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Mrs. L. Mullane



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Pre Cal 11

   The following is a list of outcomes you need to know for Pre-Calculus 11


 

CONCEPT

I have no idea what it is!

I need some help with this.

Yes!

I know this!

Chapter 1  Sequences and Series

I can Identify the assumption(s) made when defining an arithmetic sequence or series.

 

 

 

I can provide and justify an example of an arithmetic sequence.

 

 

 

I can come up with an equation for determining the general term of an arithmetic sequence.

 

 

 

I can describe the relationship between arithmetic sequences and linear functions.

 

 

 

I can determine t1, d, n, or tn in a problem that involves an arithmetic sequence.

 

 

 

I can come up with the equation for determining the sum of n terms of an arithmetic series

 

 

 

I can determine t1, d, n,, or Sn in a problem that involves an arithmetic series.

 

 

 

I can solve word problems that involve an arithmetic sequence or series.

 

 

 

I can identify assumptions made when identifying a geometric sequence or series.

 

 

 

I can provide and justify an example of a geometric sequence.

 

 

 

I can come up with the equation for determining the general term of a geometric sequence.

 

 

 

I can determine t1, r, n, or tn in a problem that involves a geometric sequence.

 

 

 

I can come up with the equation for determining the sum of n terms of a geometric series.

 

 

 

I can determine t1, r, n,or Sn in a problem that involves a geometric series.

 

 

 

I can generalize, using inductive reasoning, a rule for determining the sum of an infinite geometric series.

 

 

 

I can explain why a geometric series is convergent or divergent.

 

 

 

I can solve a problem that involves a geometric sequence or series.

 

 

 


 

CONCEPT

I have no idea what it is!

I need some help with this.

Yes!

I know this!

Chapter 3  Quadratic Functions

I can explain why a function given in the form

y = a(x – p)2 + q is a quadratic function.

 

 

 

I can compare the graphs of a set of functions of the form

y = ax2 to the graph of y = x2, and generalize, using inductive reasoning, a rule about the effect of a. (vertical stretch)

 

 

 

I can compare the graphs of a set of functions of the form

y = x2 + q to the graph of y = x2, and generalize, using inductive reasoning, a rule about the effect of q. (vertical translation)

 

 

 

I can compare the graphs of a set of functions of the form

y = (x – p)2 to the graph of y = x2, and generalize, using inductive reasoning, a rule about the effect of p. (Horizontal translation)

 

 

 

I can sketch the graph of y = a(x – p)2 + q, using transformations, and identify the vertex, domain and range, direction of opening, axis of symmetry, and x- and y-intercepts.

 

 

 

I can explain the reasoning for the process of completing the square as shown in a given example.

 

 

 

I can write a quadratic function given in the form

y = ax2 + bx + c as a quadratic function in the form

y = a(x – p)2 + q by completing the square.

 

 

 

I can identify, explain, and correct errors in an example of completing the square.

 

 

 

I can determine the characteristics of a quadratic function given in the form y = ax2 + bx + c, and explain the strategy used.

 

 

 

I can sketch the graph of a quadratic function given in the form y = ax2 + bx + c.

 

 

 

I can verify, with or without technology, that a quadratic function in the form y = ax2 + bx + c represents the same function as a given quadratic function in the form

y = a(x – p)2 + q.

 

 

 

I can write a quadratic function that models a given situation, and explain any assumptions made.

 

 

 

I can solve a problem, with or without technology, by analyzing a quadratic function.

 

 

 


 

CONCEPT

I have no idea what it is!

I need some help with this.

Yes!

I know this!

Chapter 4  Solving Quadratic Equations

I can explain, using examples, the relationship among the roots of a quadratic equation, the zeros of the corresponding quadratic function, and the x-intercepts of the graph of the quadratic function.

 

 

 

I can derive the quadratic formula, using deductive reasoning.

 

 

 

I can solve a quadratic equation of the form ax2 + bx + c = 0 by using strategies such as

·         Determining square roots

·         Factoring

·         Completing the square

·         Applying the quadratic formula

·         Graphing its corresponding functions.

 

 

 

I can select a method for solving a quadratic equation, justify the choice, and verify the solution.

 

 

 

I can explain, using examples, how the discriminant may be used to determine whether a quadratic equation has two, one, or no real roots, and relate the number of zeros to the graph of the corresponding quadratic function.

