Course Study Guide
Welcome to the IB Standard Level Maths Applications and Interpretations Course. Below we have a complete revision guide, which include video lessons, practice questions and other recourses to help you revise and master the IB SL A&I course.
Do you have suggestions? Email: addvancemaths@gmail.com with your ideas!
Thank you to Christos Nikolaidis and Transum for their excellent resources.
Chapter 1: Measuring Space: Accuracy and 2D Geometry
| Learning Objectives | Video | Practice | |
| Be able to round to a given number of significant figures. | Rounding Practice – Transum | ||
| Be able to calculate measurement error and percentage error. | Percentage Error Practice Questions | ||
| Know and use the laws of exponents. | Laws of Indices Videos | Laws of Indices – Transum | |
| Be able to use standard form, writing large and small numbers in standard form. | Standard Form Video | Standard Form – Transum | |
| Be able to use Pythagoras theorem to calculate lengths of right-angled triangles, and apply this to geometry problems. | Pythagoras Theorem Video | Pythagoras Practice Transum Pythagoras Problems | |
| Use Trigonometry (SOHCAHTOA) to calculate the lengths and angles of right-angled triangles. | SOHCAHTOA Lengths SOHCAHTOA Angles | Transum SOHCAHTOA Practice SOHCAHTOA Problems | |
| Understand Angles of Depression and Elevation, and be able to solve problems based on this. | SOHCAHTOA Problems Video | Angles of Elevation and Depression Questions | |
| Be able to calculate the arc length and perimeter of a sector. | Sectors Video | Arc Lengths Practice – Transum Arcs and Sectors Exam Style Questions for A&I ✍️ Arcs and Sectors Mark Scheme ✅ |
Chapter 2: Representing Space: Non-Right Angled Trigonometry and Volumes
| Learning Objectives | Video | Practice | |
| Before we begin, check you are confident with Trigonometry from Chapter 1. | Trigonometry Playlist | ||
| Know the sine rule. Be able to use the sine rule to calculate lengths and angles of non-right angled triangles. (for triangles where you already know an angle and it’s opposite side) | Sine Rule Video | Sine Rule – Transum | |
| Know the cosine rule. Be able to use the cosine rule to calculate lengths and angles of non-right angles triangles. | Cosine Rule | Cosine Rule Practice – Transum | |
| Be able to apply the sine and cosine rules to geometry problems. | Advanced Trigonometry Problems Video | Transum – Sine and Cosine Problems | |
| Be able to calculate the area of non-right angled triangles given just an angle and the two adjacent sides. | Area of a Triangle Using Sine | Area of Triangle Using Sine – Practice | |
| Be able to calculate the area of a sector. | Sectors Video | Area of a Sector – Transum | |
| Be able to calculate the volume of prisms. | Volume and Surface Area of Prisms Video | Volume of a Prism – Transum | |
| Be able to calculate the surface area of prisms. | See above | Surface Area – Transom | |
| Be able to calculate the volume of more 3D shapes: Pyramid, Cone, Cylinder and Sphere. | 3D Shapes Volume and Surface Area Video | ||
| Be able to calculate the lengths and angles inside 3D shapes using trigonometry (3D Trig). | 3D Trigonometry Video | 3D Trigonometry Transum 3D Trigonometry – Corbett Maths | |
| Know how to solve problems with shapes in 3D Space and 3D coordinates. | Revision page for 3D Coordinates |
Chapter 3: Representing and Describing Data: Descriptive Statistics
| Learning Objective | Video | Practice |
| Understand the term “Univariate Data”: It means data with only one variable (like one list of measures). Understand the term “Bivariate Data”: It means data with two variables. | ||
| Understand the measures of central tendency: Mode/Modal Class, Mean & Median | Mean, Median, Mode and Range | Mean, Median, Mode and Range – Transum |
| Understand the measures of dispersion: Range and Interquartile Range. | Interquartile Range | See below |
| Be able to plot and interpret Boxplots. | Boxplots | Transum – Boxplots 1 Transum- Boxplots 2 |
| Understand the concept of an outlier, and know how to identify outliers from a data set. | Outliers | Outliers Worksheet |
| Be able to calculate standard deviation (and variance) and explain what it represents. You will use your GDC to calculate Standard Deviation. 📟 | Standard Deviation Video Desmos: Statistics on a Data Set | Standard Deviation Practice – Transum |
| Use the GDC to find measures of central tendency and measures of spread. | Averages and Measures of Spread on the CG50 – Video! | |
| Know that multiplying all numbers in the data set by a constant also results in multiplying the mean and standard deviation by the same constant. | ||
| Know the different types of sampling techniques. | Sampling Techniques Video | |
| Be able to interpret cumulative frequency graphs. | Cumulative Frequency Graphs Video | Cumulative Frequency Transum Cumulative Frequency Corbett Maths |
