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Maths: AI HL - Concept Videos
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All Topics
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Solving first-order differential equations
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Applications of differential equations in growth and decay problems
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Definition and calculation of limits
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Continuity of functions at a point
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Squeeze theorem
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Definition of a derivative (rate of change)
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Differentiation rules (power, product, quotient, chain rule)
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Applications of derivatives in optimization problems
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Indefinite integrals and their properties
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Definite integrals and the area under a curve
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Applications of integration in areas and volumes
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Solving non-right-angled triangles
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Law of Sines and its applications
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Law of Cosines and its applications
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Equation of a straight line and slope-intercept form
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Distance formula, midpoint formula and area of triangle
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Equations of circles and their properties
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Definitions of sine, cosine and tangent using right-angled triangles
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Unit circle and angle measurement
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Pythagorean identity and other trigonometric identities
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Exponential functions and their graphs
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Logarithmic functions and their properties
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Solving exponential and logarithmic equations
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Binomial expansion and coefficients
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Applications of binomial expansions
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Definition and general term of arithmetic sequences
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Sum of an arithmetic sequence
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Applications of arithmetic sequences in real-world contexts
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Definition and general term of geometric sequences
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Sum of a geometric sequence
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Applications of geometric sequences in finance and growth models
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Polynomial functions and their graphs
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Rational expressions and their simplification
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Polynomial long division and synthetic division
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Measures of central tendency (mean, median, mode)
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Measures of spread (range, variance, standard deviation)
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Box plots and histograms
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Basic probability concepts and rules
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Conditional probability and Bayes' theorem
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Discrete and continuous random variables
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Binomial distribution and its properties
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Normal distribution and its properties
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Standardization and Z-scores
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Confidence intervals and hypothesis testing
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T-tests and chi-square tests
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Regression analysis
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Formulating a research question
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Using mathematical models in the exploration
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Writing the mathematical exploration report
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Developing problem-solving strategies
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Real-world applications of mathematics
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Using mathematical models in investigations
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Definition and types of functions (one-to-one, onto etc.)
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Domain and range of functions
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Inverses of functions and their graphs
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Translation, reflection, stretching and compression
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The effect of transformations on the graph of a function
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Composition and inverse of functions
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Sine, cosine and tangent functions
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Trigonometric identities and equations
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