, while quantitative continuous data could be the exact height measurements of those students.

This page provides a solid foundation for students preparing for the AQA Core Maths examination, emphasizing the importance of data classification in numerical analysis.

View

Histograms: Visualizing Continuous Data

This page focuses on histograms, a powerful graphical tool for visualizing continuous data. Key topics covered include:

How to create a histogram
Interpreting histograms
Finding mean and median from histograms
Using frequency density

The page explains that in a histogram, the area of each bar represents the frequency, with bar width representing class width and bar height representing frequency density.

Definition: Frequency density is the frequency divided by the class width, used as the y-axis in histograms.

Example: To find the mean from a histogram, multiply the midpoint of each class by its frequency, sum these products, and divide by the total frequency.

Highlight: Histograms are particularly useful for visualizing the distribution of continuous data and identifying patterns or skewness.

The page also provides formulas for calculating mean and median from grouped data represented in histograms. This information is crucial for students preparing for AQA Core Maths examinations, especially for questions involving data analysis and interpretation in Core Maths Paper 1 topics.

View

Comparing Graphs and Charts: Choosing the Right Visualization

This final page provides an overview of various graphs and charts used in data visualization, helping students choose the most appropriate method for different types of data. The types of graphs and charts discussed include:

Pictograms
Pie Charts
Bar Charts
Vertical Line Graphs
Stem and Leaf Diagrams
Box Plots
Histograms

For each type, the page outlines its key features, advantages, and the types of data it's best suited for.

Highlight: Choosing the right type of graph or chart is crucial for effective data presentation and analysis in AQA Core Maths.

Example: Pie charts are excellent for showing proportions of qualitative data, while histograms are ideal for visualizing the distribution of continuous data.

Vocabulary: A pictogram uses pictures or symbols to represent data, making it visually appealing but potentially less precise than other methods.

This page is essential for students preparing for Core Maths Paper 1 Past papers and examinations, as it helps them understand when to use each type of graph or chart for optimal data representation. Mastering these concepts is crucial for success in AQA Level 3 Mathematical Studies and beyond.

View

Estimation: Fermi Estimation Technique

This page introduces the Fermi estimation technique, a powerful method for making educated guesses about quantities that are difficult to measure directly. The page outlines a four-step process for Fermi estimation:

State assumptions
Identify information needed to answer the question
Provide estimates for the required information
Calculate an estimated answer

Definition: Fermi estimation, named after physicist Enrico Fermi, is a method of making approximate calculations with little or no actual data.

Example: Estimating the number of piano tuners in Chicago by breaking down the problem into smaller, more manageable parts.

Highlight: Fermi estimation is a valuable skill in Core Maths estimation problems and real-world scenarios where precise data is unavailable.

This technique is particularly useful for students preparing for the AQA Level 3 Mathematical Studies examination, as it helps develop critical thinking and problem-solving skills. Mastering Fermi estimation can significantly improve performance in Core Maths Paper 1 topics related to estimation and approximation.

View

Cumulative Frequency: Analyzing Data Distribution

This page focuses on cumulative frequency diagrams, a powerful tool for analyzing data distribution. Key points covered include:

How to create a cumulative frequency diagram
Interpreting cumulative frequency graphs
Finding quartiles and median from cumulative frequency diagrams

The page provides step-by-step instructions for drawing cumulative frequency diagrams and explains how to use them to find important statistical measures.

Definition: Cumulative frequency is the running total of frequencies, showing how many data points fall below each value in a dataset.

Example: To find the median from a cumulative frequency graph, locate the point where the cumulative frequency is half the total frequency.

Highlight: Cumulative frequency diagrams are particularly useful for finding percentiles and quartiles in large datasets.

This page is crucial for students studying Level 3 mathematical studies AQA numerical data analysis. Understanding cumulative frequency is essential for success in Core Maths Paper 1 Past papers and future examinations, particularly in questions related to data distribution and analysis.

View

Box Plots: Visualizing Data Distribution

This page delves into the details of box plots, a powerful tool for visualizing data distribution. Key points covered include:

Components of a box plot (minimum, lower quartile, median, upper quartile, maximum)
Formulas for calculating quartiles and median
Interpreting box plots
Comparing multiple datasets using box plots

The page provides step-by-step instructions for creating box plots and explains how to interpret various features of the plot.

Definition: The interquartile range (IQR) is the difference between the upper quartile (UQ) and lower quartile (LQ), representing the middle 50% of the data.

Example: In a box plot, the median line closer to the lower quartile indicates a positively skewed distribution.

Highlight: Box plots are particularly useful for identifying outliers and comparing distributions across multiple datasets.