| Know how to interpret scatter graphs, and recognise strong/weak and positive/negative correlation. | Scatter Graphs and Correlation Video | Estimating Correlation – Transum |
| Chapter Practice | Statistics Basic Concepts ✍️ Statistics Basic Concepts MarkScheme✅ |
Chapter 4: Dividing Up Space: Coordinate Geometry, Lines and Voronoi Diagrams
| Learning Objectives | Video | Practice | |
| Before we begin, you should be familiar with straight line graphs. | Straight Line Graphs Video | Transum – Straight Line Graphs Equation of a Line – Corbett Maths This worksheet is fantastic. Well worth completing in full. Answers available here. | |
| Be able to find the midpoint between two coordinates. | Midpoints Video | Midpoints – Transum | |
| Be able to find the distance between two points using Pythagoras theorem. | Video coming soon | Distance between coordinates – Transum | |
| Understand the concept of a gradient, and recognise what is meant by positive, negative or zero gradient. Be able to recognise the y-intercept of a line. Hence, find the equation of a straight line. | Straight Line Graphs Video | Gradient of a Line – Transum y=mx+c Transum (also see Equation of a Line Worksheet above) | |
| Be able to find the equation of parallel and perpendicular lines. | Straight Line Graphs Problems Perpendicular Bisectors on Graphs | Parallel and Perpendicular Lines – Maths Genie ✍️ Parallel and Perpendicular Lines – Maths Genie Answers ✅ | |
| Introduction to Voronoi | Desmos Activity – Voronoi | Reflection: Why do you think Voronoi diagrams are useful? Could these be part of your IA? | |
| Understand and interpret Voronoi Diagrams. | Voronoi Diagrams Video Voronoi Revision Page | Transum – Voronoi Practice Voronoi Exam Practice ✍️ Voronoi Practice Questions ✍️ Voronoi Practice Questions Markscheme ✅ |
Casio CG50 Full Guide!
Your calculator is your best friend when solving A&I maths problems. Learn how to use it effectively with this handy guide!
Chapter 5: Modelling Constant Dates of Change: Linear Functions
| Learning Objectives | Video | Practice | |
| Understand the following terms: Relation, Mapping Diagram, Function, Domain and Range. | |||
| Understand the concept of domain and range. | Domain and Range Video Domain and Range Desmos Activity | ||
| Understand what a function is, and how to present them. | Functions Video | ||
| Use the vertical line test to see if a relation is a function. | Vertical Line Test Video | ||
| Know how to model real world scenarios using linear models. | Linear Models Video | ||
| Understand the idea of ‘rate of change’: The rate of change of a function is the increase/decrease of the dependent variable for every unit the independent variable increases. | |||
| Understand the terms increasing and decreasing functions. Increasing Function: A function with a positive rate of change. Decreasing Function: A function with a negative rate of change. | Functions Exam Style Questions ✍️ Functions Mark Scheme ✅ | ||
| Arithmetic Sequences: Know what an arithmetic sequence is. Know how to find the nth term of an arithmetic sequence. Be able to find the sum of the first n terms of an arithmetic sequence. Solve problems about arithmetic sequences. | nth term video Arithmetic Sequences Video | nth term – Transum Sum of an Arithmetic Sequence – Transum Exam Style Questions on Arithmetic Sequences Maths Genie ✍️ | |
| Be able to interpret Sigma Notation for summation. Be able to use Sigma Notation for summation. | Sigma Notation Video | Sigma Notation – Transum | |
| Understand the concept of simple interest. Be able to answer questions based on simple interest. | Simple Interest Video | Simple Interest – Transum | |
| Know the concepts of extrapolation and interpolation. | Video Coming Soon | Coming Soon: Suggest a Resource? | |
| Chapter 5 Practice Questions | Lines Exam Style Questions ✍️ Lines Exam Style Questions Answers✅ |
Chapter 6: Modelling Relationships: Linear Correlation of Bivariate Data
| Learning Objective | Video | Practice |
| Be able to interpret scatter graphs, and interpret the correlation as positive, negative or no correlation, as well as strong or weak correlation. | Scatter Graphs and Correlation Video | Estimating Correlation – Transum |
| Understand how to calculator the Pearson Product Moment Correlation Coefficient and understand how this can be used to measure the strength of the correlation. You will use your GDC to calculate PPMCC. 📟 | Pearson’s Product Moment Correlations Coefficient Video Desmos Link: PPMCC Interactive | See below |
| Be able to use technology to calculate the equation of the least square regression line. You will use your GDC to calculate regression equation. 📟 | Regression Line Video | |
| Be able to interpret the least square regression line. | See above | Chapter Practice Questions ✍️ Chapter Practice Questions MarkScheme |
Chapter 7: Quantifying Uncertainty: Probability, Binomial and Normal Distributions
| Learning Objectives | Video | Practice | |
