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Mathematics » Pre-Calculus

Pre-Calculus

I. Sequence and Series
  1. What is the difference between sequences and series and what are the different types?
  2. What are the different types of sequences and series?
  3. What is an arithmetic sequence/series?
  4. How do we find the sum of a finite arithmetic sequence/series?
  5. What is a geometric sequence/series?
  6. How do we find the sum of a finite geometric sequence/series?
  7. How do we find the sum of an infinite geometric series?
II. Algebraic Skills
 
  1. Review long division and introduce the remainder theorem.
  2. What is the factor theorem?
  3. What is synthetic division and how can it be used as a tool?
  4. What are the zeros or roots of a polynomial function?
  5. How can we find the rational zeros of a polynomial function?
  6. How do we find the irrational zeros of a polynomial function?
  7. How can upper and lower bounds be used to determine the roots of a polynomial equation?
  8. How can we apply polynomial equations to real-life situations?
  9. What is Decartes Rule of Signs?
  10. How can we determine the nature of the roots of a polynomial equation?
  11. What is the relationship between roots and coefficients?
  12. How do we solve equations have complex roots?
  13. How do we find the polynomial functions whose zeros are complex numbers?
  14. What is the fundamental theorem of Algebra?
III. Review of the Graphing Calculator
 
  1. How do we store and retrieve numbers and expressions?
  2. How do we graph a function?
  3. How can the zeros of a function be calculated?
  4. How can we evaluate and deselect a function?
  5. How can a z-box and zoom in-out be used in tracing a function and locating the zeros?
IV. Functions
 
  1. How can the domain and range of a function be found?
  2. How can square root functions and Dirichelet functions be evaluated?
  3. How can the circle and absolute value functions be drawn and evaluated?
  4. How do graphs of functions change when functions change?
  5. What is rational function and greatest integer function?
  6. What is function notation?
  7. How can functions be used as mathematical models?
  8. What are quadratic functions?
  9. What are the extreme values of quadratics?
  10. What are increasing, decreasing, inverse and composite functions?
VI. Trigonometry
 
  1. What are the different trigonometric ratios and what is the Unit Circle?
  2. How do we solve linear trigonometric equations?
  3. How do we solve quadratic trigonometric equations?
  4. Review the graphs of trigonometric functions.
VII. Complex numbers, Cartesian (Rectangular) and Polar Forms
 
  1. How can operations of complex numbers be performed?
  2. What is the geometric representation of a complex number?
  3. What is the polar form of a complex number?
  4. How can we switch from Cartesian to rectangular and rectangular to Cartesian?
  5. How can we multiply and divide complex numbers in polar form?
    What is DeMoivie’s Theorem?
  6. How can DeMoivie’s Theorem be used to find the roots of a complex number in polar form?
VIII. Matrices
 
  1. What are matrices?
  2. How can matrices be added and subtracted?
  3. How can we multiply one matrix by another matrix?
  4. What is the multiplicative identity and inverses of a two-by-two matrix?
  5. How can we solve a system of equations using A-1B and Cramer’s Rule?
  6. How can the minors, cofactors, determinants, adjoints and multiplicative inverse of a t matrix be found?
  7. How can we solve a system of equations with three variables?
  8. What are partial fractions?