 

 

 

I can identify and correct errors in a solution to a quadratic equation.

 

 

 

I can solve a problem by

·         analyzing a quadratic equation

·         determining and analyzing a quadratic equation

 

 

 

I can factor a given polynomial expression that requires the identification of common factors.

 

 

 

I can determine whether a given binomial is a factor for a given polynomial expression, and explain why or why not.

 

 

 

I can factor a given polynomial expression of the form

·        

·        

 

 

 

I can factor a given polynomial expression that has a quadratic pattern, including

·        

·        

 

 

 


 

CONCEPT

I have no idea what it is!

I need some help with this.

Yes!

I know this!

Chapter 8  System of Equations

I can model a situation, using a system of linear-quadratic or quadratic-quadratic equations.

 

 

 

I can relate a system of linear-quadratic or quadratic-quadratic equations to the context of a given problem.

 

 

 

I can determine and verify the solution of a system of linear-quadratic or quadratic-quadratic equations graphically, with technology.

 

 

 

I can determine and verify the solution of a system of linear-quadratic or quadratic-quadratic equations algebraically.

 

 

 

I can explain the meaning of the points of intersection of a system of linear-quadratic or quadratic-quadratic equations.

 

 

 

I can explain, using examples, why a system of linear-quadratic or quadratic-quadratic equations may have zero, one, two, or an infinite number of solutions.

 

 

 

I can solve a problem that involves a system of linear-quadratic or quadratic-quadratic equations, and explain the strategy used.

 

 

 

Chapter 9 Linear and Quadratic Inequalities

I can explain, using examples, how test points can be used to determine the solution region that satisfies an inequality.

 

 

 

I can explain, using examples, when a solid or broken line should be used in the solution for an inequality.

 

 

 

I can sketch, with or without technology, the graph of a linear or quadratic inequality.

 

 

 

I can solve a problem that involves a linear or quadratic inequality.

 

 

 

I can determine the solution of a quadratic inequality in one variable, using strategies such as case analysis, graphing, roots and test points, or sign analysis; and explain the strategy used.

 

 

 

I can represent and solve a problem that involves a quadratic inequality in one variable.

 

 

 

I can interpret the solution to a problem that involves a quadratic inequality in one variable.

 

 

 


 

CONCEPT

I have no idea what it is!

I need some help with this.

Yes!

I know this!

Chapter 5 Radical Expressions and Equations

I can compare and order radical expressions with numerical radicands in a given set.

 

 

 

I can express an entire radical with a numerical radicand as a mixed radical.

 

 

 

I can express a mixed radical with a numerical radicand as an entire radical.

 

 

 

I can perform one or more operations to simplify radical expressions with numerical or variable radicands.

 

 

 

I can rationalize the denominator of a radical expression with monomial or binomial denominators.

 

 

 

I can describe the relationship between rationalizing a binomial denominator of a rational expression and the product of the factors of a difference of squares expression.

 

 

 

I can explain, using examples, that ,


 

 

 

I can identify the values of the variable for which a given radical expression is defined.

 

 

 

I can solve a problem that involves radical expressions

 

 

 

I can determine any restrictions on values for the variable in a radical equation.

 

 

 

I can determine the roots of a radical equation algebraically, and explain the process used to solve the equation.

 

 

 

 I can verify, by substitution, that the values determined in solving a radical equation algebraically are roots of the equation.

 

 

 

I can explain why some roots determined in solving a radical equation algebraically are extraneous.

 

 

 

I can solve problems by modelling a situation using a radical equation.

 

 

 


 

CONCEPT

I have no idea what it is!

I need some help with this.

Yes!

I know this!

Chapter 2 Trigonometry

I can sketch an angle in standard position, given the measure of the angle.

 

 

 

I can determine the reference angle for an angle in standard position.

 

 

 

I can explain, using examples, how to determine the angles from 0° to 360° that have the same reference angle as a given angle.

 

 

 

I can illustrate, using examples, that any angle from 90° to 360° is the reflection in the x-axis and/or the y-axis of its reference angle.

 

 

 

I can determine the quadrant in which a given angle in standard position terminates.

 

 

 

I can draw an angle in standard position given any point

P (x, y) on the terminal arm of the angle.

 

 

 

I can illustrate, using examples, that the points P (x, y),

P (−x, y), P (−x, −y), and P (x, −y) are points on the terminal sides of angles in standard position that have the same reference angle.