| Before we begin: You should be familiar with ideas of probability theory, including the probability scale and probability trees. | Introduction to Probability Video Probability Trees Video | Probability Questions Probability Trees | |
| Be familiar with and understand the terms: Experiment Trials Outcome Event Sample Space Experimental Probability Theoretical Probability | |||
| Represent a sample space using a Venn Diagram, and be able to calculate probabilities from a Venn Diagram. | Venn Diagrams Playlist | ||
| Understand what intersection, union and complement in Venn Diagram and Sets. | See above | Probability – Venn Diagrams Exam Questions ✍️ Probability – Venn Diagrams Exam Questions Markscheme ✅ | |
| Understand what a sample space diagram is. Be able to draw a sample space diagram, and interpret it to calculate probabilities. | Sample Space Diagrams Video | ||
| Know what mutually exclusive means, and be able to test for mutual exclusivity. | Video Coming Soon | ||
| Know the concept of independent events. | Video Coming Soon | ||
| Use Probability Trees to Calculate Probability of dependent and independent events. | Probability Trees Video | Probability Trees – Transum Probability Trees – Exam Questions ✍️ Probability Trees – Exam Questions Answers ✅ | |
| Understand what is meant by a probability distribution. Know how to identify a probability distribution. (sum of probabilities must add to 1). Use a simple probability distribution function. | Video Coming Soon | ||
| Be able to calculate the expected value. | Video Coming Soon | ||
| Know what the Binomial Distribution is, and when to apply it. Be able to calculate the probability of an event happening using the binomial distribution. | Binomial Distribution using the GDC | Binomial Distribution Exam Style Questions ✍️ Binomial Distribution Exam Style Questions Answers ✅ | |
| Be familiar with the idea of the normal distribution. | Normal Distribution Video Desmos Activity on Normal Distribution | Normal Distribution Exam Style Questions ✍️ Normal Distribution Exam Style Questions Answers ✅ | |
| Be able to use the inverse binomial distribution. | Video coming soon. | See above. | |
| Know and understand the standardised normal distribution. | Video coming soon. Desmos Activity on the Standardised Normal Distribution. |
Need Revision Tips?
Our revision page has everything you need to master the art of revision. Our tips are helpful for every IB subject, not just maths!
Chapter 8: Testing for Validity: Spearman’s Hypothesis Testing and Chi-Squared Test for Independence
We are unable to find resources at this time for this chapter. We are working to develop our own resources eventually however this takes time. Please refer to your textbooks for practice in this topic. Apologies for any inconvenience.
| Learning Objectives | Video | Practice | |
| Know Spearman’s Rank Correlation Coefficient is a measure of how correlated the ranking of two variables are. Be able to calculate Spearman’s correlation coefficient and interpret this in context. | Spearman’s Video – Revision Village | Coming Soon Suggest an Activity 📨 | |
| Understand what is meant by chi-squared tests for independence. | Notes on Chi-Squared – SaveMyExams Chi Squared Hypothesis Testing – Addvance Maths | Chi Squared Exam Questions Chi Squared Answers | |
| Understand the concept of hypothesis testing, and use this in the context of probability experiments. | Hypothesis Testing – Revision Village | Coming Soon Suggest an Activity 📨 | |
| Understand the concept of degrees of freedom. | Coming Soon | Coming Soon Suggest an Activity 📨 | |
| Be able to use t-tests to check if two sets of data are significantly different. | Coming Soon | Coming Soon Suggest an Activity 📨 |
Chapter 9: Modelling Relationships with Functions and Power Functions
| Learning Objectives | Video | Practice | |
| Before we begin, you should be confident manipulating and solving quadratics: Factorising and expanding double brackets. You should also be confident knowing how to plot a quadratic graph, and it’s general shape. | Quadratics Revision Page – This is helpful for this entire Chapter. | Quadratics Revision Page | |
| Know how to solve a quadratic equation using the quadratic formula. | The Quadratic Formula – Video | Quadratic Formula -Transum | |
| Know the key features of a quadratic graph, and be able to find the coordinates from the equation. Including: Roots Vertex y-intercept Line of Symmetry | Quadratic Graphs – Video | Graph Match – Transum | |
| Be able to find the equation of a quadratic given some of it’s features. | See above | ||
| Solve problems involving quadratics. | Quadratic Problems Video | ||
| Be able to use your GDC to find a quadratic from three coordinates using quadratic regression. | Coming Soon | ||
| Be familiar with cubic graph. | Cubic Graphs – Video | ||
