Statistics

• How to show the distribution, the central tendencies, and the variation within a data set. 

• Bivariate data analysis both by hand and with the calculator.

Rational Expressions

• Rewrite simple rational expressions in different forms; write a(x)/b(x) in forms q(x) + r(x)/b(x), where a9x), b(x), q(x) and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using long division.

• Identify the effect on replacing f(x) by f(x) + k, kf(x), and f(x + k) for specific values of k (both positive and

• negative). Experiment with cases and illustrate an explanation of the effects on the graph using technology.

• Rewrite simple rational expressions in different forms; write a(x)/b(x) in forms q(x) + r(x)/b(x), where a9x), b(x), q(x) and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, or the for the more complicated example, a computer algebra system.

• Understand that rational expressions form a system analogous to the rational numbers, closed under multiplications, and division by a nonzero rational expression; multiply, and divide rational expressions.

Geometric Measurement and Dimension 

• Explain volume formulas and use them to solve problems 

• Visualize relationships between two-dimensional and three-dimensional objects

Quadratics 

• Introduce quadratic polynomials  shifting basic parabolas into vertex form.

• Completing the square

• Finding the zeroes of a quadratic function

• 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. Experiment with cases and illustrate an explanation of the effects on the graph using technology

• Use the structure of an expression to identify ways to rewrite it.

•  Understand the inverse relationship between exponents and logarithms. For exponential models, express as a logarithm the solution to abet = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology

Expressing Geometric Properties with Equations

• Translate between the geometric description and the equation for a conic section

• Use coordinates to prove simple geometric theorems algebraically

Polynomials 

Adding, multiplying, and factoring polynomials

Exponential and logarithmic functions

Graph exponential and logarithmic functions, showing intercepts and end behavior.

Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or decay.

Circles

• Understand and apply theorems

• Find arc lengths and areas of sectors of circles

Exponents 

Exponent rules and the development of negative and zero exponents.  

Develop the concepts of exponential growth and decay (from a fraction perspective). 

Geometric sequences

Radicals 

Solve simple radical equations in one variable, and give examples showing how extraneous solutions may arise.

Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

Solve an equation of the form f(x) = c for a simple function that has an inverse and write an expression for the inverse.

Similarity, Right Triangles, and Trigonometry

• Understand similarity in terms of similarity

transformations

• Prove theorems involving similarity

• Define trigonometric ratios and solve

problems involving right triangles

• Apply trigonometry to general triangles

Systems of Linear Equations and Inequalities

Graphical, substitution, elimination methods for solving systems of equations and inequalities

Radicals 

Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Graph square root, cube root, and piecewise-defined functions and absolute value functions.

Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x) ... f(x+k) for specific values of k (both positive and negative); ... Experiment with cases and illustrate an explanation on the effects on the graph using technology.

Congruence

• Experiment with transformations in the plane

• Understand congruence in terms of rigid

motions

• Prove geometric theorems

• Make geometric constructions