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.
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.
3 concepts with notes
Distance between two points, midpoint of two points, and finding gradient using two points
Gradient-intercept form, point-gradient form, vertical lines, horizontal lines, standard form of a line
Parallel and perpendicular lines, intersection of 2 straight lines, solving a two-variable system of equations
3 concepts with notes
Domain and range of functions, function as a model, interval notation
Graphing functions with a calculator, characteristics of a function, even and odd functions, x and y intercepts, horizontal and vertical asymptotes, maxima and minima
Composing functions, inverse functions, graphing and evaluating inverse functions, computing inverses and domain restrictions
4 concepts with notes
More types of modelling, including natural log, sinusoidal, and logistic. More with piecewise models.
4 concepts with notes
Exponents, properties of exponents, and solving exponential equations
Definition and evaluation of logarithms, properties of logs, e and the natural log, change of base rule
Graphing exponential functions, exponential growth and decay, logarithmic inverse functions.
3 concepts with notes
7 concepts with notes
Introduction to the definition, properties, and general term of an arithmetic sequence
Introduction to definition, identification, and general term of geometric sequences
Definition and general term of geometric series, finite and infinite series, convergence
Working with sequences on a calculator, computations and applications of a calculator
Compound growth, depreciation, interest, inflation, real value
5 concepts with notes
Introduction to the concept of matrices, their properties, and basic matrix operations.
The concept of an identity matrix and inverse matrices, and determinants. Finding inverses with technology, or by hand for (2×2) matrices
Understanding how (2×2) matrices transform points and shapes on the plane. Explanations of the common IB transformations.
Solving and interpreting systems of linear equations through the lens of matrices.
Find eigenvalues & eigenvectors, and using them to diagonalize and find powers of matrices.
4 concepts with notes
Vertical and horizontal translations, dilations, reflecting over axes
Reciprocal functions, quadratic denominators, graphs of rational linear functions
Graphing absolute value functions, squared functions, piecewise functions, graphing 1/f(x)
5 concepts with notes
Sine and cosine rules, finding general area of a triangle
Angles of elevation and depression, true bearings, projections and more
Measuring angles in radians, circumference & arc lengths and sector areas
Spheres, cylinders, prisms, right cones, right pyramids, and combinations of solids
2 concepts with notes
What a Voronoi diagram is, perpendicular bisectors, terminology and construction.
A deeper dive into common uses of Voronoi diagrams on the IB exam
4 concepts with notes
Graphs, domain, and range of sinx and cosx, general sinusoidal functions, modeling periodic phenomena, tanx and reciprocal trig functions, inverse trig functions
Solving equations involving trigonometric functions and understanding solution domains
Applications of trigonometric identities such as sin2θ+cos2θ=1, sin2θ=2sinθcosθ and more identities for HL students
3 concepts with notes
Arithmetic of complex numbers in cartesian form, including conjugates, and the Argand diagram (complex plane).
Introduction, definition, and properties of the complex modulus
6 concepts with notes
Addition, subtraction and scalar multiplication, computed algebraically and geometrically
Vector form, cartesian form, parametric form, modeling with vectors
Parallel lines in 3D, coincident, skew and intersecting lines
Vector and scalar product forms of a plane, cartesian equation of a plane
Intersection of a line and plane, angle between line and plane, intersection and angle between two planes, intersection of 3 planes
5 concepts with notes
🚧 🚧 Under construction 🚧 🚧
Email james@perplex.org to request this lesson urgently.
🚧 🚧 Under construction 🚧 🚧
Email james@perplex.org to request this lesson urgently.
🚧 🚧 Under construction 🚧 🚧
Email james@perplex.org to request this lesson urgently.
🚧 🚧 Under construction 🚧 🚧
Email james@perplex.org to request this lesson urgently.
🚧 🚧 Under construction 🚧 🚧
Email james@perplex.org to request this lesson urgently.
7 concepts with notes
Power rule, chain rule, product rule, quotient rule, derivatives of ex, ax, loga(x), trigonometric, and inverse trigonometric functions
Definitions of tangent and normal, finding tangent and normal lines to a function
Increasing and decreasing intervals, stationary points (maxima and minima), and optimisation
Definition of the second derivative, concavity, inflexion points
Taking the nth derivative, inductive proofs with the nth derivative
5 concepts with notes
Concept of an integral, areas with definite integrals, and basic anti-derivative solving skills
Antiderivatives of polynomials, trigonometric, inverse trigonometric, exponential, and logarithmic functions
The reverse chain rule, integration by substitution, integration by parts, additional strategies
Computations involving distance, displacement, velocity, and acceleration
Finding the volume of a solid revolved around a function or axis to create a 3D figure
4 concepts with notes
An introduction to differential equations and how to solve them.
Solving differential equations with second derivatives using a coupled system technique.
5 concepts with notes
Theoretical and experimental probability, complementary events, expected number of outcomes, sample space
Venn diagrams, intersection and union of events, conditional probability, independent events
Bayes' theorem with 2 and 3 events, sum of conditional probabilities
7 concepts with notes
Learn different ways to measure the "center," or typical values, of a set of data: mean, median, and mode.
Learn the concept of dispersion, range, IQR, outliers, and box and whisker plots.
Learn about standard deviation and variance, which we use to measure how tightly or loosely clustered the data is around the mean.
In this lesson, we learn about different ways to visualize data.
Regressions of y on x, regressions of x on y, the correlation coefficient r, the rank correlation coefficient rs, extrapolation and interpolation of data.
2 concepts with notes
Regressions of y on x, regressions of x on y, the correlation coefficient r, the rank correlation coefficient rs, extrapolation and interpolation of data.
🚧 🚧 Under construction 🚧 🚧
Email james@perplex.org to request this lesson urgently.
5 concepts with notes
Introduction and properties of random variables, probability distributions, expected value and variance, linear transformations of r.v.'s
Concept of the binomial distribution, binomial PDF and CDF, expectation and variance of binomial distribution
Introduction and definition of the normal distribution, standard deviations, normal and inverse normal calculations, z-values, normal standardization
6 concepts with notes
Exploring a simplified coin flip example to lay the foundation of null and alternative hypotheses, p-values and significance levels.
Testing whether observations fit predictions, and whether events are independent, using a χ² distribution.
Using chi squared tests where numerical categories need to be combined, and goodness of fit tests using estimated parameters.
Using the t-distribution to compare a sample mean to a population mean with unknown variance.
Z-tests when the standard deviation is known, confidence intervals using Z and T distributions, critical values & regions, type Ⅰ vs ⅠⅠ errors.
3 concepts with notes
Compound growth, depreciation, interest, inflation, real value