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  • Perplex

    Concept Lessons

    Access comprehensive explorations for all concepts in your objective, including problems, helpful visuals, and AI features.

    What you'll find in every lesson:

    High-quality explanations: Each lesson is carefully crafted to help you truly understand the concept, not just memorize it.

    Checkpoint exercises: Practice as you learn with interactive problems designed to reinforce your understanding.

    AI-powered discussions: Engage with thought-provoking questions that help reveal your misconceptions.

    What you'll find in every lesson:

    High-quality explanations: Each lesson is carefully crafted to help you truly understand the concept, not just memorize it.

    Checkpoint exercises: Practice as you learn with interactive problems designed to reinforce your understanding.

    AI-powered discussions: Engage with thought-provoking questions that help reveal your misconceptions.

    Concept Lessons

    Access comprehensive explorations for all concepts in your objective, including problems, helpful visuals, and AI features.

    58 Lessons Available

    What you'll find in every lesson:

    High-quality explanations: Each lesson is carefully crafted to help you truly understand the concept, not just memorize it.

    Checkpoint exercises: Practice as you learn with interactive problems designed to reinforce your understanding.

    AI-powered discussions: Engage with thought-provoking questions that help reveal your misconceptions.

    What you'll find in every lesson:

    High-quality explanations: Each lesson is carefully crafted to help you truly understand the concept, not just memorize it.

    Checkpoint exercises: Practice as you learn with interactive problems designed to reinforce your understanding.

    AI-powered discussions: Engage with thought-provoking questions that help reveal your misconceptions.

    Cartesian plane & lines

    3 concepts with notes

    Distance, Midpoint, & Gradient

    Distance between two points, midpoint of two points, and finding gradient using two points

    Start Lesson

    Equations of a Line

    Gradient-intercept form, point-gradient form, vertical lines, horizontal lines, standard form of a line

    Start Lesson

    Line Intersections & Systems of Equations

    Parallel and perpendicular lines, intersection of 2 straight lines, solving a two-variable system of equations

    Start Lesson

    Function Theory

    3 concepts with notes

    Functions and their properties

    Domain and range of functions, function as a model, interval notation

    Start Lesson

    Function Graphs

    Graphing functions with a calculator, characteristics of a function, even and odd functions, x and y intercepts, horizontal and vertical asymptotes, maxima and minima

    Start Lesson

    Function Composition & Inverses(Plus Only)

    Composing functions, inverse functions, graphing and evaluating inverse functions, computing inverses and domain restrictions

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    Modelling

    2 concepts with notes

    Basic Modelling Skills

    Using functions to fit real world data and make predictions

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    Direct and Inverse Proportions

    A lesson on direct and inverse proportions.

    Start Lesson

    Exponents & Logarithms

    4 concepts with notes

    Exponential Algebra

    Exponents, properties of exponents, and solving exponential equations

    Start Lesson

    Logarithm algebra

    Definition and evaluation of logarithms, properties of logs, e and the natural log, change of base rule

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    Radicals and Roots

    Nth roots, fractional and rational exponents, conjugates.

    Start Lesson

    Exp & Log functions(Plus Only)

    Graphing exponential functions, exponential growth and decay, logarithmic inverse functions.

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    Approximations & Error

    3 concepts with notes

    Rounding Numbers

    Rounding, significant figures, decimal places

    Start Lesson

    Scientific Notation

    Converting numbers to and from scientific notation (a×10k)

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    Error

    Approximations error bounds

    Start Lesson

    Sequences & Series

    7 concepts with notes

    Arithmetic Sequences

    Introduction to the definition, properties, and general term of an arithmetic sequence

    Start Lesson

    Geometric Sequences

    Introduction to definition, identification, and general term of geometric sequences

    Start Lesson

    Arithmetic Series(Plus Only)

    Definition of series, formula for arithmetic series

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    Σ summation notation(Plus Only)

    Summation notation, properties of sums

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    Geometric Series(Plus Only)

    Definition and general term of geometric series, finite and infinite series, convergence

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    Sequence Mode (Calculator)(Plus Only)

    Working with sequences on a calculator, computations and applications of a calculator

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    Compounding (Appreciation & Depreciation)(Plus Only)

    Compound growth, depreciation, interest, inflation, real value

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    2D & 3D Geometry

    5 concepts with notes

    Right angled triangles

    Pythagoras's theorem, SOHCAHTOA, finding side length from angles

    Start Lesson

    Non-right-angled triangles(Plus Only)

    Sine and cosine rules, finding general area of a triangle

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    Applied triangle geometry

    Angles of elevation and depression, true bearings, projections and more

    Start Lesson

    Circles: Radians, arcs and sectors(Plus Only)

    Measuring angles in radians, circumference & arc lengths and sector areas

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    3D solids(Plus Only)

    Spheres, cylinders, prisms, right cones, right pyramids, and combinations of solids

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    Voronoi Diagrams

    2 concepts with notes

    Properties of Voronoi Diagrams

    What a Voronoi diagram is, perpendicular bisectors, terminology and construction.

