Pre-Calculus Standards and Resources

Pre-Calculus Unit 7: Vectors

In this unit, students will:

  • Recognize vectors as mathematical objects having both magnitude and direction.
  • Add / Subtract vectors using a variety of methods: end to end, parallelogram, and component wise.
  • Multiply vectors by a scalar.
  • Interpret operations on vectors (+, –, ×) geometrically.
  • Understand why the magnitude of the sum of two vectors is usually less than (sometimes equal to) the sum of their magnitudes
  • Use vectors to solve problems.
  • Apply matrix transformations to vectors.
  • Plot complex numbers in the complex plane.
  • write complex numbers in rectangular and polar form
  • Interpret operations on complex numbers (+, –, ×, ÷, conjugate) geometrically.
  • Use the complex plane to find the distance between two complex numbers.
  • Use the complex plane to find the average of two complex numbers.

Pre-requisite skills

Sample Test

Pre-Calculus Unit 6:  Triangles

In this unit, students will:
  • Expand the use of trigonometric functions beyond right triangles into more general triangles.
  • Develop the trigonometric formula for area of a triangle.
  • Use the Laws of Sines and Cosines to solve problems.

Pre-requisite skills

Sample Assessment:



Pre-Calculus Unit 5:  Trigonometric Identities

In this unit, students will:
  • Build upon their work with trigonometric identities with addition and subtraction formulas.
  • Will look at addition and subtraction formulas geometrically.
  • Prove addition and subtraction formulas.
  • Use addition and subtraction formulas to solve problems.

Pre-requisite skills:

Sample Assessment:

Pre-Calculus Unit 4: Trig Graphs


  • Realize transformations of y = sin(x) and y = cos(x) behave just as transformations of other parent functions.
  • Learn that the concepts of amplitude, midline, frequency, and period are related to the transformations of trigonometric functions.
  • Learn how to look at a graph of a transformed sine or cosine function and to write a function to represent that graph explore several real-world settings and represent the situation with a trigonometric function that can be used to answer questions about the situation.
  • Pre-requisite skills:

Example Summative:

PreCalculus Unit 3: Basic Trig

In this unit, students will:

  • Expand their understanding of angle with the concept of a rotation angle.
  • Explore the definition of radian.
  • Define angles in standard position and consider them in relationship to the unit circle.
  • Make connections to see how a real number is connected to the radian measure of an angle in standard position which is connected to an intercepted arc on the unit circle which is connected to a terminal point of this arc whose coordinates are connected to the sine and cosine functions.
  • Gain a better understanding of the unit circle and its connection to trigonometric functions.


Unit Two – Conics

In this unit, students will:
  • Build upon the understanding of the algebraic representations of circles and parabolas.
  • Develop the understanding of the geometric description and equations for the conic sections, parabolas, ellipses, and hyperbolas.


Pre-requisite skills: review:

Sample post test:


Unit One – Matrices

In this unit students will:

  • Represent and manipulate data using matrices.
  • Define the order of a matrix as the number of rows by the number of columns.
  • Add and subtract matrices and know these operations are possible only when the dimensions are equal.
  • Recognize that matrix addition and subtraction are commutative.
  • Multiply matrices by a scalar and understand the distributive and associative properties apply to matrices.
  • Multiply matrices and know when the operation is defined.
  • Recognize that matrix multiplication is not commutative.
  • Understand and apply the properties of a zero matrix.
  • Understand and apply the properties of an identity matrix.
  • Find the determinant of a square matrix and understand that it is a nonzero value if and only if the matrix has an inverse.
  • Use 2 X 2 matrices as transformations of a plane and determine the area of the plane using the determinant
  • Write a system of linear equations as a matrix equation and use the inverse of the coefficient matrix to solve the system.