| Be able to find the inverse function, and recognise that an inverse function is a reflection in the line y=x. | Inverse Function Video | Desmos Activity – Inverse Functions Worksheet: Inverse Functions | |
| Understand the concepts of direct proportion and inverse proportion. Be able to solve problems associated with direct and inverse proportion. | Direct and Inverse Proportion Video | Direct Proportion – Transum Inverse Proportion – Transum | |
| Understand the concept of optimisation as finding the maximum or minimum value of a function. Be able to find the maximum or minimum value of a quadratic model. | Coming Soon | ||
| Chapter 9 Practice Questions | Quadratic Exam Style Questions ✍️ Quadratic Exam Style Questions Answers ✅ |
Chapter 10: Modelling Rates of Changes: Exponential and Logarithmic Functions
| Learning Objectives | Video | Practice | |
| Know the concept of a geometric sequence. Be able to solve problems relating to Geometric Sequences. | Geometric Sequences Video | ||
| Be able to use the sum formula for geometric sequences to solve problems. | Sum of a Geometric Sequence – Video | ||
| Understand the concept of compound interest. | Compound Interest – Video | Compound Interest – Transum | |
| Be able to calculate compound interest for different compounding periods. | Compound Interest on the Casio CG50 Video | ||
| Be able to calculate annuity using a GDC. | Annuities Video for the Casio CG50 | Financial Maths Revision Page Includes exam style questions. | |
| Be familiar with exponential graphs. Recognise how the equation of the asymptote is related to the equation of the exponential function. | Desmos Activity – Explore Exponential Graphs Coming Soon | See below | |
| Understand that exponential models can be used to model real-life scenarios where there is a constant percentage change. | |||
| Understand logarithms as the inverse of exponentials (powers). | Logarithms Video – Note some of the examples here are beyond the scope of A&I course. | Exponentials and Logarithms Exam Style Questions ✍️ Exponentials and Logarithms Exam Style Questions ✅ |
Chapter 11: Modelling Periodic Phenomena: Trigonometry Functions
| Learning Objectives | Video | Practice | |
| Before we begin: Be familiar with sine, cosine and tangent graphs. | Sin, Cos and Tan Graphs Video | ||
| Know how to manipulate the sin and cos graphs through function transformations. | Transformations of Trigonometric Graphs Video Modelling with Trigonometry Functions Video Trigonometric Transforms Desmos Activity | Reflection: Could this model an interesting real world phenomenon? Could you use this as part of your IA? Modelling with Trig Exam Questions✍️ Markscheme ✅ | |
| Understand how to use CAST Diagrams | Introduction to CAST Diagrams Video Desmos Activity: CAST Diagrams | ||
| Memorise the Special Angles for sin, cos and tan. | Special Angles Link | ||
| How all of your trigonometric identities including: The pythagorean identity tan(x) is sin(x)/cos(x) Double Angle Identities for Sine and Cosine. | Trigonometric Identities Video | ||
| Solve Trigonometric Equations. | Solving Trigonometric Equations Video | ||
| Use CAST Diagrams to Solve Trigonometric Problems with repeated solutions. | See above | Solving Trig Equations ✍️ Markscheme ✅ |
Chapter 12: Analysing Rates of Change: Differential Calculus
| Learning Objectives | Video | Practice | |
| Understand how to differentiate polynomial functions. | Introduction to Differentiation | Differentiation Practice Transum | |
| Interpret the derivative to see if a function is increasing or decreasing. | Increasing and Decreasing Functions Video | ||
| Apply differentiation to real world scenarios. | Coming Soon | ||
| Be able to find the equation of a tangent to a curve. | Finding the tangent video. Desmos – What is a Tangent/Normal? Desmos Activity – Finding the equation of a tangent. | Differentiation: Finding the equation of the tangent practice. – Transum | |
| Optimisation: Be able to find the maximum and minimum points of a function using differentiation. | Optimisation by Differentiation Video | Optimisation Exam Style Questions ✍️ Optimisation Exam Style Questions Answers ✅ Extra Practice on Optimisation ✍️✅ |
Chapter 13: Approximating Irregular Spaces: Integration
| Learning Objectives | Video | Practice | |
| Know how to integrate polynomial functions. | Intro to Integration | Integration 1: Simple Integration 2: Definite Integrals Integration 3: Harder Integrals | |
| Know that integration helps you to find the area under a curve. Be able to calculate the area under a curve using definite integrals. | Integration: Area Under a Curve Desmos Activity -Trapezium Rule | Integration Exam Style Questions ✍️ Integration Exam Style Questions Answers ✅ | |
| Know how to approximate areas using the trapezium rule | Coming Soon Desmos Activity -Trapezium Rule | Trapezium Rule – Transum |
Commend Terms
Below is a helpful document from IB which gives you excellent guidance for your exam.
Addvance Maths 