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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

  1. Adding and subtracting rational expressions 7
  2. Comparing features of functions
  3. Experimental probability
  4. Adding and subtracting radicals
  5. Trigonometry 2
  6. Distinguish between linear and exponential models
  7. Factoring polynomials by grouping
  8. Solving systems of two linear equations
  9. Evaluating composite functions
  10. Equation of a circle in factored form

Vectors

  1. Recognizing vector quantities
  2. Scaling vectors
  3. Graphically adding and subtracting vectors
  4. Adding and subtracting vectors in rectangular form
  5. Components of vectors
  6. Unit vectors
  7. Adding vectors in magnitude and direction form
  8. Vector word problems

Matrices

  1. Matrix dimensions
  2. Representing relationships with matrices
  3. Scalar matrix multiplication
  4. Matrix addition and subtraction
  5. Matrix transpose
  6. Multiplying a matrix by a matrix
  7. Multiplying a matrix by a vector
  8. Defined and undefined matrix operations
  9. Properties of matrix multiplication
  10. Zero and identity matrices
  11. Geometric transformations with matrix multiplication
  12. Determinant of a 2x2 matrix
  13. Inverse of a 2x2 matrix
  14. Determinant of a 3x3 matrix
  15. Inverse of a 3x3 matrix
  16. Writing systems of equations as matrix equations
  17. Solving matrix equations

Parametric equations and polar coordinates

Imaginary and complex numbers

  1. Simplify powers of the imaginary unit
  2. The imaginary unit and complex numbers
  3. Plot complex numbers on the complex plane
  4. Adding and subtracting complex numbers
  5. Complex plane operations
  6. Distance and midpoint on the complex plane
  7. Equivalent forms of expressions with complex numbers
  8. Multiplying complex numbers
  9. Dividing complex numbers
  10. Find the absolute value of complex numbers
  11. Complex number polar form intuition
  12. Rectangular and polar forms of complex numbers
  13. Multiplying and dividing complex numbers in polar form
  14. Powers of complex numbers

Probability and combinatorics

  1. Simple probability
  2. Probabilities of compound events
  3. Independent probability
  4. Dependent probability
  5. Permutations
  6. Combinations
  7. Permutations and combinations
  8. Probability with permutations and combinations

Sequences, series and induction

  1. Explicit formulas for arithmetic sequences
  2. Recursive formulas for arithmetic sequences
  3. Arithmetic series
  4. Find the next term of a geometric sequence, given the first few terms
  5. Find any term of a geometric sequence, given the formula of the sequence
  6. Explicit formulas for geometric sequences
  7. Find recursive formulas for geometric sequences
  8. Modeling with sequences
  9. Calculating finite geometric series
  10. Finite geometric series word problems
  11. Understanding series
  12. Infinite geometric series
  13. Model real-world situations with arithmetic and geometric sequences
  14. Find the next term of an arithmetic sequence, given the first few terms

Hyperbolic functions

  1. Asymptotes of a hyperbola

Partial fraction expansion

  1. Partial fraction expansion

Limits

  1. Two-sided limits from graphs
  2. One-sided limits from graphs
  3. Finding limits numerically
  4. Two-sided limits using algebra
  5. Two-sided limits using advanced algebra

Miscellaneous

Users can view other Math Missions here.

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