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    Applications of Voronoi Diagrams

    A deeper dive into common uses of Voronoi diagrams on the IB exam

    Start Lesson

    Differentiation

    5 concepts with notes

    Limits and Derivatives

    The concept (and basic properties) of limits and derivatives

    Start Lesson

    Differentiation rules

    Power rule, chain rule, product rule, quotient rule, derivatives of ex, ax, loga​(x), trigonometric, and inverse trigonometric functions

    Start Lesson

    Tangents and normals(Plus Only)

    Definitions of tangent and normal, finding tangent and normal lines to a function

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    Applications of the First Derivative(Plus Only)

    Increasing and decreasing intervals, stationary points (maxima and minima), and optimisation

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    n^th Derivative(Plus Only)

    Taking the nth derivative, inductive proofs with the nth derivative

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    Integration

    4 concepts with notes

    Definite Integrals, Areas, and Basic Anti-Derivatives

    Concept of an integral, areas with definite integrals, and basic anti-derivative solving skills

    Start Lesson

    Techniques of Integration(Plus Only)

    The reverse chain rule, integration by substitution, integration by parts, additional strategies

    Upgrade to Plus

    Kinematics(Plus Only)

    Computations involving distance, displacement, velocity, and acceleration

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    Volumes of Revolution(Plus Only)

    Finding the volume of a solid revolved around a function or axis to create a 3D figure

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    Probability

    4 concepts with notes

    Probabilistic Events

    Theoretical and experimental probability, complementary events, expected number of outcomes, sample space

    Start Lesson

    Combined Events(Plus Only)

    Venn diagrams, intersection and union of events, conditional probability, independent events

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    Dependence(Plus Only)

    Tree diagrams, selection with/without replacement, dependence

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    Bayes' Theorem(Plus Only)

    Bayes' theorem with 2 and 3 events, sum of conditional probabilities

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    Descriptive Statistics

    6 concepts with notes

    Population & Data

    Understand the basics of population, data collection, and sampling.

    Start Lesson

    Measuring Center

    Learn different ways to measure the "center," or typical values, of a set of data: mean, median, and mode.

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    Quartiles and Box & Whisker Plots(Plus Only)

    Learn the concept of dispersion, range, IQR, outliers, and box and whisker plots.

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    Standard Deviation and Variance(Plus Only)

    Learn about standard deviation and variance, which we use to measure how tightly or loosely clustered the data is around the mean.

    Upgrade to Plus

    Frequency Tables, Histograms and cumulative frequency diagrams(Plus Only)

    In this lesson, we learn about different ways to visualize data.

    Upgrade to Plus

    Linear Regression(Plus Only)

    Regressions of y on x, regressions of x on y, the correlation coefficient r, the rank correlation coefficient rs​, extrapolation and interpolation of data.

    Upgrade to Plus

    Bivariate Statistics

    1 concept with notes

    Linear Regression(Plus Only)

    Regressions of y on x, regressions of x on y, the correlation coefficient r, the rank correlation coefficient rs​, extrapolation and interpolation of data.

    Upgrade to Plus

    Distributions & Random Variables

    3 concepts with notes

    Discrete random variables

    Introduction and properties of random variables, probability distributions, expected value and variance, linear transformations of r.v.'s

    Start Lesson

    Binomial Distribution(Plus Only)

    Concept of the binomial distribution, binomial PDF and CDF, expectation and variance of binomial distribution

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    Normal Distribution(Plus Only)

    Introduction and definition of the normal distribution, standard deviations, normal and inverse normal calculations, z-values, normal standardization

    Upgrade to Plus

    Inference & Hypotheses

    3 concepts with notes

    Hypothesis Testing and p-values

    Exploring a simplified coin flip example to lay the foundation of null and alternative hypotheses, p-values and significance levels.

    Start Lesson

    χ² tests

    Testing whether observations fit predictions, and whether events are independent, using a χ² distribution.

    Start Lesson

    Student's t-test

    Using the t-distribution to compare a sample mean to a population mean with unknown variance.

    Start Lesson

    Financial Mathematics

    3 concepts with notes

    Compounding (Appreciation & Depreciation)(Plus Only)

    Compound growth, depreciation, interest, inflation, real value

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    Loans

    A lesson on loans.

    Start Lesson

    Annuities

    A lesson on annuities.

    Start Lesson