South Carolina flagSouth Carolina: Pre-Calculus Math Standards

42 standards · 3 domains

MEASUREMENT, GEOMETRY, AND SPATIAL REASONING

  • PC.MGSR.1.1 Identify and graph different conic sections given the equations in standard form.
  • PC.MGSR.1.2 Identify different conic sections in general form and complete the square to convert the equation of a conic section into standard form.
  • PC.MGSR.1.3 Define polar coordinates and relate polar coordinates to Cartesian coordinates.
  • PC.MGSR.2.1 Determine the area of a triangle to solve problems.
  • PC.MGSR.2.2 Prove and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles.
  • PC.MGSR.2.3 Derive the formulas for the length of an arc and the area of a sector in a circle and apply these formulas to solve mathematical and real-world situations.
  • PC.MGSR.2.4 Determine geometrically the values of the sine, cosine, and tangent for π/6, π/4, and π/3 by special triangles, and use the unit circle to express the values of sine, cosine, and tangent for π-x, π+x, and 2π-x in terms of their values for x, where x is any real number.
  • PC.MGSR.2.5 Define the six trigonometric ratios in terms of x, y, and r using the unit circle centered at the origin of the coordinate plane and interpret radian measures of angles as a rotation both counterclockwise and clockwise around the unit circle.
  • PC.MGSR.2.6 Explain symmetry, both odd and even, and periodicity of trigonometric functions.

NUMERICAL REASONING

  • PC.NR.1.1 Identify the identity and zero matrices for any dimension and add, subtract, and multiply matrices.
  • PC.NR.1.2 Find the additive and multiplicative inverses of square matrices.
  • PC.NR.1.3 Explain the role of the determinant in determining if a square matrix has a multiplicative inverse.
  • PC.NR.1.4 Find the determinant of a square matrix if and only if the matrix has a multiplicative inverse.
  • PC.NR.2.1 Represent vector quantities as directed line segments and represent magnitude and direction of vectors in component form.
  • PC.NR.2.2 Find the components of a vector by adding and subtracting vectors on a coordinate plane using a variety of methods.
  • PC.NR.2.3 Solve problems, including real-life situations, that can be represented by vectors.
  • PC.NR.2.4 Add and subtract vectors and multiply vectors by a scalar to find the resultant vector.
  • PC.NR.3.1 Represent complex numbers on the complex plane in rectangular and polar form, including real and imaginary numbers, and explain why the rectangular and polar forms of a given complex number represent the same number.
  • PC.NR.3.2 Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation.

PATTERNS, ALGEBRA, AND FUNCTIONAL REASONING

  • PC.PAFR.1.1 Combine and compose functions algebraically, tabularly, and graphically.
  • PC.PAFR.1.2 Find the inverse of functions and verify algebraically, numerically, and graphically.
  • PC.PAFR.1.3 Compare the key features of a function and its inverse function and use the relationship to model real-world situations and solve problems.
  • PC.PAFR.1.4 Graph and describe the effect on the graph f(x) of f(x)+k, f(x-k), kf(x), and f(kx), for specific values of both negative and positive values of k.
  • PC.PAFR.2.1 Graph rational functions and describe their key features.
  • PC.PAFR.2.2 Solve rational equations and inequalities in one variable and explain when extraneous solutions may arise.
  • PC.PAFR.2.3 Transform rational expressions in different forms.
  • PC.PAFR.2.4 Graph piecewise-defined functions, including step functions and absolute value functions, and describe their key features.
  • PC.PAFR.3.1 Transform radical expressions as expressions with rational exponents and extend the properties of integer exponents to rational exponents.
  • PC.PAFR.3.2 Solve radical equations and describe how extraneous solutions may arise.
  • PC.PAFR.3.3 Analyze and graph radical functions.
  • PC.PAFR.4.1 Graph logarithmic functions and describe their key features.
  • PC.PAFR.4.2 Use the definition of a logarithm, logarithmic properties, and the inverse relationship between exponential and logarithmic functions to solve problems, including real-life context.
  • PC.PAFR.4.3 Model real-life situations and solve problems involving exponential and logarithmic functions.
  • PC.PAFR.5.1 Graph trigonometric functions and their inverses and describe their key features.
  • PC.PAFR.5.2 Restrict the domain of a trigonometric function to define the six inverse trigonometric functions, graph the inverse function, and evaluate inverse trigonometric expressions.
  • PC.PAFR.5.3 Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions and interpret them in terms of the context.
  • PC.PAFR.6.1 Apply the fundamental trigonometric identities to simplify expressions and verify other identities.
  • PC.PAFR.6.2 Apply the sum, difference, double-angle, and half-angle formulas for sine, cosine, and tangent and use them to solve problems.
  • PC.PAFR.6.3 Model real-life situations and solve problems involving trigonometric equations.
  • PC.PAFR.7.1 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically, and understand that such systems may have zero, one, or two solutions.
  • PC.PAFR.7.2 Solve an equation of the form f(x)=g(x) graphically by identifying the x-coordinate(s) of the point(s) of intersection of the graphs of y=f(x) and y=g(x).
  • PC.PAFR.7.3 Represent a system of linear equations as a single matrix equation in a vector variable.