This page is essential for students preparing for AQA Level 3 Mathematical Studies Past papers, as box plots are a common topic in data analysis questions. Understanding how to create and interpret box plots is crucial for success in Core Maths Paper 1 examinations.

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Subjects

Maths

Mechanics

Data presentation & interpretation

AQA AS Core Maths Paper 1 Revision Notes PDF - Easy Study Guide

danica

@danica_n

14 Followers

Core Maths Paper 1 Revision Notes: A Comprehensive Guide for AQA Level 3 Mathematical Studies

This document provides essential revision notes for the AQA Level 3 Mathematical Studies (Core Maths) Paper 1. It covers key topics including:

Numerical Data Analysis
Estimation
Graphical Data Analysis
Personal Finance (excluding Tax and National Insurance)

The notes are designed to help students prepare for the AQA Certificate Level 3 Mathematical Studies (1350) examination, which has been taught since September 2014 with exams from June 2016.

Key features of these revision notes include:

Detailed explanations of data types and analysis methods
Step-by-step guides for creating and interpreting various graphs and charts
Formulas and techniques for statistical calculations
Practical examples and applications of core mathematical concepts

These AQA AS Core Maths Paper 1 revision notes are an invaluable resource for students looking to excel in their Core Maths Paper 1 examination.

28/05/2023

1114

Maths

Outliers and Data Distribution in Box Plots

This page focuses on identifying outliers and interpreting data distribution using box plots. Key topics covered include:

Definition and identification of outliers
Formula for calculating outlier boundaries
Interpreting box plot shapes (positive skew, negative skew, symmetrical distribution)
Comparing multiple box plots

The page explains that outliers are values that fall more than 1.5 times the interquartile range (IQR) below the lower quartile or above the upper quartile.

Definition: An outlier is a data point that differs significantly from other observations in a dataset.

Example: If the IQR is 11 and the upper quartile is 72.5, any value above 89 (72.5 + 1.5 * 11) would be considered an outlier.

Highlight: Understanding outliers and data distribution is crucial for accurate data interpretation in AQA Core Maths examinations.

The page also discusses how to interpret the shape of box plots, explaining concepts like positive skew (median closer to lower quartile) and negative skew (median closer to upper quartile).

Percentiles: Understanding Data Distribution

This page introduces the concept of percentiles, a crucial statistical measure for understanding data distribution. Key points covered include:

Definition of percentiles
Relationship between percentiles and quartiles
Examples of common percentiles and their interpretations

Definition: A percentile is a measure used in statistics indicating the value below which a given percentage of observations in a group of observations falls.

Example: The median (50th percentile or P50) has 50% of the data before it.

Highlight: Understanding percentiles is crucial for interpreting data distribution and making comparisons between different datasets.

Stem and Leaf Diagrams: Organizing and Visualizing Data

This page focuses on stem and leaf diagrams, a powerful tool for organizing and visualizing numerical data. The key points covered include:

Structure of stem and leaf diagrams
How to create a stem and leaf diagram
Interpreting stem and leaf diagrams
Using back-to-back stem and leaf diagrams for data comparison

Example: In a stem and leaf diagram with the stem "2" and leaves "3, 4, 5", this represents the values 23, 24, and 25.

Highlight: Stem and leaf diagrams are particularly useful for finding the median and identifying patterns in the data distribution.

Vocabulary: Back-to-back stem and leaf diagrams allow for the comparison of two sets of data side by side.

Graphical Data Analysis: Overview of Key Techniques

This page provides an overview of various graphical data analysis techniques crucial for the AQA Core Maths curriculum. The main topics covered include:

Box Plots
Cumulative Frequency Graphs
Histograms
Comparing Graphs and Charts

The page emphasizes the importance of these techniques in visualizing and interpreting data distributions, making comparisons, and identifying patterns.

Highlight: Graphical data analysis is a fundamental skill in Core Maths Revision AQA, essential for interpreting complex datasets and drawing meaningful conclusions.

Vocabulary: Box plots, also known as box-and-whisker plots, provide a visual summary of the distribution of a dataset.

The page also introduces key formulas for calculating quartiles and the interquartile range (IQR), which are essential for creating box plots and identifying outliers.

This overview sets the stage for more detailed explanations of each graphical technique in the subsequent pages, preparing students for Core Maths Paper 1 Past papers and examinations.

Numerical Data Analysis: Understanding Data Types and Collection Methods

This page introduces the fundamental concepts of numerical data analysis, focusing on different types of data and their characteristics.

