West Virginia: Transition Mathematics for Seniors Math Standards
6 standards · 65 domains
USE UNITS AS A WAY TO UNDERSTAND PROBLEMS AND TO GUIDE THE SOLUTION OF MULTI-STEP PROBLEMS; CHOOSE AND INTERPRET UNITS CONSISTENTLY IN FORMULAS; CHOOSE AND INTERPRET THE SCALE AND THE ORIGIN IN GRAPHS AND DATA DISPLAYS.
UNDERSTAND THAT POLYNOMIALS FORM A SYSTEM ANALOGOUS TO THE INTEGERS, NAMELY, THEY ARE CLOSED UNDER THE OPERATIONS OF ADDITION, SUBTRACTION, AND MULTIPLICATION; ADD, SUBTRACT AND MULTIPLY POLYNOMIALS.
CREATE EQUATIONS AND INEQUALITIES IN ONE VARIABLE AND USE THEM TO SOLVE PROBLEMS. INCLUDE EQUATIONS ARISING FROM LINEAR AND QUADRATIC FUNCTIONS AND SIMPLE RATIONAL AND EXPONENTIAL FUNCTIONS.
CREATE EQUATIONS IN TWO OR MORE VARIABLES TO REPRESENT RELATIONSHIPS BETWEEN QUANTITIES; GRAPH EQUATIONS ON COORDINATE AXES WITH LABELS AND SCALES.
REPRESENT CONSTRAINTS BY EQUATIONS OR INEQUALITIES AND BY SYSTEMS OF EQUATIONS AND/OR INEQUALITIES AND INTERPRET SOLUTIONS AS VIABLE OR NONVIABLE OPTIONS IN A MODELING CONTEXT. FOR EXAMPLE, REPRESENT INEQUALITIES DESCRIBING NUTRITIONAL AND COST CONSTRAINTS ON COMBINATIONS OF DIFFERENT FOODS.
REARRANGE FORMULAS TO HIGHLIGHT A QUANTITY OF INTEREST, USING THE SAME REASONING AS IN SOLVING EQUATIONS.
SOLVE SIMPLE RATIONAL AND RADICAL EQUATIONS IN ONE VARIABLE AND GIVE EXAMPLES SHOWING HOW EXTRANEOUS SOLUTIONS MAY ARISE.
SOLVE LINEAR EQUATIONS AND INEQUALITIES IN ONE VARIABLE, INCLUDING EQUATIONS WITH COEFFICIENTS REPRESENTED BY LETTERS.
EXPLAIN EACH STEP IN SOLVING A SIMPLE EQUATION AS FOLLOWING FROM THE EQUALITY OF NUMBERS ASSERTED AT THE PREVIOUS STEP, STARTING FROM THE ASSUMPTION THAT THE ORIGINAL EQUATION HAS A SOLUTION. CONSTRUCT A VIABLE ARGUMENT TO JUSTIFY A SOLUTION METHOD.
SOLVE QUADRATIC EQUATIONS IN ONE VARIABLE. USE THE METHOD OF COMPLETING THE SQUARE TO TRANSFORM ANY QUADRATIC EQUATION IN X INTO AN EQUATION OF THE FORM (X – P)^2 = Q THAT HAS THE SAME SOLUTIONS. DERIVE THE QUADRATIC FORMULA FROM THIS FORM. SOLVE QUADRATIC EQUATIONS BY INSPECTION (E.G., FOR X^2 = 49), TAKING SQUARE ROOTS, COMPLETING THE SQUARE, THE QUADRATIC FORMULA AND FACTORING, AS APPROPRIATE TO THE INITIAL FORM OF THE EQUATION. RECOGNIZE WHEN THE QUADRATIC FORMULA GIVES COMPLEX SOLUTIONS AND WRITE THEM AS A ± BI FOR REAL NUMBERS A AND B.
PROVE THAT, GIVEN A SYSTEM OF TWO EQUATIONS IN TWO VARIABLES, REPLACING ONE EQUATION BY THE SUM OF THAT EQUATION AND A MULTIPLE OF THE OTHER PRODUCES A SYSTEM WITH THE SAME SOLUTIONS.
CHOOSE A LEVEL OF ACCURACY APPROPRIATE TO LIMITATIONS ON MEASUREMENT WHEN REPORTING QUANTITIES.
SOLVE A SIMPLE SYSTEM CONSISTING OF A LINEAR EQUATION AND A QUADRATIC EQUATION IN TWO VARIABLES ALGEBRAICALLY AND GRAPHICALLY.
EXPLAIN WHY THE X-COORDINATES OF THE POINTS WHERE THE GRAPHS OF THE EQUATION Y = F(X) AND Y = G(X) INTERSECT ARE THE SOLUTION OF THE EQUATION F(X) = G (X); FIND THE SOLUTION APPROXIMATELY (E.G., USING TECHNOLOGY TO GRAPH THE FUNCTIONS, MAKE TABLES OF VALUES OR FIND SUCCESSIVE APPROXIMATIONS).
SOLVE SYSTEMS OF LINEAR EQUATIONS EXACTLY AND APPROXIMATELY (E.G., WITH GRAPHS), FOCUSING ON PAIRS OF LINEAR EQUATIONS IN TWO VARIABLES.
