Student “I Can Statements” for Math Standards Pre-calculus I can statement Standard # met I can determine if an equation defines a function by determining if it can be solved for y, and if each x value determines a unique y value. I can determine the (implied) domain for a given function. I can determine a reasonable domain for a function describing a “real life” problem. I can evaluate a given function, obtaining a numerical or algebraic result. Understand the definition of a function and be able to use functional notation, evaluate a function, and determine its domain. I can find a maximum or minimum value of a function on a closed interval from graphical information. I can find the zero of a function on a given interval using graphical information. Obtain information and draw conclusions from graphs of functions and other relations. I can complete the square to write a quadratic function in the form Use various forms for quadratic functions to identify vertex, line of symmetry, and intercepts. Be able to graph a quadratic, and produce an equation from a given graph. f ( x) a x h k given a more general form of the function. 2 I can identify the vertex and axis of symmetry by utilizing the information found in the form given in target #1, or by using the formula for the xcoordinate of the vertex, x b . 2a I can solve a quadratic equation to determine the intercepts for the graph of a given quadratic function. I can use the form given in target #1 to write the equation of a quadratic function, given its graph. I can sketch the graph of a given quadratic equation, and identify the vertex, axis of symmetry, and intercepts for the graph of the function. I can identify a right triangle from a diagram or when given sides a, b, and c. I can identify the legs and hypotenuse of a right triangle. I can solve a2 + b2 = c2 for a missing value. I can recognize common Pythagorean triples. Apply the Pythagorean Theorem and its converse to solve problems and logically justify results. Identify intercepts, zeros, maxima, minima, and intervals of increase and decrease from the graph of a function. I can determine the objects defined in the given essential outcome by examining the graph of a given function. I can identify a vertical translation, horizontal translation, or reflection over the x or y-axis for a given function based on its equation, and I can rewrite the equation for a given function using given transformations. I can sketch a graph for a translated function with or without the use of a graphing utility. I can sketch a graph for any of the functions stated in essential outcome #6 with or without the use of a graphing utility. Sketch the graphs of common non linear functions (parent functions), such as square roots, absolute value, and quadratic functions. I can add, subtract, and multiply given polynomials and recognize the degree of the result. I can divide polynomials using long division, or synthetic division if appropriate. I can express the quotient for a division of polynomials. Perform basic algebraic operations with polynomial functions, including division and synthetic division. Determine how translations affect the symbolic and graphical forms of a function, and use graphing technology to examine translations. I can rewrite the result of a polynomial division using the form: P( x) D( x)Q( x) R( x) or as a polynomial with a rational function remainder. I can add, subtract, multiply and divide complex numbers and express the results in standard form. I can solve a quadratic equation that has non-real solutions. I can use radian and/or degree measure to represent angles. I can evaluate trig function using the unit circle. I can use domain and period to evaluate sine and cosine functions. I can apply the formula for arc length (s = r ), and use the concepts of linear and angular speed to solve applied problems. Find complex solutions to quadratic equations, and perform algebraic operations with complex numbers. Translate problem statements into mathematical models (equations and inequalities) including quadratics and solve the problems using appropriate methods. Develop skills with graphing calculator operations including producing a graph in a given window, find function values graphically (tracing) or numerically (use a table), solve an equation numerically or graphically. Define and use the properties of the unit circle. I can use reference angles to evaluate trig functions. I can use trigonometric functions to model and solve real-life problems. I can use a calculator to evaluate trig functions, including the reciprocal functions vis-à-vis the inverse functions. I can graph sine and cosine utilizing the properties of amplitude, period, horizontal and vertical shift. I can find the sum of n terms of an arithmetic or geometric series, and can determine the sum of a convergent infinite geometric series. I can solve applied problems involving sequences and series. I can prove summation formulas using the Principle of Mathematical Induction. I can expand binomials using the Binomial Theorem I can use factorial notation to calculate binomial coefficients, and apply counting principles, including permutations and combinations. Find values of all trig functions, their reciprocals and inverse functions. Apply properties of sequences and series, especially arithmetic and geometric sequences.

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# Precalculus