Mississippi State Standards for Mathematics: Grade 11

MS.G. Geometry

G.1. Number and Operations: Compute and determine the reasonableness of a result in mathematical and real-world situations with and without technology.

1.a. Apply problem-solving skills to solve and verify the solutions for unknown measures in similar polygons. (DOK 2)

1.b. Given exact irrational solutions, determine the best rational estimation. (DOK 2)

1.c. Solve real-world or application problems that involve square roots and the Pythagorean Theorem. (DOK 3)

G.2. Algebra: Understand relations, functions, and patterns. Analyze change using various geometric properties.

2.a. Represent data from geometric and real-world contexts with expressions, formulas, tables, charts, graphs, relations, and functions. (DOK 2)

2.b. Recognize and write the equation of a circle in standard form (x-h)2 + (y-k)2 = r2 and identify the center and radius. (DOK 2)

2.c. Use slope to analyze and write equations for parallel and perpendicular lines. (DOK 2)

2.d. Apply the Midpoint and Distance Formulas to solve application problems involving the coordinate plane. (DOK 2)

2.e. Determine the effects of rigid (translations, rotations, and reflections) and non-rigid (dilations) motions and compositions when performed on objects on the coordinate plane. (DOK 2)

G.3. Geometry: Investigate, apply, and prove properties and theorems from postulates and definitions related to angles, lines, circles, polygons, and two- and three-dimensional figures. Explore applications of patterns and transformational geometry.

3.a. Use inductive reasoning to make conjectures and deductive reasoning to make valid conclusions. (DOK 3)

3.b. Develop and evaluate mathematical arguments and proofs to include paragraph, two-column, and flow chart forms. (DOK 3)

3.c. Identify, classify, and apply angle relationships formed by parallel lines cut by transversals. (DOK 2)

3.d. Use the properties of altitudes, medians, angle bisectors, and perpendicular bisectors of triangles to solve problems. (DOK 2)

3.e. Classify triangles and apply postulates and theorems to test for triangle inequality, congruence, and similarity. (DOK 2)

3.f. Determine and justify if a given shape could be tessellated. (DOK 2)

3.g. Describe and draw cross-sections of prisms, cylinders, pyramids, and cones. (DOK 1)

3.h. Graph a vector and determine the magnitude and direction of a given vector. (DOK 2)

3.i. Given the pre-image or image, find figures obtained by applying reflections, translations, rotations, and dilations; describe and justify the method used. (DOK 2)

G.4. Measurement: Select and apply various strategies, tools, and formulas to calculate length, surface area, volume, and angle measurements.

4.a. Use the properties of circles using arc, angle, and segment relationships to find missing measures. (DOK 2)

4.b. Solve real-world applications and mathematical problems to find missing measurements in right triangles by applying special right triangle relationships, geometric means, or trigonometric functions. (DOK 2)

4.c. Solve real-world and mathematical problems involving the lateral area, surface area and volume of three-dimensional figures, including prisms, cylinders, cones, pyramids, and spheres. (DOK 2)

4.d. Explain and use the properties of 45-45-90 and 30-60-90 triangles. (DOK 2)

4.e. Apply the relationships of sine, cosine, and tangent to problems involving right triangles. (DOK 2)

G.5. Data Analysis and Probability: Represent, analyze, and make inferences based on data with and without the use of technology.

5.a. Apply multiple strategies and representations, including area models, to solve probability problems. (DOK 2)

MS.AII. Algebra II

AII.1. Number and Operations: Understand relationships among numbers and compute fluently. Verify with technology.

1.d. Perform computations, including addition, scalar multiplication, multiplication, determinants, and inverses on matrices. (DOK 1)

1.e. Solve applications and problems in mathematical settings involving arithmetic and geometric sequences and series. (DOK 3)

1.f. Explain and use the inverse relationship between exponential and logarithmic expressions. (DOK 2)

1.g. Use the properties of logarithms to simplify logarithmic expressions and to find their approximate values. (DOK 1)

1.h. Solve application problems involving exponential functions related to growth and decay. (DOK 3)

AII.2. Algebra: Use algebraic concepts to identify patterns, use multiple representations of relations and functions, and apply operations to expressions, equations, and inequalities.

2.f. Factor sums and differences of cubes and factor polynomials by grouping. (DOK 2)

2.g. Solve radical equations. (DOK 2)

2.h. Write equivalent forms of rational expressions using real and complex conjugates. (DOK 2)

2.i. Solve equations involving rational expressions and verify solutions. (DOK 2)

2.j. Explain the results of compositions of functions. (DOK 2)

2.k. Explain the Binomial Theorem and use it to expand binomial expressions raised to positive integral powers. (DOK 2)

2.l. Interpret the zeros and maximum or minimum value(s) of quadratic functions. (DOK 2)

AII.3. Geometry: Use coordinate geometry to specify locations, describe relationships, and apply transformations to analyze algebraic relationships.

AII.4. Measurement: Understand measurable attributes of objects and apply appropriate techniques and formulas to determine measurements.

AII.5. Data Analysis and Probability: Use technology to represent, analyze, and make inferences based on data.

5.b. Solve simple combinations. (DOK 2)

5.c. Model a data set using the median-fit-method with a linear equation and make predictions based on the model and the equation. (DOK 3)

5.d. Identify the difference between permutations and combinations and use them to solve real-world problems. (DOK 2)

MS.AA. Advanced Algebra

AA.1. Number and Operations: Understand and perform computations with different representations of numbers.

AA.2. Algebra: Use algebraic concepts to identify patterns and use multiple representations of relations and functions. Apply operations to expressions and equations.