The main types of data discussed are:

Primary Data: Original data collected specifically for the current investigation.
Secondary Data: Data originally collected for other purposes but used for the current investigation.
Quantitative Data: Numerical data, further divided into discrete and continuous.
Qualitative Data: Non-numerical data capturing attitudes or qualities.

Each data type is explained with its pros and cons, helping students understand when to use each type in their analyses.

Definition: Primary data is data collected specifically for the current investigation, while secondary data is obtained from existing sources.

Highlight: Understanding the differences between data types is crucial for selecting appropriate analysis methods and interpreting results accurately.

Example: Quantitative discrete data might include the number of students in a class, while quantitative continuous data could be the exact height measurements of those students.

This page provides a solid foundation for students preparing for the AQA Core Maths examination, emphasizing the importance of data classification in numerical analysis.

Histograms: Visualizing Continuous Data

This page focuses on histograms, a powerful graphical tool for visualizing continuous data. Key topics covered include:

How to create a histogram
Interpreting histograms
Finding mean and median from histograms
Using frequency density

The page explains that in a histogram, the area of each bar represents the frequency, with bar width representing class width and bar height representing frequency density.

Definition: Frequency density is the frequency divided by the class width, used as the y-axis in histograms.

Example: To find the mean from a histogram, multiply the midpoint of each class by its frequency, sum these products, and divide by the total frequency.

Highlight: Histograms are particularly useful for visualizing the distribution of continuous data and identifying patterns or skewness.

Comparing Graphs and Charts: Choosing the Right Visualization

Pictograms
Pie Charts
Bar Charts
Vertical Line Graphs
Stem and Leaf Diagrams
Box Plots
Histograms

For each type, the page outlines its key features, advantages, and the types of data it's best suited for.

Highlight: Choosing the right type of graph or chart is crucial for effective data presentation and analysis in AQA Core Maths.

Example: Pie charts are excellent for showing proportions of qualitative data, while histograms are ideal for visualizing the distribution of continuous data.

Vocabulary: A pictogram uses pictures or symbols to represent data, making it visually appealing but potentially less precise than other methods.

Estimation: Fermi Estimation Technique

State assumptions
Identify information needed to answer the question
Provide estimates for the required information
Calculate an estimated answer

Definition: Fermi estimation, named after physicist Enrico Fermi, is a method of making approximate calculations with little or no actual data.

Example: Estimating the number of piano tuners in Chicago by breaking down the problem into smaller, more manageable parts.

Highlight: Fermi estimation is a valuable skill in Core Maths estimation problems and real-world scenarios where precise data is unavailable.

Cumulative Frequency: Analyzing Data Distribution

This page focuses on cumulative frequency diagrams, a powerful tool for analyzing data distribution. Key points covered include:

How to create a cumulative frequency diagram
Interpreting cumulative frequency graphs
Finding quartiles and median from cumulative frequency diagrams

The page provides step-by-step instructions for drawing cumulative frequency diagrams and explains how to use them to find important statistical measures.

Definition: Cumulative frequency is the running total of frequencies, showing how many data points fall below each value in a dataset.

Example: To find the median from a cumulative frequency graph, locate the point where the cumulative frequency is half the total frequency.

Highlight: Cumulative frequency diagrams are particularly useful for finding percentiles and quartiles in large datasets.

Box Plots: Visualizing Data Distribution

This page delves into the details of box plots, a powerful tool for visualizing data distribution. Key points covered include:

Components of a box plot (minimum, lower quartile, median, upper quartile, maximum)
Formulas for calculating quartiles and median
Interpreting box plots
Comparing multiple datasets using box plots

The page provides step-by-step instructions for creating box plots and explains how to interpret various features of the plot.

Definition: The interquartile range (IQR) is the difference between the upper quartile (UQ) and lower quartile (LQ), representing the middle 50% of the data.

Example: In a box plot, the median line closer to the lower quartile indicates a positively skewed distribution.

Highlight: Box plots are particularly useful for identifying outliers and comparing distributions across multiple datasets.

Can't find what you're looking for? Explore other subjects.

Knowunity is the #1 education app in five European countries

Knowunity has been named a featured story on Apple and has regularly topped the app store charts in the education category in Germany, Italy, Poland, Switzerland, and the United Kingdom. Join Knowunity today and help millions of students around the world.

Download in

Google Play

Download in

App Store

4.9+

Average app rating

13 M

Pupils love Knowunity

#1

In education app charts in 12 countries

950 K+

Students have uploaded notes

Still not convinced? See what other students are saying...

iOS User

I love this app so much, I also use it daily. I recommend Knowunity to everyone!!! I went from a D to an A with it :D

Philip, iOS User

The app is very simple and well designed. So far I have always found everything I was looking for :D

Lena, iOS user