# Precalculus Math Mission

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The ** Precalculus Math Mission** is a set of skills on Khan Academy. This mission consists of intensive practice on various topics including vectors, matrices, parametric equations, polar coordinates, complex numbers, advanced probability, sequences and series, and beginning limit calculus.

## Mission Specifics

### Mission Foundations

- Adding and subtracting rational expressions 7
- Comparing features of functions
- Experimental probability
- Adding and subtracting radicals
- Trigonometry 2
- Distinguish between linear and exponential models
- Factoring polynomials by grouping
- Solving systems of two linear equations
- Evaluating composite functions
- Equation of a circle in factored form

### Vectors

- Recognizing vector quantities
- Scaling vectors
- Graphically adding and subtracting vectors
- Adding and subtracting vectors in rectangular form
- Components of vectors
- Unit vectors
- Adding vectors in magnitude and direction form
- Vector word problems

### Matrices

- Matrix dimensions
- Representing relationships with matrices
- Scalar matrix multiplication
- Matrix addition and subtraction
- Matrix transpose
- Multiplying a matrix by a matrix
- Multiplying a matrix by a vector
- Defined and undefined matrix operations
- Properties of matrix multiplication
- Zero and identity matrices
- Geometric transformations with matrix multiplication
- Determinant of a 2x2 matrix
- Inverse of a 2x2 matrix
- Determinant of a 3x3 matrix
- Inverse of a 3x3 matrix
- Writing systems of equations as matrix equations
- Solving matrix equations

### Parametric equations and polar coordinates

### Imaginary and complex numbers

- Simplify powers of the imaginary unit
- The imaginary unit and complex numbers
- Plot complex numbers on the complex plane
- Adding and subtracting complex numbers
- Complex plane operations
- Distance and midpoint on the complex plane
- Equivalent forms of expressions with complex numbers
- Multiplying complex numbers
- Dividing complex numbers
- Find the absolute value of complex numbers
- Complex number polar form intuition
- Rectangular and polar forms of complex numbers
- Multiplying and dividing complex numbers in polar form
- Powers of complex numbers

### Probability and combinatorics

- Simple probability
- Probabilities of compound events
- Independent probability
- Dependent probability
- Permutations
- Combinations
- Permutations and combinations
- Probability with permutations and combinations

### Sequences, series and induction

- Explicit formulas for arithmetic sequences
- Recursive formulas for arithmetic sequences
- Arithmetic series
- Find the next term of a geometric sequence, given the first few terms
- Find any term of a geometric sequence, given the formula of the sequence
- Explicit formulas for geometric sequences
- Find recursive formulas for geometric sequences
- Modeling with sequences
- Calculating finite geometric series
- Finite geometric series word problems
- Understanding series
- Infinite geometric series
- Model real-world situations with arithmetic and geometric sequences
- Find the next term of an arithmetic sequence, given the first few terms

### Hyperbolic functions

### Partial fraction expansion

### Limits

- Two-sided limits from graphs
- One-sided limits from graphs
- Finding limits numerically
- Two-sided limits using algebra
- Two-sided limits using advanced algebra

### Miscellaneous

Users can view other Math Missions here.