AA.3. Geometry: Recognize, analyze, and graph conic sections.

AA.4. Data Analysis and Probability: Apply simple probability and curve fitting to data.

MS.T. Trigonometry

T.1. Number and Operations: Represent and compare numbers in various forms and perform operations.

T.2. Number and Operations: Investigate basic concepts of vectors and operations with vectors.

T.3. Algebra: Compare and produce equivalent forms of trigonometric expressions and solve trigonometric equations.

T.4. Geometry: Use geometric modeling to analyze trigonometric relationships.

4.f. Use the graph of polar coordinates and associated equations to model real-world applications and mathematical situations. (DOK 2)

T.5. Measurement: Select and apply formulas to determine length and area.

MS.PC. Pre-Calculus

PC.1. Number and Operations: Explore and illustrate the characteristics and operations connecting sequences and series.

PC.2. Algebra: Analyze, manipulate, and solve equations and inequalities.

PC.3. Geometry: Recognize, sketch, and transform graphs of functions.

PC.4. Data Analysis and Probability: Adapt curves to data.

PC.5. Explore and apply fundamental principles of probability.

MS.DM. Discrete Mathematics

DM.1. Number and Operations: Explore relationships among number systems.

DM.2. Algebra: Use algebraic methods to represent simple and complex relationships among statements. Use models to represent patterns and operations.

DM.3. Geometry: Use geometric models to describe and analyze mathematical relationships, establish the validity of conjectures, and determine solutions to real applications.

3.j. Determine the number of walks between two vertices using powers of the adjacency matrix. (DOK 2)

3.k. Explain why a graph is a tree. (DOK 2)

3.l. Determine the level, parent, siblings, ancestors, descendants and height of a rooted tree. (DOK 1)

3.m. Determine the shortest route in a spanning tree. (DOK 2)

DM.4. Data Analysis and Probability: Investigate and explain strategies for solving simple games.

MS.C. Calculus

C.1. Number and Operations: Compute and determine the reasonableness of results in mathematical and real world situations.

C.2. Algebra: Demonstrate basic knowledge of functions, including their behavior and characteristics.

C.3. Algebra: Evaluate limits and communicate an understanding of the limiting process.

C.4. Algebra: Use the definition and formal rules of differentiation to compute derivatives.

C.5. Algebra: Apply derivatives to find solutions in a variety of situations.

5.e. Model rates of change to solve related rate problems. (DOK 2)

5.f. Solve optimization problems. (DOK 2)

C.6. Algebra: Employ various integration properties and techniques to evaluate integrals.

6.a. State and apply the First and Second Fundamental Theorem of Calculus. (DOK 2)

6.b. Apply the power rule and u-substitution to evaluate indefinite integrals. (DOK 2)

C.7. Geometry: Use geometric concepts to gain insights into, answer questions about, and graph various implications of differentiation.

7.a. Demonstrate and explain the differences between average and instantaneous rates of change. (DOK 2)

7.b. Apply differentiation techniques to curve sketching. (DOK 2)

7.c. Apply Rolle's Theorem and the Mean Value Theorem and their geometric consequences. (DOK 2)

7.d. Identify and apply local linear approximations. (DOK 1)

7.e. Analyze curves with attention to non-decreasing functions (monotonicity) and concavity. (DOK 2)

C.8. Measurement: Adapt integration methods to model situations to problems.

8.a. Apply integration to solve problems of area. (DOK 2)

8.b. Utilize integrals to model and find solutions to real-world problems such as calculating displacement and total distance traveled. (DOK 2)

C.9. Measurement: Apply appropriate techniques, tools, and formulas to determine values for the definite integral.

9.a. Interpret the concept of definite integral as a limit of Riemann sums over equal subdivisions. (DOK 3)

MS.S. Statistics

S.1. Number and Operations: Explore phenomena using probability and simulation. Compute appropriate statistical and probabilistic measures.

1.i. Apply the concept of a random variable to generate and interpret probability distributions. (DOK 2)

S.2. Algebra: Analyze one and two variable data using algebraic concepts and methods.

S.3. Geometry: Design an appropriate form of displaying data collected, whether in tabular or graphic form.

S.4. Data Analysis and Probability: Collect, read, interpret, and analyze data as it relates to the real world.

S.5. Data Analysis and Probability: Design a study by clarifying a question and deciding upon a method of data collection and analysis.

MS.SMT. Survey of Mathematical Topics

SMT.1. Number and Operations: Compute, analyze, and develop a variety of skills necessary to manage personal and business finance to include aspects of employer-employee decision making and consumer credit.

1.j. Identify and evaluate modes of transportation. (DOK 2)

1.k. Identify and explain the components and processes involved in the stock market and apply them to real world applications. (DOK 2)

SMT.2. Algebra: Identify and apply the practices that affect employer and employee decision-making.

SMT.3. Algebra: Demonstrate an understanding of the impact of consumer credit.

SMT.4. Data Analysis and Probability: Collect and apply information for planning a trip.

MS.IE. Introduction to Engineering

IE.1. Number and Operations: Compute unit conversions and illustrate graphical interpretations.

IE.2. Algebra: Apply algebraic equations and functions to engineering situations.

IE.3. Geometry: Apply geometric principles to engineering situations.

IE.4. Measurement: Apply fundamental concepts of measurement such as time, distance, area, and volume with principles of engineering in a variety of contexts. Note: This is a projects-based course. The teaching strategies to accompany the following three items are an integral part of the course.

IE.5. Data Analysis and Probability: Interpret charts, graphs, and other data obtained from actual or hypothetical engineering events and situations.