Course Study Guide
Welcome to the IB Standard Level Maths Analysis and Approaches 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&A course.
Thanks to Christos Nikolaidis, MathsGenie, Transum and others for supplying their resources.
Formula Booklet: Click here to download the IB SL A&A Formula Booklet
Chapter 1: Sequences and Series
📈 Desmos Activities for Chapter 1
Chapter 2: Functions
| Learning Objective | Videos | Practice |
| Introduction to Functions | See below | |
| Functions and Composite Functions | Functions and Composite Functions | Functions Exam Questions✍️ Functions Exam Questions Answers✅ Note, some of these questions require knowledge of future topics. |
| Domain and Range of a Function | Domain and Range of a Function | Desmos activity – Domain and Range Functions: Domain and Range✍️ Functions: Domain and Range Answers✅ |
| Inverse Functions | Inverse Functions | Desmos Activity – Inverse Functions Inverse Functions and Composite Functions✍️ Inverse and Composite Functions Answers✅ |
📈 Desmos Activities for Chapter 2
Chapter 3: Linear and Quadratic Functions
| Learning Objective | Videos | Practice |
| Straight Line Graphs | Straight Line Graphs Playlist | Straight Line Graphs Questions✍️ Straight Line Graphs Questions Answers✅ Straight Line Graphs Extension Questions✍️ Straight Line Graphs Extension Questions Answers✅ |
| Graph Transformations | Graph Transformations Playlist | Desmos Activity – Predicting Graph Transformations Transum Activity: Graph Transformations. Graph Transformations Questions✍️ Graph Transformations Answers ✅ |
| Quadratic Equations and Graphs | Quadratic Graphs Playlist (watch all of these videos) | Quadratic Equations Exam Questions ✍️ Answers at the bottom of the sheet. |
| Quadratic Discriminant Questions | Quadratic Discriminant | Quadratic Discriminant Questions ✍️ Discriminant Answers ✅ |
Chapter 4: Rational Functions
| Learning Objective | Video | Practice |
| Reciprocal Graphs | Reciprocal Graphs | Desmos Activity – Rational Functions |
| Sketching Rational Functions | Sketching Rational Functions | Rational Functions Exam Questions ✍️ Answers ✅ |
Chapter 5: Differentiation
Chapter 6: Statistics – Univariate Data
Essential Video!
Before you begin this chapter, let’s start with a video on how to find the averages and measures of spread using the GDC!
| Learning Objective | Video | Practice |
| 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 | |
| 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 |
| Chapter Practice | Statistics Basic Concepts ✍️ Statistics Basic Concepts MarkScheme✅ |
📈Desmos Activity for Chapter 6
Chapter 7: Statistics – Modelling Relationships
| 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 |
| Understand the concepts of interpolation and extrapolation from a graph. | Coming Soon | 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 Lines Video | Chapter Practice Questions ✍️ Chapter Practice Questions MarkScheme✅ |
Chapter 8: Probability
| Learning Objective | Video | Practice |
| Understand what probability represents and how to calculate theoretical probability. Understand how to calculate the expected number of occurrences. | Introduction to Probability | See below |
| Be able to represent a probability space using a sample space diagram. Be able to interpret a sample space diagram. | Sample Space Diagrams | See below |
| Be able to represent probabilities using Venn Diagrams. | Probability Rules | See below |
| Understand how to use the addition rule to calculate the probability of a combination of events. | See above | Venn Diagrams Questions ✍️ Venn Diagrams Answers ✅ |
| Be able to check to see if two events are mutually exclusive. | See above | See below |
| Be able to check to see if two events are independent of each other using the multiplication rule. | See above | See below |
| Understand the concept of conditional probability, and be able to calculate the probability of one event happening dependent on another event. | See above | See below |
| Use probability trees to calculate the probability of independent and dependent events. | Probability Trees | Probability Questions✍️ Probability Questions Answers✅ |
Chapter 9: Exponents and Logarithms
| Learning Objective | Video | Practice |
| Known and use the laws of exponents (indices/power): – Multiplication rule – Division rule – The power of zero – Negative exponents – Fractional Exponents | Laws of Exponents Video | Transum: Exponents Rules Practice |
| Be able to solve exponential equations by using the laws of exponents. | Coming Soon | Transum Exponential Equations Exponential Equations✍️ Exponential Equations Marksheme✅ |
