Oklahoma State Standards for Mathematics: Grade 12

OK.AI. Algebra I

AI.1. Number Sense and Algebraic Operations - The student will use expressions and equations to model number relationships.

AI.1.1. Equations and Formulas

AI.1.1.a. Translate word phrases and sentences into expressions and equations and vice versa.

AI.1.1.b. Solve literal equations involving several variables for one variable in terms of the others.

AI.1.1.c. Use the formulas from measurable attributes of geometric models (perimeter, circumference, area and volume), science, and statistics to solve problems within an algebraic context.

AI.1.1.d. Solve two-step and three-step problems using concepts such as rules of exponents, rate, distance, ratio and proportion, and percent.

AI.1.2. Expressions

AI.1.2.a. Simplify and evaluate linear, absolute value, rational and radical expressions.

AI.1.2.b. Simplify polynomials by adding, subtracting or multiplying.

AI.1.2.c. Factor polynomial expressions.

AI.2. Relations and Functions - The student will use relations and functions to model number relationships.

AI.2.1. Relations and Functions

AI.2.1.a. Distinguish between linear and nonlinear data.

AI.2.1.b. Distinguish between relations and functions.

AI.2.1.c. Identify dependent and independent variables, domain and range.

AI.2.1.d. Evaluate a function using tables, equations or graphs.

AI.2.2. Linear Equations and Graphs

AI.2.2.a. Solve linear equations by graphing or using properties of equality.

AI.2.2.b. Recognize the parent graph of the functions y = k, y = x, y = |x|, and predict the effects of transformations on the parent graph.

AI.2.2.c. Slope

AI.2.2.d. Develop the equation of a line and graph linear relationships given the following: slope and y-intercept, slope and one point on the line, two points on the line, x-intercept and y-intercept, a set of data points.

AI.2.2.e. Match equations to a graph, table, or situation and vice versa.

AI.2.3. Linear Inequalities and Graphs

AI.2.3.a. Solve linear inequalities by graphing or using properties of inequalities.

AI.2.3.b. Match inequalities (with 1 or 2 variables) to a graph, table, or situation and vice versa.

AI.2.4. Solve a system of linear equations by graphing, substitution or elimination.

AI.2.5. Nonlinear Functions

AI.2.5.a. Match exponential and quadratic functions to a table, graph or situation and vice versa.

AI.2.5.b. Solve quadratic equations by graphing, factoring, or using the quadratic formula.

AI.3. Data Analysis, Probability and Statistics - The student will use data analysis, probability and statistics to formulate and justify predictions from a set of data.

AI.3.1. Data Analysis

AI.3.1.a. Translate from one representation of data to another and understand that the data can be represented using a variety of tables, graphs, or symbols and that different modes of representation often convey different messages.

AI.3.1.b. Make valid inferences, predictions, and/or arguments based on data from graphs, tables, and charts.

AI.3.1.c. Solve two-step and three-step problems using concepts such as probability and measures of central tendency.

AI.3.2. Collect data involving two variables and display on a scatter plot; interpret results using a linear model/equation and identify whether the model/equation is a line best fit for the data.

OK.G. Geometry

G.1. Logical Reasoning - The student will use deductive and inductive reasoning to solve problems.

G.1.1. Identify and use logical reasoning skills (inductive and deductive) to make and test conjectures, formulate counter examples, and follow logical arguments.

G.1.2. State, use, and examine the validity of the converse, inverse, and contrapositive of ''if-then'' statements.

G.1.3. Compare the properties of Euclidean geometry to non-Euclidean geometries (for example, elliptical geometry, as shown on the surface of a globe, does not uphold the parallel postulate).

G.2. Properties of 2-Dimensional Figures - The student will use the properties and formulas of geometric figures to solve problems.

G.2.1. Use geometric tools (for example, protractor, compass, straight edge) to construct a variety of figures.

G.2.2. Line and Angle Relationships

G.2.2.a. Use the angle relationships formed by parallel lines cut by a transversal to solve problems.

G.2.2.b. Use the angle relationships formed by two lines cut by a transversal to determine if the two lines are parallel and verify, using algebraic and deductive proofs.

G.2.2.c. Use relationships between pairs of angles (for example, adjacent, complementary, vertical) to solve problems.

G.2.3. Polygons and Other Plane Figures

G.2.3.a. Identify, describe, and analyze polygons (for example, convex, concave, regular, pentagonal, hexagonal, n-gonal).

G.2.3.b. Apply the interior and exterior angle sum of convex polygons to solve problems, and verify using algebraic and deductive proofs.

G.2.3.c. Develop and apply the properties of quadrilaterals to solve problems (for example, rectangles, parallelograms, rhombi, trapezoids, kites).

