Mathematics: Applications and Interpretation HL

Official HL update coverage

Complex numbers, vector product, Poisson models, and HL hypothesis tests aligned to the latest IB AI HL emphasis.

Add and subtract complex numbers Use real and imaginary components when adding or subtracting complex numbers. Multiply complex numbers Multiply complex numbers and identify a requested component. Use complex conjugates Use conjugates to simplify products and quotients. Calculate modulus of complex numbers Calculate the modulus as distance from the origin. Calculate argument of complex numbers Calculate or interpret the argument of a complex number. Use polar multiplication of complex numbers Multiply moduli and add arguments in polar form. Apply de Moivre powers Use de Moivre theorem to find a modulus or argument after a power. Find roots of unity spacing Use equal angular spacing for roots on the complex unit circle. Calculate vector product components Calculate one component of a vector product. Calculate vector product magnitude Use vector lengths and angle to calculate cross-product magnitude. Use vector product for area Use cross-product magnitude to calculate parallelogram or triangle area. Use scalar triple product volume Use a scalar triple product to calculate volume. Calculate Poisson probabilities Calculate exact Poisson probabilities from a mean rate. Use cumulative Poisson probabilities Add Poisson probabilities to answer at-most or at-least questions. Use Poisson approximation to binomial Use \(np\) as a Poisson mean when events are rare. Test a Poisson mean Standardise a sample mean from Poisson counts for a mean test. Test a normal population mean Calculate a z statistic for the population mean of a normal distribution. Test a correlation coefficient Calculate the t statistic for testing a population correlation coefficient. Interpret correlation test p-values Use a p-value to decide whether sample correlation is statistically significant. Interpret Poisson test technology output Use technology output from a Poisson mean test to make a decision. Apply Dijkstra tentative labels Update shortest-path tentative labels using edge weights. Choose Prim algorithm edges Choose the next minimum edge that connects a new vertex. Choose Kruskal algorithm edges Choose the next minimum edge that does not form a cycle. Calculate Chinese postman repeat distance Add the shortest required repeat distance to the total edge length. Judge Hamiltonian cycle conditions Use given cycle information to decide whether a Hamiltonian cycle is shown. Compare route algorithm outputs Compare candidate route lengths from network algorithms. Apply two-dimensional matrix transformations Map a point using a 2 by 2 transformation matrix. Use determinants as area scale factors Calculate the area scale factor from a determinant. Interpret inverse transformation matrices Use an inverse matrix to recover an original coordinate. Use matrix powers for repeated transformations Interpret repeated transformations through powers of a matrix. Find complex roots in polar form Find modulus or argument information for roots of a complex number. Convert rectangular complex numbers to polar form Convert a rectangular complex number to modulus-argument form. Convert polar complex numbers to rectangular form Use modulus and argument to find a rectangular component. Combine sinusoidal models with amplitude Use harmonic combination to find resultant amplitude. Combine sinusoidal models with phase angle Use coefficients of sine and cosine to find a phase angle. Choose a model from residual evidence Use residual evidence to choose between model types. Evaluate modelling assumptions Judge whether a modelling assumption is supported by the context. Check model domain restrictions Check whether an input value lies inside the model domain. Refine models using residual direction Use residual direction to decide how a model should be adjusted. Interpret parameters in a modelling chain Interpret a calculated parameter inside a multi-step modelling process.