| Recognise the graph of exponential functions. Be able to find the horizontal asymptote of a function, the domain, range and the general shape of the curve. Hence be able to sketch the curve. | Coming Soon Exponential Graphs Desmos | |
| Be able to use logarithms to solve exponential equations. | Intro to Logarithms Video | Transum: Logarithms Logarithms Questions✍️ Logarithms Questions MarkScheme✅ |
| Know the laws of logarithms and use these to manipulate logarithmic expressions. | See above | |
| Know the constant e and that the natural log, ln, is a log with base e. | See above | |
| Be able to use the change of base formula to change between different bases with logs. | Coming Soon | |
| Be able to solve equations using logs. | Solving Problems with Logarithms Video | See above |
| Be able to solve problems associated with exponential models. | Modelling with Exponential Equations | |
| Be able to differentiate the natural logarithm and exponential equations. | Differentiating e^x and ln(x) Video | Differentiating e and ln(x) Practice – Transum✍️ |
Chapter 10: Integration
| Learning Objective | Video | Practice |
| Understand that Integration is the opposite of differentiation. Know how to integration polynomial functions. | Intro to Integration | Integration 1: Simple Integration 2: Definite Integrals Integration 3: Harder Integrals |
| Use integration to calculate the area under a curve. Use integration to calculate the area between two curves. | Area under and between curves Integration Desmos Activity Evaluating Integrals on the CG50 | Integration Exam Style Questions ✍️ Integration Exam Style Questions Answers ✅ |
| Know how to integrate common functions including ex, sin(x) and cos(x). | Further Integration Video | |
| Use your GDC to evaluate definite integrals. | Evaluating Definite Integrals with the CG50 | |
| Chapter 10 Exam Practice | Indefinite Integrals Exam Questions ✍️ Indefinite Integrals Exam Questions Markscheme ✅ Definite Integrals (Area) Exam Questions ✍️ Definite Integrals (Area) Exam Questions Markscheme ✅ |
Chapter 11: 2D and 3D Trigonometry
| Learning Objectives | Video | Practice |
| Know how to find the midpoint in 3D space, and find the distance between two coordinates in 3D. | Coming Soon | |
| Know how to calculate the volume and surface area of prisms, cones, spheres and pyramids. | Volumes of 3D Prisms Video Nets and Surface Area of 3D Shapes Volume & Surface Area of Cones, Pyramids and Spheres Geogebra Activity – Surface Area – Drag the sliders to see the unfolding net of a cylinder. | Volume of Prisms – Transum Volume of a Pyramid – Transum Surface Area of a Cylinder – Transum Surface Area of a Pyramids – Transum Surface Area of a Cone – Transum Surface Area of a Sphere – Transum |
| Be able to use trigonometry (SOHCAHTOA) to calculate lengths and angles of triangles. | Trigonometry Playlist | Transum SOHCAHTOA Practice SOHCAHTOA Problems |
| Understand that right-angled triangles naturally occur inside of 3D structures, and that we can use trigonometry to calculate lengths and angles in 3D. Be able to use trigonometry in 3D. | 3D Trigonometry Video | 3D Trig Corbett Maths Questions ✍️ 3D Trig Corbett Maths Answers ✅ |
| Know how to calculate the area of a triangle using sine. For when you are given an angle and two adjacent lengths | Area of a Triangle Using Sine | Area of Triangle Using Sine – Practice |
| 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 |
Chapter 12: Trigonometric 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 13: More Calculus
| Learning Objectives | Video | Practice |
| Know how to differentiate sin, cos and tan. | Differentiating Trigonometric Functions Video | |
| Apply differentiation to real world scenarios. | Coming Soon | |
| Be able to integrate sin and cos. | Further Integration Video | Harder Integration Practice |
| Be able to use Integration by Substitution. | Integration by Substitution | Integration by Substitution Practice |
| Be able to apply differentiation and integration to Kinematics. | Kinematics – Differentiation Video Kinematics: Integration Video | Kinematics Exam Style Questions ✍️ Kinematics Exam Style Questions Answers ✅ |
Chapter 14: Probability 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. |
Command Terms
Below is a very helpful document from IB which guides you with exam technique.
Past Paper Worked Solutions…
Finished? Time to practice: IB Past Papers (A&A SL)
Course in development: the remainder of this course guide is still in development. Please check back soon. This YouTube playlist will be helpful.
If you have any feedback on this course guide, please email addvancemaths@gmail.com
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