| NUMBER SENSE - Grade 11/12 | |
| 1 Students understand the use of matrices to organize information and perform simple operations. | |
| 1.1 Students use matrices to represent and organize data and identify and interpret the meaning of a matrix cell for a given context | |
| 1.2 Students perform and interpret the meaning of matrix addition, subtraction, multiplication, scalar multiplication and the inverse and determinant in simple cases | |
| 1.3 Students use matrices to represent and solve systems of two linear equations in two variables or three linear equations in three variables | |
| 1.4 Students use matrices to translate, reflect, rotate, or scale polygonal figures represented on the coordinate plane | |
| GEOMETRY - Grade 11/12 | |
| 1 Students identify, give information about, and write equations for circles, parabolas, ellipses, and hyperbolas. ( | |
| 1.1 Students determine the center and radius of a circle, the center, vertices, foci, and axes of an ellipse or hyperbola, and the vertex, axis of symmetry, focus, and directrix of a parabola given an equation in standard form and use this information to sketch a graph the figure | |
| 1.2 Students identify a general quadratic equation in two variables (no xy term) as a circle, a parabola, an ellipse, or an hyperbola, and write these equations in standard form given information about the figures | |
| 1.3 Students express translations and rotations of conic sections through corresponding changes to their equations | |
| 2 Students use periodic functions and trigonometric relationships in geometric applications. | |
| 2.1 Students use similarity, right triangles, the Law of Sines, and the Law of Cosines to determine measurements of objects which are difficult to measure directly | |
| SYMBOLS AND ALGEBRA - Grade 11/12 | |
| 1 Students perform operations with vectors in the coordinate plane and solve practical problems using vectors. | |
| 1.1 Students add, subtract, find scalar products, dot products, and norms of vectors noting the field properties which apply | |
| 1.2 Students determine, interpret, and use a unit directional vector, perpendicular components, and norms to express vectors in the coordinate plane | |
| 1.3 Students graph and interpret complex numbers as vectors and in polar form | |
| 1.4 Students graph polar equations (e.g., roses, lemniscates), analyze the results of parameter changes on the graphs, and classify the equations according to their graph | |
| FUNCTIONS - Grade 11/12 | |
| 1 Students investigate periodic behavior, identify the characteristics of, and graph trigonometric functions. | |
| 1.1 Students understand and explain the relationship between triangle trigonometry and the unit circle/wrapping function approach to trigonometry | |
| 1.2 Students find the exact values of the trigonometric functions of multiples of 30 degrees (pi/6) and 45 degrees (pi/4) and their related angles as found in the unit circle, including converting radians to degrees and vice versa | |
| 1.3 Students given the value of one trigonometric function, find the values of other trigonometric functions | |
| 1.4 Students solve trigonometric equations that include both infinite solutions and restricted domain solutions and solve basic trigonometric inequalities | |
| 1.5 Students make substitutions using the basic trigonometric identities | Trigonometric identities, including addition, double angle, and half-angle formulas |
| 1.6 Students identify key characteristics (e.g., domain, range, amplitude, period, phase shift, and vertical shift) of and graph trigonometric functions and their inverse | |
| 1.7 Students analyze and solve problems involving periodic phenomena | e.g., theoretically perfect biological rhythms, sound waves, and tidal variations |
| 1.8 Students apply transformations to the graph of a trigonometric functions, predict and analyze the results on the graph of the function | |
| 2 Students investigate, identify the characteristics of, and graph polynomial and rational functions. | |
| 2.1 Students determine the zeros, y-intercepts, end behavior, relative maximum and minimum points, and symmetry of polynomial functions and graph them | |
| 2.2 Students determine the zeros, asymptotes, y-intercepts, end behavior, relative maximum and minimum points, symmetry of rational functions and graph them | |
| 2.3 Students determine the intervals where a polynomial function is increasing or decreasing | |
| 2.4 Students given the graph of a function, graph its reciprocal | |
| 2.5 Students analyze and explain the reasons behind the effect changing coefficients, exponents, and other parameters has on functions and their graphs | |
| 3 Students use graphs to represent and describe continuity of functions | |
| 3.1 Students graph and analyze step and piecewise defined functions | |
| 3.2 Students define and apply the properties of limits of functions including infinite sequences, series, and areas under curves | |
| STATISTICS, DATA ANALYSIS, AND PROBABILITY - Grade 11/12 | |
| 1 Students demonstrate an understanding of experimental and theoretical probability in more complex situations. | |
| 1.1 Students compute theoretical probability of compound, complementary, independent, and dependent events | |
| 1.2 Students judge the validity of simulations to estimate probabilities of events | |
| 1.3 Students describe the features of the normal curve and use it to compute percentiles and cumulative probabilities | |
| 1.4 Students use the Central Limit Theorem and confidence intervals in the formation of conclusions based on sample data and justify conclusions reached | |
| MATHEMATICAL REASONING - Grade 11/12 | |
| 1 Students will relate properties of real numbers to functions and matrices and use deductive and inductive logic | |
| 1.1 Students derive and prove standard algebraic formulas | Derive the general form of a circle |
| 1.2 Students apply and explain the method of mathematical induction |
Prove a formula for the sum of the first n consecutive even integers. Prove a formula for n consecutive squares beginning with 16. |
| 1.3 Students use direct and recursive methods to prove and derive formulas and statements | Prove the binomial theorem and De Moivre's theorem |
| 1.4 Students use properties from number systems to justify steps in combining and simplifying functions and matrices | |
| 1.5 Students prove basic trigonometric identities and make substitutions using the basic identities | Trigonometric identities including addition, double angle, and half-angle formulas |