4th Year Course (South Dakota Content Standards)

Number and Quantity (N)

• Y4.N.CN.3 Find complex conjugates and use them to find moduli and quotients.
• Y4.N.CN.4 Show complex numbers in rectangular and polar form on the complex plane and explain why both forms name the same number.
• Y4.N.CN.5 Show adding, subtracting, multiplying and conjugating complex numbers geometrically and use this to compute.
• Y4.N.CN.6 Find distance between complex numbers as the modulus of the difference and midpoints as averages.
• Y4.N.CN.8 Extend polynomial identities to complex numbers, e.g. factoring x² + 4.
• Y4.N.CN.9 Know the Fundamental Theorem of Algebra and show it holds for quadratics.
• Y4.N.VM.1 Recognize vectors as having size and direction, draw them as directed segments and use vector notation.
• Y4.N.VM.2 Write vectors in component form.
• Y4.N.VM.3 Solve velocity and other problems that vectors can represent.
• Y4.N.VM.4 Add and subtract vectors.
  • Y4.N.VM.4a Add vectors tip-to-tail, by components and by the parallelogram rule, knowing magnitudes do not simply add.
  • Y4.N.VM.4b Find the magnitude and direction of a sum of two vectors given in that form.
  • Y4.N.VM.4c Treat v − w as v + (−w) and show subtraction graphically and by components.
• Y4.N.VM.5 Multiply a vector by a scalar.
  • Y4.N.VM.5a Show scalar multiples graphically by scaling or reversing, and compute them by components.
  • Y4.N.VM.5b Find the magnitude and direction of cv.
• Y4.N.VM.6 Represent and manipulate data with matrices.
• Y4.N.VM.7 Multiply matrices by scalars.
• Y4.N.VM.8 Add, subtract and multiply matrices of suitable sizes.
• Y4.N.VM.9 Know square-matrix multiplication is not commutative but is associative and distributive.
• Y4.N.VM.10 See zero and identity matrices as acting like 0 and 1, and link a nonzero determinant to having an inverse.
• Y4.N.VM.11 Multiply a vector by a matrix to get another vector, treating matrices as vector transformations.
• Y4.N.VM.12 Treat 2 × 2 matrices as plane transformations and read the absolute determinant as an area factor.

Algebra (A)

• Y4.A.SSE.4 Derive and use the finite geometric series sum formula (ratio not 1) to solve problems (modeling).
• Y4.A.SSE.5 Write sums of series in summation notation.
• Y4.A.APR.5 Know and use the Binomial Theorem to expand (x + y) to a positive integer power, e.g. with Pascal's triangle.
• Y4.A.APR.7 See rational expressions as closed like rational numbers and add, subtract, multiply and divide them.
• Y4.A.REI.8 Write a linear system as one matrix equation.
• Y4.A.REI.9 Solve linear systems with matrices, using technology for 3 × 3 or larger.
• Y4.A.REI.13 Solve two-variable inequalities (linear, quadratic, polynomial, rational) by algebra and by graphing.

Functions (F)

• Y4.F.IF.7 Graph symbolic functions showing key features, by hand or with technology (modeling).
  • Y4.F.IF.7d Graph rational functions, marking zeros, all asymptote types (vertical, horizontal, slant) and end behavior.
  • Y4.F.IF.7e Graph exponential and log functions showing how they relate, intercepts and end behavior.
  • Y4.F.IF.7f Graph all six trig functions with key features and transformations.
• Y4.F.BF.1 Write a function for a relationship between two quantities (modeling).
  • Y4.F.BF.1c Compose functions in context.
• Y4.F.BF.4 Find inverse functions.
  • Y4.F.BF.4b Check by composition that two functions are inverses.
  • Y4.F.BF.4c Read inverse values from a graph or table.
  • Y4.F.BF.4d Restrict a domain to make a non-invertible function invertible.
• Y4.F.BF.5 Use the inverse link between exponents and logarithms to solve problems.
• Y4.F.BF.6 Use reciprocals to define cotangent, cosecant and secant.
• Y4.F.TF.3 Use special triangles for trig values at π/3, π/4 and π/6 and the unit circle for π − x, π + x and 2π − x.
• Y4.F.TF.4 Use the unit circle to explain odd/even symmetry and periodicity of trig functions.
• Y4.F.TF.6 See that restricting a trig function to an always-increasing or always-decreasing domain allows an inverse.
• Y4.F.TF.7 Solve trig equations from models with inverse functions and technology, and interpret the results (modeling).
• Y4.F.TF.9 Prove and use the sum, difference, half-angle and double-angle trig formulas.
• Y4.F.TF.10 Use the basic trig identities.
  • Y4.F.TF.10a Verify trig identities.
  • Y4.F.TF.10b Evaluate trig functions.
  • Y4.F.TF.10c Write equivalent trig expressions.
  • Y4.F.TF.10d Solve trig equations.

Geometry (G)

• Y4.G.SRT.9 Derive A = ½ab sin C using an altitude and use it to solve problems.
• Y4.G.SRT.10 Prove the Law of Sines and Law of Cosines and apply them to any triangle.
• Y4.G.GPE.3 Analyze conic sections with equations and graphs.
  • Y4.G.GPE.3a Classify the graph of a second-degree equation with no xy term as a circle, parabola, ellipse or hyperbola.
  • Y4.G.GPE.3b Complete the square to put a conic's equation in standard form.
  • Y4.G.GPE.3c Write a conic's equation from its graph and the reverse.

Statistics and Probability (S)

• Y4.S.CP.9 Compute probabilities of compound events with permutations and combinations.
• Y4.S.MD.1 Give each event in a sample space a number and graph the probability distribution.
• Y4.S.MD.2 Find the expected value of a random variable and see it as the distribution's mean.
• Y4.S.MD.3 Build a distribution from theoretical probabilities and find its expected value.
• Y4.S.MD.4 Build a distribution from empirical probabilities and find its expected value.
• Y4.S.MD.5 Weigh decisions by attaching probabilities to payoffs and finding expected values.
  • Y4.S.MD.5a Find the expected payoff of a game of chance.
  • Y4.S.MD.5b Compare strategies by their expected values, e.g. insurance deductibles.
• Y4.S.MD.6 Use probability to make fair decisions, e.g. drawing lots or random numbers.
• Y4.S.MD.7 Analyze decisions and strategies with probability, e.g. product or medical testing.

Precalculus Topics (PC)

• Y4.PC.PC.1 Define polar coordinates and relate them to Cartesian coordinates, with and without technology.
• Y4.PC.PC.2 Model and solve problems with polar equations using graphs and algebra.
• Y4.PC.PE.1 Plot a parametric function and draw conclusions about the figure it makes.
• Y4.PC.PE.2 Convert between parametric equations and an x-y equation and use them to model problems.
• Y4.PC.L.1 Test continuity at a point, classify discontinuities and use limits to describe breaks and end behavior.
• Y4.PC.L.2 Know the definition and graphical meaning of limits of functions and sequences and estimate them with graphs, tables and technology.
• Y4.PC.L.3 Evaluate limits with algebra and limit properties, including one-sided ones and ones at infinity.
• Y4.PC.S.1 Define arithmetic and geometric sequences and series and solve and check word problems with them.