GRAPH THE SOLUTIONS TO A LINEAR INEQUALITY IN TWO VARIABLES AS A HALF-PLANE (EXCLUDING THE BOUNDARY IN THE CASE OF A STRICT INEQUALITY) AND GRAPH THE SOLUTION SET TO A SYSTEM OF LINEAR INEQUALITIES IN TWO VARIABLES AS THE INTERSECTION OF THE CORRESPONDING HALF-PLANES.
UNDERSTAND A FUNCTION FROM ONE SET (CALLED THE DOMAIN) TO ANOTHER SET (CALLED THE RANGE) ASSIGNS TO EACH ELEMENT OF THE DOMAIN EXACTLY ONE ELEMENT OF THE RANGE. IF F IS A FUNCTION AND X IS AN ELEMENT OF ITS DOMAIN, THEN F(X) DENOTES THE OUTPUT OF F CORRESPONDING TO THE INPUT X. THE GRAPH OF F IS THE GRAPH OF THE EQUATION Y = F(X).
WRITE ARITHMETIC AND GEOMETRIC SEQUENCES BOTH RECURSIVELY AND WITH AN EXPLICIT FORMULA, USE THEM TO MODEL SITUATIONS, AND TRANSLATE BETWEEN THE TWO FORMS.
INTERPRET THE PARAMETERS IN A LINEAR OR EXPONENTIAL FUNCTION IN TERMS OF A CONTEXT.
FOR A FUNCTION THAT MODELS A RELATIONSHIP BETWEEN TWO QUANTITIES, INTERPRET KEY FEATURES OF GRAPHS AND TABLES IN TERMS OF THE QUANTITIES, AND SKETCH GRAPHS SHOWING KEY FEATURES GIVEN A VERBAL DESCRIPTION OF THE RELATIONSHIP. KEY FEATURES INCLUDE: INTERCEPTS; INTERVALS WHERE THE FUNCTION IS INCREASING, DECREASING, POSITIVE OR NEGATIVE; RELATIVE MAXIMUMS AND MINIMUMS; SYMMETRIES; END BEHAVIOR; AND PERIODICITY.
DISTINGUISH BETWEEN SITUATIONS THAT CAN BE MODELED WITH LINEAR FUNCTIONS AND WITH EXPONENTIAL FUNCTIONS.
INTERPRET THE EQUATION Y = MX + B AS DEFINING A LINEAR FUNCTION, WHOSE GRAPH IS A STRAIGHT LINE, GIVE EXAMPLES OF FUNCTIONS THAT ARE NOT LINEAR.
SOLVE QUADRATIC EQUATIONS WITH REAL COEFFICIENTS THAT HAVE COMPLEX SOLUTIONS.
DESCRIBE QUALITATIVELY THE FUNCTIONAL RELATIONSHIP BETWEEN TWO QUANTITIES BY ANALYZING A GRAPH.
IDENTIFY THE EFFECT ON THE GRAPH OF REPLACING F(X) BY F(X) + K, K F(X), F(KX), AND F(X + K) FOR SPECIFIC VALUES OF K (BOTH POSITIVE AND NEGATIVE); FIND THE VALUE OF K GIVEN THE GRAPHS.
GRAPH FUNCTIONS EXPRESSED SYMBOLICALLY AND SHOW KEY FEATURES OF THE GRAPH, BY HAND IN SIMPLE CASES AND USING TECHNOLOGY FOR MORE COMPLICATED CASES.
- M.TMS.32.a Graph linear and quadratic functions and show intercepts, maxima, and minima.
- M.TMS.32.b Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
OBSERVE USING GRAPHS AND TABLES THAT A QUANTITY INCREASING EXPONENTIALLY EVENTUALLY EXCEEDS A QUANTITY INCREASINGLY LINEARLY, QUADRATICALLY, OR (MORE GENERALLY) AS A POLYNOMIAL FUNCTION.
WRITE A FUNCTION DEFINED BY AN EXPRESSION IN DIFFERENT BUT EQUIVALENT FORMS TO REVEAL AND EXPLAIN DIFFERENT PROPERTIES OF THE FUNCTION. USE THE PROCESS OF FACTORING AND COMPLETING THE SQUARE IN A QUADRATIC FUNCTION TO SHOW ZEROS, EXTREME VALUES, AND SYMMETRY OF THE GRAPH, AND INTERPRET THESE IN TERMS OF A CONTEXT.
COMPARE PROPERTIES OF TWO FUNCTIONS EACH REPRESENTED IN A DIFFERENT WAY (ALGEBRAICALLY, GRAPHICALLY, NUMERICALLY IN TABLES, OR BY VERBAL DESCRIPTIONS).
CONSTRUCT LINEAR AND EXPONENTIAL FUNCTIONS, INCLUDING ARITHMETIC AND GEOMETRIC SEQUENCES, GIVEN A GRAPH, A DESCRIPTION OF A RELATIONSHIP, OR TWO INPUT-OUTPUT PAIRS (INCLUDE READING THESE FROM A TABLE).
WRITE A FUNCTION THAT DESCRIBES A RELATIONSHIP BETWEEN TWO QUANTITIES.
- M.TMS.37.a Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.
- M.TMS.37.b Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.