Intermediate Algebra Targets                Name: _______________________

Objectives for Unit 1 (Lines, Functions, and Systems)

(Textbook Chapters 1 and 2)

1.1 I can describe essential characteristics of linear relationships and can recognize and provide examples of linear and non-linear relationships.

1.2 I can use linear equations and functions to solve problems and model linear relationships.

1.3 I can solve linear equations and write them in different forms.

1.4 I can solve linear inequalities and write them in different forms.

1.5 I can solve linear systems (*using both elimination and substitution methods) and can represent the solution symbolically and graphically.

1.6 I can use a table of values to identify the solution of a system of linear equations or inequalities.

1.7 I can compare two solution methods in terms of their strengths and limitations.

1.8 I can identify, describe, and interpret the slope of a linear function in context.

1.9 I can find and interpret the x- and y-intercepts of the graph of a given linear function.

1.10 I can determine when two linear equations represent parallel, perpendicular, and intersecting lines.

1.11 I can explain what it means to solve equations, inequalities, and systems, and I can use this knowledge to check my answers for reasonableness and correctness.

1.12 I can determine a reasonable domain and range for a given function or relation.

1.13 I can recognize and provide examples of functional and non-functional relationships.

1.14 I can find an approximate line of best fit for a data set by hand.

1.15 I can use linear regression technology to find the equation of the best fit line and interpret the slope, intercept, and correlation coefficient in the context of the data.

Objectives for Unit 2 (Exponents, Polynomials Operations, and Factoring)

(Textbook Chapter 3)

2.1 I can explain the rules of exponents in terms of ordinary multiplication and division of monomials. (e.g.  x1x2 = (x)(xx) = x3; e.g. x1/2 means √x because (x1/2)2 = x; etc.)

2.2 I can use the rules of exponents to simplify simple expressions.

2.3 I can use the rules of exponents to simplify complex expressions.

2.4 I can add and subtract polynomials of varying degrees (linear, quadratic, cubic, etc.).

2.5 I can multiply two or more polynomials of varying degrees and simplify the result.

2.6 I can factor out the greatest common factor from polynomial expressions.

2.7 I can factor expressions of the form x2 + bx + c by inspection.

2.8 I can use one or more of the “ac-methods” (e.g. the box method, factor by grouping, or common factor quotient) to factor expressions of the form ax2 + bx + c, where a ≠ 1.

2.9 I can recognize when a quadratic expression is not factorable (i.e., is prime).

2.10 I can recognize special forms of quadratic expressions (difference of squares, sum of squares, and perfect square trinomials), and use that knowledge to quickly expand or factor the expression (if possible).

Objectives for Unit 3 (Quadratic Functions) (Textbook Chapter 4)

Note, many objectives from Unit 1 and especially Unit 2 are still relevant.

  1. I can describe the vertex and general shape of the graph of a quadratic function when it is given in vertex form.

3.2 I can use quadratic functions to find a mathematical model when I have information about the vertex and an additional data point.

3.3 I can describe a reasonable domain and range for a quadratic model based on the context and the point(s) at which the model breaks down.

3.4 I can sketch the graph of a given quadratic function that accurately depicts the symmetry, vertex, x-intercepts, y-intercept, and general shape of the graph (without using graphing technology).  

3.5 I can convert quadratic functions from vertex form to standard form.

3.6 I can use completing the square in simple cases
 (e.g. Express in vertex form: f(x) = 2x
2 + 8x – 3).

3.7 I can state the square root property and use it to solve quadratic equations.

3.8 I can state the famous quadratic formula and use it to solve quadratic equations.

3.9 I can state the zero product property and use factoring to solve quadratic equations.

3.10 I can describe situations where it is and is not efficient to use the following methods to solve quadratic equations: (a) the square root method,  (b) completing the square, (c) the quadratic formula, (d) zero product property, and (e) factoring.

3.11 I can state and use the Pythagorean Theorem to express the quantitative relationships.

And at least ONE  of the following advanced targets (you choose):

3.12 I can use completing the square in general cases. (Recommended if going on to Mth123)
 (e.g. to solve 2
x2 + 6x + 4 = 8; e.g. to derive the quadratic formula from ax2 + bx + c = 0).

3.13 I can use quadratic regression technology (e.g. calculator or Geogebra) to model a situation and discuss the limitations of using a quadratic model. (Recommended if going on to Statistics)

3.14 I can write a quadratic function to model a situation using three data points that do not include the vertex. (Recommended if you like systems of 3 equations with 3 unknowns)


Objectives for Unit 4 (Exponential Functions and Logarithms) (Textbook Chapters 5 and 6)

Note: several objectives from Unit 2 are relevant as well.

4.1  I can recognize situations for which an exponential growth or exponential decay model is appropriate.

4.2  I can explain how different values for the parameters of exponential functions [of the form f(t) = abkt or f(t) = abt/k] produce either exponential growth and exponential decay, how they influence the growth or decay rate, and how they influence the y-intercept.

4.3  I can solve exponential equations by inspection or by a guess-check-revise strategy.
 
(Note: Later, we will learn to use logarithms for this purpose as well). 

4.4  I can use exponential functions of the form f(t) = abkt or f(t) = abt/k to model an exponential growth or decay relationship.

4.5  I can solve problems involving exponential functions (e.g. depreciation, half-life, and compound interest).

4.6  I can describe the difference between the natural logarithm (usually denoted ln(x)) and the common logarithm (usually denoted log(x)).

4.7 I can use logarithms to solve equations involving exponential functions.

4.8 I can describe and sketch the graph of a given exponential function.

Objectives for Unit 5 (Rational Functions and Radical Functions) (Textbook Chapters 7 and 8)

Note: several objectives from Unit 2 on factoring are relevant as well. (Note: Targets 5.1 and 5.5 have been struck due to course time constraints.)

5.2  I can use rational functions to answer questions about inverse variation and other situations involving ratios of quantities.

5.3  I can describe the behavior of a given rational function, including identifying any domain restrictions and identifying the locations of x-intercepts, vertical asymptotes, and holes in the function’s graph.

5.4  I can simplify rational expressions using factoring.

5.6  I can solve equations involving rational functions.

5.7  I can solve equations involving a single radical function.

5.8  I can solve equations involving more than one radical function.

5.9  I check for extraneous solutions when it is appropriate to do so [e.g. when solving rational functions and when solving radical functions involving even roots].

Created by Jon Hasenbank, S13 – Ok to use or adapt for educational purposes