G.2.3.d. Use properties of 2-dimensional figures and side length, perimeter or circumference, and area to determine unknown values and correctly identify the appropriate unit of measure of each.

G.2.4. Similarity

G.2.4.a. Determine and verify the relationships of similarity of triangles, using algebraic and deductive proofs.

G.2.4.b. Use ratios of similar 2-dimensional figures to determine unknown values, such as angles, side lengths, perimeter or circumference, and area.

G.2.5. Congruence

G.2.5.a. Determine and verify the relationships of congruency of triangles, using algebraic and deductive proofs.

G.2.5.b. Use the relationships of congruency of 2-dimensional figures to determine unknown values, such as angles, side lengths, perimeter or circumference, and area.

G.2.6. Circles

G.2.6.a. Find angle measures and arc measures related to circles.

G.2.6.b. Find angle measures and segment lengths using the relationships among radii, chords, secants, and tangents of a circle.

G.3. Triangles and Trigonometric Ratios - The student will use the properties of right triangles and trigonometric ratios to solve problems.

G.3.1. Use the Pythagorean Theorem and its converse to find missing side lengths and to determine acute, right, and obtuse triangles, and verify using algebraic and deductive proofs.

G.3.2. Apply the 45-45-90 and 30-60-90 right triangle relationships to solve problems, and verify using algebraic and deductive proofs.

G.3.3. Express the trigonometric functions as ratios and use sine, cosine, and tangent ratios to solve real-world problems.

G.3.4. Use the trigonometric ratios to find the area of a triangle.

G.4. Properties of 3-Dimensional Figures - The student will use the properties and formulas of geometric figures to solve problems.

G.4.1. Polyhedra and Other Solids

G.4.1.a. Identify, describe, and analyze polyhedra (for example, regular, decahedral).

G.4.1.b. Use properties of 3-dimensional figures; side lengths, perimeter or circumference, and area of a face; and volume, lateral area, and surface area to determine unknown values and correctly identify the appropriate unit of measure of each.

G.4.2. Similarity: Use ratios of similar 3-dimensional figures to determine unknown values, such as angles, side lengths, perimeter or circumference of a face, area of a face, and volume.

G.4.3. Create a model of a 3-dimensional figure from a 2-dimensional drawing and make a 2-dimensional representation of a 3-dimensional object (for example, nets, blueprints, perspective drawings).

G.5. Coordinate Geometry - The student will solve problems with geometric figures in the coordinate plane.

G.5.1. Find the distance between two points; the midpoint of a segment; and calculate the slopes of parallel, perpendicular, horizontal, and vertical lines.

G.5.2. Properties of Figures

G.5.2.a. Given a set of points determine the type of figure formed based on its properties.

G.5.2.b. Use transformations (reflection, rotation, translation) on geometric figures to solve problems within coordinate geometry.

OK.AII. Algebra II

AII.1. Number Systems and Algebraic Operations - The student will perform operations with rational, radical, and polynomial expressions, as well as expressions involving complex numbers.

AII.1.1. Rational Exponents

AII.1.1.a. Convert expressions from radical notations to rational exponents and vice versa.

AII.1.1.b. Add, subtract, multiply, divide, and simplify radical expressions and expressions containing rational exponents.

AII.1.2. Polynomial and Rational Expressions

AII.1.2.a. Divide polynomial expressions by lower degree polynomials.

AII.1.2.b. Add, subtract, multiply, divide, and simplify rational expressions, including complex fractions.

AII.1.3. Complex Numbers

AII.1.3.a. Recognize that to solve certain problems and equations, number systems need to be extended from real numbers to complex numbers.

AII.1.3.b. Add, subtract, multiply, divide, and simplify expressions involving complex numbers.

AII.2. Relations and Functions - The student will use the relationships among the solution of an equation, zero of a function, x-intercepts of a graph, and factors of a polynomial expression to solve problems involving relations and functions.

AII.2.1. Functions and Function Notation

AII.2.1.a. Recognize the parent graphs of polynomial, exponential, radical, quadratic, and logarithmic functions and predict the effects of transformations on the parent graphs, using various methods and tools which may include graphing calculators.

AII.2.1.b. Add, subtract, multiply, and divide functions using function notation.

AII.2.1.c. Combine functions by composition.

AII.2.1.d. Use algebraic, interval, and set notations to specify the domain and range of functions of various types.

AII.2.1.e. Find and graph the inverse of a function, if it exists.

AII.2.2. Systems of Equations

AII.2.2.a. Model a situation that can be described by a system of equations or inequalities and use the model to answer questions about the situation.

