High School Number and Quantity (Colorado Academic Standards)

Standard 1: Number and Quantity

• MA.HS.N-RN.A Extend exponent properties to rational exponents.
  • 1. Explain how rational exponents are defined by extending the rules for integer exponents (e.g. 5^(1/3) as the cube root of 5).
  • 2. Rewrite expressions with radicals and rational exponents using exponent properties.
• MA.HS.N-RN.B Explain when sums and products of rational and irrational numbers are rational.
  • 1. (+) Explain why sums and products of rationals are rational and why mixing a rational and an irrational (nonzero) gives an irrational. (being checked)
• MA.HS.N-Q.A Reason with quantities and units to solve problems.
  • 1. Use units to understand and guide multistep problems, read units in formulas and choose scales and origins for graphs and data displays.
  • 2. Define suitable quantities when building a descriptive model.
  • 3. Report quantities with a level of accuracy that fits the limits of measurement.
• MA.HS.N-CN.A Do arithmetic with complex numbers.
  • 1. Know the number i with i² = −1 and that every complex number is a + bi with real a and b.
  • 2. Add, subtract and multiply complex numbers using i² = −1 and properties of operations.
  • 3. (+) Use complex conjugates to find moduli and quotients.
• MA.HS.N-CN.B Represent complex numbers and their operations on the complex plane.
  • 1. (+) Plot complex numbers in rectangular and polar form and explain why both forms give the same number.
  • 2. (+) Show complex addition, subtraction, multiplication and conjugation geometrically on the complex plane.
  • 3. (+) Find distances and midpoints in the complex plane using the modulus and averages.
• MA.HS.N-CN.C Use complex numbers in polynomial identities and equations.
  • 1. Solve quadratics with real coefficients whose solutions are complex.
  • 2. (+) Extend polynomial identities to complex numbers, e.g. x² + 4 = (x + 2i)(x − 2i).
  • 3. (+) Know the Fundamental Theorem of Algebra and show it holds for quadratics.
• MA.HS.N-VM.A Represent and model with vectors.
  • 1. (+) Recognize vectors as having magnitude and direction and use suitable notation for them.
  • 2. (+) Find vector components by subtracting initial-point coordinates from terminal-point coordinates.
  • 3. (+) Solve problems about velocity and other vector quantities.
• MA.HS.N-VM.B Perform operations on vectors.
  • 1. (+) Add and subtract vectors.
  • 1.a. Add vectors end to end, by components and with the parallelogram rule, knowing magnitudes do not simply add.
  • 1.b. Find the magnitude and direction of the sum of two vectors given in magnitude-direction form.
  • 1.c. Understand v − w as v + (−w) and show subtraction graphically and by components.
  • 2. (+) Multiply a vector by a scalar.
  • 2.a. Show scalar multiples graphically (scaling and possibly reversing) and by components.
  • 2.b. Find the magnitude and direction of a scalar multiple cv.
• MA.HS.N-VM.C Perform operations on matrices and apply them.
  • 1. (+) Use matrices to represent and work with data, such as payoffs or networks.
  • 2. (+) Multiply matrices by scalars.
  • 3. (+) Add, subtract and multiply matrices of suitable sizes.
  • 4. (+) Know matrix multiplication is not commutative but is associative and distributive.
  • 5. (+) Know zero and identity matrices act like 0 and 1; a square matrix has an inverse exactly when its determinant is nonzero.
  • 6. (+) Multiply a vector by a matrix and treat matrices as transformations of vectors.
  • 7. (+) Use 2 × 2 matrices as transformations of the plane and link the determinant's absolute value to area.