High School Number and Quantity (Alaska Standards)

The Real Number System

• N-RN.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).
• N-RN.2 Rewrite expressions with radicals and rational exponents using exponent properties.
• N-RN.3 Explain why sums and products of rationals are rational and why mixing a rational and an irrational (nonzero) gives an irrational.

Quantities

• N-Q.1 Use units to understand and guide multistep problems, read units in formulas and choose scales and origins for graphs and data displays.
• N-Q.2 Define suitable quantities when building a descriptive model.
• N-Q.3 Report quantities with a level of accuracy that fits the limits of measurement.

The Complex Number System

• N-CN.1 Know the number i with i² = −1 and that every complex number is a + bi with real a and b.
• N-CN.2 Add, subtract and multiply complex numbers using i² = −1 and properties of operations.
• N-CN.3 (+) Use complex conjugates to find moduli and quotients.
• N-CN.4 (+) Plot complex numbers in rectangular and polar form and explain why both forms give the same number.
• N-CN.5 (+) Show complex addition, subtraction, multiplication and conjugation geometrically on the complex plane.
• N-CN.6 (+) Find distances and midpoints in the complex plane using the modulus and averages.
• N-CN.7 Solve quadratics with real coefficients whose solutions are complex.
• N-CN.8 (+) Extend polynomial identities to complex numbers, e.g. x² + 4 = (x + 2i)(x − 2i).
• N-CN.9 (+) Know the Fundamental Theorem of Algebra and show it holds for quadratics.

Vector & Matrix Quantities

• N-VM.1 (+) Recognize vectors as having magnitude and direction and use suitable notation for them.
• N-VM.2 (+) Find vector components by subtracting initial-point coordinates from terminal-point coordinates.
• N-VM.3 (+) Solve problems about velocity and other vector quantities.
• N-VM.4 (+) Add and subtract vectors.
• N-VM.5 (+) Multiply a vector by a scalar.
• N-VM.6 (+) Use matrices to represent and work with data, such as payoffs or networks.
• N-VM.7 (+) Multiply matrices by scalars.
• N-VM.8 (+) Add, subtract and multiply matrices of suitable sizes.
• N-VM.9 (+) Know matrix multiplication is not commutative but is associative and distributive.
• N-VM.10 (+) Know zero and identity matrices act like 0 and 1; a square matrix has an inverse exactly when its determinant is nonzero.
• N-VM.11 (+) Multiply a vector by a matrix and treat matrices as transformations of vectors.
• N-VM.12 (+) Use 2 × 2 matrices as transformations of the plane and link the determinant's absolute value to area.