Mathematics: Applications and Interpretation HL
Statistics and probability
Official Mathematics: applications and interpretation HL strand for the current first-assessment-2021 syllabus.
Calculate states from transition matrices
Develop calculate states from transition matrices through finite, checked AI HL practice aligned to current syllabus point AIHL 4.19.
Calculate Spearman rank correlation
Develop calculate spearman rank correlation through finite, checked AI HL practice aligned to current syllabus point AIHL 4.10.
Interpret chi-square tests for independence
Develop interpret chi-square tests for independence through finite, checked AI HL practice aligned to current syllabus point AIHL 4.11.
Construct confidence intervals for means
Develop construct confidence intervals for means through finite, checked AI HL practice aligned to current syllabus point AIHL 4.16.
Test population means with normal models
Develop test population means with normal models through finite, checked AI HL practice aligned to current syllabus point AIHL 4.18.
Find steady states of Markov chains
Develop find steady states of markov chains through finite, checked AI HL practice aligned to current syllabus point AIHL 4.19.
Calculate expected values of discrete distributions
Develop calculate expected values of discrete distributions through finite, checked AI HL practice aligned to current syllabus point AIHL 4.7.
Calculate Poisson point probabilities
Develop calculate poisson point probabilities through finite, checked AI HL practice aligned to current syllabus point AIHL 4.17.
Calculate sample-mean parameters using the central limit theorem
Develop calculate sample-mean parameters using the central limit theorem through finite, checked AI HL practice aligned to current syllabus point AIHL 4.15.
Calculate reverse conditional probabilities from trees
Develop calculate reverse conditional probabilities from trees through finite, checked AI HL practice aligned to current syllabus point AIHL 4.6.
Combine expectations and variances of independent variables
Develop combine expectations and variances of independent variables through finite, checked AI HL practice aligned to current syllabus point AIHL 4.14.
Calculate unbiased sample variance from population variance
Develop calculate unbiased sample variance from population variance through finite, checked AI HL practice aligned to current syllabus point AIHL 4.14.
Calculate sums of squared residuals
Develop calculate sums of squared residuals through finite, checked AI HL practice aligned to current syllabus point AIHL 4.13.
Interpret coefficients of determination
Develop interpret coefficients of determination through finite, checked AI HL practice aligned to current syllabus point AIHL 4.13.
Standardize normal observations
Develop standardize normal observations through finite, checked AI HL practice aligned to current syllabus point AIHL 4.9.
Interpret p-values and significance
Develop interpret p-values and significance through finite, checked AI HL practice aligned to current syllabus point AIHL 4.11.
Interpret Type I and Type II errors
Develop interpret type i and type ii errors through finite, checked AI HL practice aligned to current syllabus point AIHL 4.18.
Test a normal mean when variance is unknown
Develop test a normal mean when variance is unknown through finite, checked AI HL practice aligned to current syllabus point AIHL 4.18.
Test matched-pair mean differences
Develop test matched-pair mean differences through finite, checked AI HL practice aligned to current syllabus point AIHL 4.18.
Interpret confidence intervals for means
Develop interpret confidence intervals for means through finite, checked AI HL practice aligned to current syllabus point AIHL 4.16.
Distinguish reliability from validity
Develop distinguish reliability from validity through finite, checked AI HL practice aligned to current syllabus point AIHL 4.12.
Interpret linear regression parameters
Develop interpret linear regression parameters through finite, checked AI HL practice aligned to current syllabus point AIHL 4.4.
Classify predictions from regression models
Develop classify predictions from regression models through finite, checked AI HL practice aligned to current syllabus point AIHL 4.4.
Select relevant variables for investigations
Develop select relevant variables for investigations through finite, checked AI HL practice aligned to current syllabus point AIHL 4.12.
Calculate exact binomial probabilities
Develop calculate exact binomial probabilities through finite, checked AI HL practice aligned to current syllabus point AIHL 4.8.
Calculate cumulative binomial probabilities
Develop calculate cumulative binomial probabilities through finite, checked AI HL practice aligned to current syllabus point AIHL 4.8.
Calculate binomial means and variances
Develop calculate binomial means and variances through finite, checked AI HL practice aligned to current syllabus point AIHL 4.8.
Calculate expected monetary values
Develop calculate expected monetary values through finite, checked AI HL practice aligned to current syllabus point AIHL 4.7.
Calculate expected values from probability trees
Develop calculate expected values from probability trees through finite, checked AI HL practice aligned to current syllabus point AIHL 4.7.
Assess Poisson model assumptions
Develop assess poisson model assumptions through finite, checked AI HL practice aligned to current syllabus point AIHL 4.17.
Combine independent Poisson variables
Develop combine independent poisson variables through finite, checked AI HL practice aligned to current syllabus point AIHL 4.17.
Find normal percentiles using technology
Develop find normal percentiles using technology through finite, checked AI HL practice aligned to current syllabus point AIHL 4.9.
Interpret inverse-normal output
Develop interpret inverse-normal output through finite, checked AI HL practice aligned to current syllabus point AIHL 4.9.
Interpret Pearson correlation and causation
Develop interpret pearson correlation and causation through finite, checked AI HL practice aligned to current syllabus point AIHL 4.4.