AII.2.2.b. Solve systems of linear equations and inequalities using various methods and tools which may include substitution, elimination, matrices, graphing, and graphing calculators.

AII.2.2.c. Use either one quadratic equation and one linear equation or two quadratic equations to solve problems.

AII.2.3. Quadratic Equations and Functions

AII.2.3.a. Solve quadratic equations by graphing, factoring, completing the square and quadratic formula.

AII.2.3.b. Graph a quadratic function and identify the x- and y-intercepts and maximum or minimum value, using various methods and tools which may include a graphing calculator.

AII.2.3.c. Model a situation that can be described by a quadratic function and use the model to answer questions about the situation.

AII.2.4. Identify, graph, and write the equations of the conic sections (circle, ellipse, parabola, and hyperbola).

AII.2.5. Exponential and Logarithmic Functions

AII.2.5.a. Graph exponential and logarithmic functions.

AII.2.5.b. Apply the inverse relationship between exponential and logarithmic functions to convert from one form to another.

AII.2.5.c. Model a situation that can be described by an exponential or logarithmic function and use the model to answer questions about the situation.

AII.2.6. Polynomial Equations and Functions

AII.2.6.a. Solve polynomial equations using various methods and tools which may include factoring and synthetic division.

AII.2.6.b. Sketch the graph of a polynomial function.

AII.2.6.c. Given the graph of a polynomial function, identify the x- and y-intercepts, relative maximums and relative minimums, using various methods and tools which may include a graphing calculator.

AII.2.6.d. Model a situation that can be described by a polynomial function and use the model to answer questions about the situation.

AII.2.7. Rational Equations and Functions

AII.2.7.a. Solve rational equations.

AII.2.7.b. Sketch the graph of a rational function.

AII.2.7.c. Given the graph of a rational function, identify the x- and y-intercepts, vertical asymptotes, using various methods and tools which may include a graphing calculator.

AII.2.7.d. Model a situation that can be described by a rational function and use the model to answer questions about the situation.

AII.3. Data Analysis and Statistics - The student will use data analysis and statistics to formulate and justify predictions from a set of data.

AII.3.1. Analysis of Collected Data Involving Two Variables

AII.3.1.a. Interpret data on a scatter plot using a linear, exponential, or quadratic model/equation.

AII.3.1.b. Identify whether the model/equation is a curve of best fit for the data, using various methods and tools which may include a graphing calculator.

AII.3.2. Measures of Central Tendency and Variability

AII.3.2.a. Analyze and synthesize data from a sample using appropriate measures of central tendency (mean, median, mode, weighted average).

AII.3.2.b. Analyze and synthesize data from a sample using appropriate measures of variability (range, variance, standard deviation).

AII.3.2.c. Use the characteristics of the Gaussian normal distribution (bell-shaped curve) to solve problems.

AII.3.2.d. Identify how given outliers affect representations of data.

AII.3.3. Identify and use arithmetic and geometric sequences and series to solve problems.

OK.PS.1. Problem Solving

PS1.1. Apply a wide variety of problem-solving strategies (identify a pattern, use equivalent representations) to solve problems from within and outside mathematics.

PS1.2. Identify the problem from a described situation, determine the necessary data and apply appropriate problem-solving strategies.

OK.PS.2. Communication

PS2.1. Use mathematical language and symbols to read and write mathematics and to converse with others.

PS2.2. Demonstrate mathematical ideas orally and in writing.

PS2.3. Analyze mathematical definitions and discover generalizations through investigations.

OK.PS.3. Reasoning

PS3.1. Use various types of logical reasoning in mathematical contexts and real-world situations.

PS3.2. Prepare and evaluate suppositions and arguments.

PS3.3. Verify conclusions, identify counterexamples, test conjectures, and justify solutions to mathematical problems.

PS3.4. Justify mathematical statements through proofs.

OK.PS.4. Connections

PS4.1. Link mathematical ideas to the real world (e.g., statistics helps qualify the confidence we can have when drawing conclusions based on a sample).

PS4.2. Apply mathematical problem-solving skills to other disciplines.

PS4.3. Use mathematics to solve problems encountered in daily life.

PS4.4. Relate one area of mathematics to another and to the integrated whole (e.g., connect equivalent representations to corresponding problem situations or mathematical concepts).

OK.PS.5. Representation

PS5.1. Use algebraic, graphic, and numeric representations to model and interpret mathematical and real world situations.

PS5.2. Use a variety of mathematical representations as tools for organizing, recording, and communicating mathematical ideas (e.g., mathematical models, tables, graphs, spreadsheets).

PS5.3. Develop a variety of mathematical representations that can be used flexibly and appropriately.