Vectors and spaces (Khan Academy)

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Let’s get our feet wet by thinking in terms of vectors and spaces. (1) Vectors Vector intro for linear algebra Real coordinate spaces Adding vectors algebraically & graphically Multiplying a vector by a scalar Vector examples Scalar multiplication Unit vector notation Unit vectors Add & subtract vectors Add vectors: magnitude & direction to component Parametric […]

Derivative applications (Khan Academy)

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The reason we study calculus, and the reason it was invented, is for its many uses in real-world problems. In particular, derivatives let us optimize functions and study their rates of change. Here we cover optimization, rates of change, L’Hopital’s rule, the mean value theorem, and more! (1) Equations of normal and tangent lines Equation […]

Taking derivatives (Khan Academy)

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Calculating derivatives. Power rule. Product and quotient rules. Chain Rule. Implicit differentiation. Derivatives of common functions. (1) Introduction to differential calculus Newton, Leibniz, and Usain Bolt (2) Using secant line slopes to approximate tangent slope Slope of a line secant to a curve Slope of a secant line example 1 Slope of a secant line […]

Limits (Khan Academy)

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Limit introduction, squeeze theorem, and epsilon-delta definition of limits (1) Limits Preparing for AP Calculus? Intro to limits Inferring limit from numerical data Estimating limit numerically Finding limits numerically (2) Estimating limits from graphs One-sided limits from graphs One-sided limits from graphs Two-sided limit at a point of discontinuity Two-sided limits from graphs Determining which […]

Graphs of trigonometric functions (Khan Academy)

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Learn how to graph trigonometric functions and how to interpret those graphs. Learn how to construct trigonometric functions from their graphs or other features. (1) The graphs of sine, cosine, and tangent Graph of y=sin(x) Graph of y=tan(x) Intersection points of y=sin(x) and y=cos(x) (2) Introduction to amplitude, midline, and extrema of sinusoidal functions Features […]

The unit circle definition of sine, cosine, and tangent (Khan Academy)

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Learn how the trigonometric ratios are extended to all real numbers using algebra. Start solving simple problems that involve this new definition of the trigonometric functions. (1) Introduction to radians Intro to radians Radians & degrees Degrees to radians Radians to degrees Radians & degrees Radian angles & quadrants (2) The unit circle definition of […]

AP statistics practice (Khan Academy)

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We’ve partnered with a group of incredible teachers and students to bring you our first round of AP statistics practice items. Look forward to a much more full offering of learning and practice content in the not too distant future! (1) Analyzing categorical data Analyzing categorical data (2) Exploring bivariate numerical data Scatterplots & correlation […]

Regression (Khan Academy)

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Fitting a line to points. Linear regression. R-squared. (1) Scatter plots Scatter plots: studying, shoe size, and test scores Scatter plot: smokers Describing trends in scatter plots Constructing a scatter plot Constructing scatter plots Comparing models to fit data example Fitting quadratic and exponential functions to scatter plots (2) Linear regression and correlation Correlation and […]

Random variables and probability distributions (Khan Academy)

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Random variables. Expected value. Probability distributions (both discrete and continuous). Binomial distribution. Poisson processes. (1) Random variables and probability distributions Random variables Discrete and continuous random variables Constructing a probability distribution for random variable Constructing probability distributions Probability density functions (2) Expected value Expected value Term life insurance and death probability Getting data from expected […]

Descriptive statistics (Khan Academy)

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Measures of central tendency and dispersion. Mean, median, mode, variance, and standard deviation. (1) Measures of central tendency Statistics intro: Mean, median, & mode Mean, median, & mode example Mean, median, and mode Comparing means of distributions Means and medians of different distributions Comparing data distributions Inferring population mean from sample mean (2) Box-and-whisker plots […]