Pre-Calculus Content & Skills

Algebra-1 content/skills

Pre-Requisite Expectations
  • Graph quadratic functions and show intercepts, maxima, and minima (F-IF.7a)
  • Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph (F-IF.8)
  • Solve quadratic equations in one variable using factoring, completing the square, and quadratic formula (A-REI.4)
  Algebra-1 tutorials  

Algebra-2 content/skills

Pre-Requisite Expectations
  • Rewrite expressions involving radicals and rational exponents using the property of exponents (N-RN.2)
  • Solve simple radical equations in one variable, and give examples showing how extraneous solutions may arise (A-REI.2)
  • Use the relation i2 = -1, and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers (N.CN2)
  • Solve quadratic equations with real coefficients that have complex solutions (N-CN.7)
  Algebra-2 tutorials   Exponent/Radicals Topics   Imaginary and Complex Numbers
Pre-Requisite Expectations from Algebra-2
  • Add, subtract, and multiply polynomials (A-APR.1)
  • Determine zeros of a polynomial when factorizations are available (A-APR.3)
  • Use long or synthetic division to rewrite rational expressions (A-APR.6)
  • Use the zeros of polynomials to construct a rough graph of a polynomial function (A-APR.3)
  Polynomial and Rational Functions Topics   Learning Expectations
  • Show how the Fundamental Theorem of Algebra is true for quadratic polynomials (N-CN.9)
  • Use polynomial identities to the complex numbers (e.g., re-write x2 + 4 as (x – 2i)(x + 2i) (N-CN.8)
  • Apply the Binomial Theorem for the expansion of (x + y)n (A-APR.5)
  • Add, subtract, multiply and divide rational expressions (A-APR.7)
  • Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior (F-IF.7d)
  • Decompose a rational function into partial fractions including rational functions with irreducible quadratic roots in the denominator (F-BF-Fairfield.6)
  Polynomials and rational functions tutorials
Pre-Requisite Expectations from Algebra-2
  • Find inverse functions (F-BF.4)
  • Express as a logarithm, the solution to abct = d, where a, c, and d are numbers and the base b is 2, 10 or e; evaluate using technology (F-LE.4)
  Inverse and Logarithms Tutorials   Learning Expectations
  • Compose functions (F-BF.1)
  • Verify by composition that one function is the inverse of another (F-BF.4b)
  • Read values of an inverse function from a graph or a table, given that the function has an inverse (F-BF.4c)
  • Produce an invertible function from a non‐invertible function by restricting the domain. (F-BF.4d)
  • Solve problems involving logarithms and exponents (F-BF.5)
  • Use the properties of logarithms to solve problems (F-BR.5)
  Exponential and Logarithmic functions tutorials
Pre-Requisite Expectations from Algebra-2
  • Understand the relationship between radians and degrees. Convert between radians and degrees (F.TF.1)
  • Use special right triangles to determine the values of sine, cosine, and tangent for (multiples of) , , (F-TF.3)
  • Explain how the unit circle in the coordinate plan enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles transversed counterclockwise around the unit circle (i.e., construct the unit circle for multiples of and ) (F-TF.2)
  Trigonometry Topics   Learning Expectations
  • Use the unit circle to express values of sine, cosine, and tangent for , , and in terms of their value of x, where x is any real number (F-TF.3)
  • Use the unit circle to explain symmetry (odd/even) of trigonometric functions (F-TF.4)
  • Use the unit circle to explain the periodicity of trigonometric functions (F-TF.4)
  • Graph sine, cosine, and tangent functions using transformations
  • Use addition and subtraction formulas for sine, cosine, and tangent (F-TF.9)
  • Use the double angle formulas to solve problems
  • Use the Law of Sine or Cosine to determine missing attributes of right and non-right triangles (G-SRT.11)
  • Determine the area of right and non-right triangles and use them to solve problems (e.g., area of irregular shapes) (G-SRT.9)
  Trigonometry tutorials
Learning Expectations
  • Solve problems involving velocity and other quantities that are represented by vectors (N-VM.3)
  • Add and subtract vectors (N-VM.4)
  • Multiply a vector by a scalar (N-VM.5)
  • Recognize the magnitude and direction of a vector (N-VM.1)
  • Multiply matrices by scalars to produce new matrices (N-VM.7)
  • Add, subtract, and multiply matrices of appropriate dimensions (N-VM.8)
  • Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers.
  • Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors (N-VM.11)
  • Work with 2x2 matrices as transformations of the plan, and the absolute value of the determinant in terms of area.
  • Represent a system of linear equations as a single matrix equation in a vector variable (A-REI.8)
  • Solve a system of equations using a matrix (A-REI.9)
  Vector and matrices tutorials
Learning Expectations
  • Use graphing calculators to verify and estimate limits
  • Know the difference between a one-sided vs. two-sided limits
  Trigonometric ratios tutorials