Khan Academy APCalculus Prep

AP Calculus Preparation at the Khan Academy

Algebra

Manipulating expressions

  • Know how to manipulate polynomial expressions.
    • Adding: (x^2 + 2x + 3) + (3x^2 – 3x) = 4x^2 – x + 3(x2+2x+3)+(3x23x)=4x2x+3left parenthesis, x, start superscript, 2, end superscript, plus, 2, x, plus, 3, right parenthesis, plus, left parenthesis, 3, x, start superscript, 2, end superscript, minus, 3, x, right parenthesis, equals, 4, x, start superscript, 2, end superscript, minus, x, plus, 3
    • Multiplying and Factoring: (x + 2)(3x – 5) \Leftrightarrow 3x^2 + x – 10(x+2)(3x5)3x2+x10
  • Know how to solve simple linear equations.

    • For example, 2x + 3 = 5x – 72x+3=5x72, x, plus, 3, equals, 5, x, minus, 7
  • Know how to solve quadratic equations, such as 2x^2 + 3x – 5 = 02x2+3x5=02, x, start superscript, 2, end superscript, plus, 3, x, minus, 5, equals, 0

  • Know the properties of exponents.

    • x^2 y^2 = (xy)^2x2y2=(xy)2x, start superscript, 2, end superscript, y, start superscript, 2, end superscript, equals, left parenthesis, x, y, right parenthesis, start superscript, 2, end superscript
    • (2^x)(2^y) = 2^{x + y}(2x)(2y)=2x+yleft parenthesis, 2, start superscript, x, end superscript, right parenthesis, left parenthesis, 2, start superscript, y, end superscript, right parenthesis, equals, 2, start superscript, x, plus, y, end superscript
  • Know how certain expressions are secretly exponentials in disguise

    • Reciprocals: For example, \dfrac{1}{x} = x^{-1}x1=x1start fraction, 1, divided by, x, end fraction, equals, x, start superscript, minus, 1, end superscript
    • Roots: For example, \sqrt{x} = x^{1/2}x=x1/2square root of, x, end square root, equals, x, start superscript, 1, slash, 2, end superscript
  • Know what logarithms are, as well as their properties.

    • y = 2^xy=2xy, equals, 2, start superscript, x, end superscript says the same thing as \log_2(y) = xlog2(y)=xlog, start subscript, 2, end subscript, left parenthesis, y, right parenthesis, equals, x.
    • \log(x) + \log(y) = \log(xy)log(x)+log(y)=log(xy)log, left parenthesis, x, right parenthesis, plus, log, left parenthesis, y, right parenthesis, equals, log, left parenthesis, x, y, right parenthesis.
    • \log(a^x) = x\log(a)log(ax)=xlog(a)log, left parenthesis, a, start superscript, x, end superscript, right parenthesis, equals, x, log, left parenthesis, a, right parenthesis.

Functions

Calculus is all about functions, so it is helpful to be pretty fluent when it comes to thinking about functions, graphing functions, and using the appropriate terminology when talking about functions.

Trigonometry

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