AP Calculus Preparation at the Khan Academy
Algebra
Manipulating expressions
 Know how to manipulate polynomial expressions.
 Adding: $(x+2x+3)+(3x−3x)=4x−x+3$left 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: $(x+2)(3x−5)⇔3x+x−10$

Know how to solve simple linear equations.
 For example, $2x+3=5x−7$2, x, plus, 3, equals, 5, x, minus, 7

Know how to solve quadratic equations, such as $2x+3x−5=0$2, x, start superscript, 2, end superscript, plus, 3, x, minus, 5, equals, 0

Know the properties of exponents.
 $xy=(xy)$x, start superscript, 2, end superscript, y, start superscript, 2, end superscript, equals, left parenthesis, x, y, right parenthesis, start superscript, 2, end superscript
 $(2)(2)=2$left 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, $x1=x$start fraction, 1, divided by, x, end fraction, equals, x, start superscript, minus, 1, end superscript
 Roots: For example, $√x=x$square root of, x, end square root, equals, x, start superscript, 1, slash, 2, end superscript

Know what logarithms are, as well as their properties.
 $y=2$y, equals, 2, start superscript, x, end superscript says the same thing as $log(y)=x$log, start subscript, 2, end subscript, left parenthesis, y, right parenthesis, equals, x.
 $log(x)+log(y)=log(xy)$log, left parenthesis, x, right parenthesis, plus, log, left parenthesis, y, right parenthesis, equals, log, left parenthesis, x, y, right parenthesis.
 $log(a)=xlog(a)$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.

Know how to represent a function with a graph.

Know the graphs of various elementary functions.
 Linear functions
 Quadratic functions
 Have at least a loose idea for what the graph of an $n$n, start superscript, t, h, end superscript degree polynomial might look like.
 Exponentials
 Logarithms

Know how to manipulate functions.

It’s also helpful to be familiar with function terminology
Geometry

Know how to compute the area of simple shapes.
Trigonometry
 Be comforatble with each of the basic trigonometry functions: $sin(x)$sine, left parenthesis, x, right parenthesis,$cos(x)$cosine, left parenthesis, x, right parenthesis and $tan(x)$tangent, left parenthesis, x, right parenthesis
 Know what each one represents.
 Know the values of these functions when $x$x takes on one of the following values: $0$0, $6π$start fraction, pi, divided by, 6, end fraction, $4π$start fraction, pi, divided by, 4, end fraction, $3π$start fraction, pi, divided by, 3, end fraction, $2π$start fraction, pi, divided by, 2, end fraction.
 Know what the graph of each of these functions looks like.