
The following is a list of outcomes you need to know for PreCalculus 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 t_{1}, d, n,
or t_{n} 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 t_{1}, d, n,,
or S_{n} 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 t_{1}, r, n,
or t_{n} 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 t_{1}, r, n,or
S_{n} 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 = ax^{2}
to
the graph of y = x^{2},
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 = x^{2} + q to the graph
of y = x^{2}, 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 = x^{2}, 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 yintercepts.




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 = ax^{2 }+ 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
= ax^{2 }+ bx + c, and explain the strategy used.




I can sketch the graph of a
quadratic function given in the form y = ax^{2} + bx + c.




I can verify, with or without
technology, that a quadratic function in the form y
= ax^{2} + 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 xintercepts 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 ax^{2}
+ 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 linearquadratic or quadraticquadratic equations.




I
can relate a system of linearquadratic or quadraticquadratic equations to
the context of a given problem.




I can determine and verify the
solution of a system of linearquadratic or quadraticquadratic equations graphically,
with technology.




I can determine and verify the
solution of a system of linearquadratic or quadraticquadratic equations
algebraically.




I can explain the meaning of
the points of intersection of a system of linearquadratic or
quadraticquadratic equations.




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




I can solve a problem that
involves a system of linearquadratic or quadraticquadratic 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 xaxis and/or the yaxis 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
nonpermissible for a given rational expression.




I can determine the nonpermissible 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 nonpermissible values of the equivalent rational expression.




I
can simplify a rational expression.




I
can explain why the nonpermissible 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 nonpermissible 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 nonpermissible 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 nonpermissible 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.
 