 

 

 

I can determine, using the Pythagorean theorem or the distance formula, the distance from the origin to a point

P (x, y) on the terminal arm of an angle.

 

 

 

I can determine the value of sinq , cosq , or tanq , given any point P (x, y) on the terminal arm of angle q .

 

 

 

I can determine the sign of a given trigonometric ratio for a given angle, without the use of technology, and explain.

 

 

 

I can solve, for all values of q , an equation of the form

sinq = a, or cosq = a, where −1  1, and an equation of the form tanq = a, where a is a real number.

 

 

 

I can determine the exact value of the sine, cosine, or tangent of a given angle with a reference angle of 30°, 45°, or 60°.

 

 

 

I can describe patterns in and among the values of the sine, cosine, and tangent ratios for angles from 0° to 360°.

 

 

 

I can sketch a diagram to represent a problem.

 

 

 

I can solve a contextual problem, using trigonometric ratios

 

 

 

 

CONCEPT

I have no idea what it is!

I need some help with this.

Yes!

I know this!

Chapter 6 Rational expressions and Equations

 

I can compare the strategies for writing equivalent forms of rational expressions to the strategies for writing equivalent forms of rational numbers.

 

 

 

I can explain why a given value is non-permissible for a given rational expression.

 

 

 

I can determine the non-permissible values for a rational expression.

 

 

 

I can determine a rational expression that is equivalent to a given rational expression by

multiplying the numerator and denominator by the same factor (limited to a monomial or a binomial), and state the non-permissible values of the equivalent rational expression.

 

 

 

I can simplify a rational expression.

 

 

 

I can explain why the non-permissible values of a given rational expression and its simplified form are the same.

 

 

 

I can identify and correct errors in a simplification of a rational expression, and explain the reasoning.

 

 

 

I can compare the strategies for performing a given operation on rational expressions to the strategies for performing the same operation on rational numbers.

 

 

 

I can determine the non-permissible values when performing operations on rational expressions

 

 

 

I can determine, in simplified form, the sum or difference of rational expressions with the same denominator.

 

 

 

I can determine, in simplified form, the sum or difference of rational expressions in which the denominators are not the same and which may or may not contain common factors.

 

 

 

I can determine, in simplified form, the product or quotient of rational expressions.

 

 

 

I can simplify an expression that involves two or more operations on rational expressions.

 

 

 

I can determine the non-permissible values for the variable in a rational equation.

 

 

 

I can determine the solution to a rational equation algebraically, and explain the process used to solve the equation.

 

 

 

I can explain why a value obtained in solving a rational equation may not be a solution of the equation.

 

 

 

I can solve problems by modelling a situation using a rational equation.

 

 

 

 

CONCEPT

I have no idea what it is!

I need some help with this.

Yes!

I know this!

Chapter 7 Absolute Value and radical Functions

 

I can determine the distance of two real numbers of the form ± a, a Î R , from 0 on a number line,

and relate this to the absolute value of

 

 

 

I can determine the absolute value of a positive or negative real number.

 

 

 

I can explain, using examples, how distance between two points on a number line can be expressed in terms of absolute value.

 

 

 

I can determine the absolute value of a numerical expression.

 

 

 

I can compare and order the absolute values of real numbers in a given set.

 

 

 

I can create a table of values for given a table of values for y = f(x).

 

 

 

I can generalize a rule for writing absolute value functions in piecewise notation.

 

 

 

I can sketch the graph of  state the intercepts, domain, and range; and explain the strategy used.

 

 

 

I can solve an absolute value equation graphically, with or without technology.

 

 

 

I can solve, algebraically, an equation with a single absolute value, and verify the solution.

 

 

 

I can explain why the absolute value equation  has no solution.

 

 

 

I can determine and correct errors in a solution to an absolute value equation.

 

 

 

I can solve a problem that involves an absolute value function.

 

 

 

I can compare the graph of   to the graph of y = f(x).


 

 

 

I can identify, given a function f(x), values of x for which  will have vertical asymptotes; and describe their


relationship to the non-permissible values of the related rational expression.

 

 

 

I can graph, with or without technology,  given


y = f(x) as a function or a graph, and explain the strategies used.

 

 

 

I can graph, with or without technology, y = f(x), given  as a function or a graph, and explain the strategies used.

 

 

 

I can provide you with a copy on request.

 



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