Select nonlinear regression models
Develop select nonlinear regression models through finite, checked AI HL practice aligned to current syllabus point AIHL 4.13.
Calculate standard deviation from summaries
Develop calculate standard deviation from summaries through finite, checked AI HL practice aligned to current syllabus point AIHL 4.2.
Construct confidence intervals when variance is unknown
Develop construct confidence intervals when variance is unknown through finite, checked AI HL practice aligned to current syllabus point AIHL 4.16.
Improve biased survey questions
Develop improve biased survey questions through finite, checked AI HL practice aligned to current syllabus point AIHL 4.12.
Calculate probabilities of unions
Develop calculate probabilities of unions through finite, checked AI HL practice aligned to current syllabus point AIHL 4.6.
Combine mutually exclusive tree paths
Develop combine mutually exclusive tree paths through finite, checked AI HL practice aligned to current syllabus point AIHL 4.6.
Calculate conditional probabilities from tables
Develop calculate conditional probabilities from tables through finite, checked AI HL practice aligned to current syllabus point AIHL 4.6.
Transform expected values
Develop transform expected values through finite, checked AI HL practice aligned to current syllabus point AIHL 4.14.
Transform variances
Develop transform variances through finite, checked AI HL practice aligned to current syllabus point AIHL 4.14.
Combine independent normal variables
Develop combine independent normal variables through finite, checked AI HL practice aligned to current syllabus point AIHL 4.15.
Construct upper binomial critical regions
Develop construct upper binomial critical regions through finite, checked AI HL practice aligned to current syllabus point AIHL 4.18.
Calculate binomial Type I errors
Develop calculate binomial type i errors through finite, checked AI HL practice aligned to current syllabus point AIHL 4.18.
Calculate expected chi-square frequencies
Develop calculate expected chi-square frequencies through finite, checked AI HL practice aligned to current syllabus point AIHL 4.11.
Calculate chi-square goodness-of-fit statistics
Develop calculate chi-square goodness-of-fit statistics through finite, checked AI HL practice aligned to current syllabus point AIHL 4.11.
Construct z confidence intervals for means
Develop construct z confidence intervals for means through finite, checked AI HL practice aligned to current syllabus point AIHL 4.16.
Conduct binomial proportion tests
Develop conduct binomial proportion tests through finite, checked AI HL practice aligned to current syllabus point AIHL 4.18.
Select lower binomial critical regions
Develop select lower binomial critical regions through finite, checked AI HL practice aligned to current syllabus point AIHL 4.18.
Calculate binomial Type II errors
Develop calculate binomial type ii errors through finite, checked AI HL practice aligned to current syllabus point AIHL 4.18.
Interpret Spearman technology output
Develop interpret spearman technology output through finite, checked AI HL practice aligned to current syllabus point AIHL 4.10.
Diagnose regression residual patterns
Develop diagnose regression residual patterns through finite, checked AI HL practice aligned to current syllabus point AIHL 4.13.
Calculate Poisson interval probabilities
Develop calculate poisson interval probabilities through finite, checked AI HL practice aligned to current syllabus point AIHL 4.17.
Calculate upper-tail Poisson probabilities
Develop calculate upper-tail poisson probabilities through finite, checked AI HL practice aligned to current syllabus point AIHL 4.17.
Construct normal critical boundaries with known variance
Develop construct normal critical boundaries with known variance through finite, checked AI HL practice aligned to current syllabus point AIHL 4.18.
Calculate one-tailed Poisson test p-values
Develop calculate one-tailed poisson test p-values through finite, checked AI HL practice aligned to current syllabus point AIHL 4.18.
Calculate normal mean test statistics with known variance
Develop calculate normal mean test statistics with known variance through finite, checked AI HL practice aligned to current syllabus point AIHL 4.18.
Conclude correlation tests from technology output
Develop conclude correlation tests from technology output through finite, checked AI HL practice aligned to current syllabus point AIHL 4.18.
Distinguish correlation significance from strength
Develop distinguish correlation significance from strength through finite, checked AI HL practice aligned to current syllabus point AIHL 4.18.
Interpret one-tailed Poisson test output
Develop interpret one-tailed poisson test output through finite, checked AI HL practice aligned to current syllabus point AIHL 4.18.
Select nonlinear model families from data structure
Develop select nonlinear model families from data structure through finite, checked AI HL practice aligned to current syllabus point AIHL 4.13.
Evaluate limitations of high coefficients of determination
Develop evaluate limitations of high coefficients of determination through finite, checked AI HL practice aligned to current syllabus point AIHL 4.13.
Calculate residuals from nonlinear models
Develop calculate residuals from nonlinear models through finite, checked AI HL practice aligned to current syllabus point AIHL 4.13.
Compare fitted models using fit and context
Develop compare fitted models using fit and context through finite, checked AI HL practice aligned to current syllabus point AIHL 4.13.
Interpret parameters in exponential models
Develop interpret parameters in exponential models through finite, checked AI HL practice aligned to current syllabus point AIHL 4.13.
Three-state Markov chains and long-term behaviour
Use column-stochastic transition matrices to calculate finite-step, steady-state, calibrated, and convergence behaviour.