Algebra 1A Midterm Topics 2015-2016

Calculator

Using the STO button to evaluate expressions

Evaluate x2−5 x+6 when x=−4

Converting a decimal to a fraction. Math → Enter → EnterConvert .56 to a fraction

Unit 1

1.1 Solving Simple Equations- Examples: 5 x=60

x+5=20

Algebra 1A Midterm Topics 2015-2016

x−5=20

x5=60

1.2 Solving Multi-Step Equations- Example: 3 x+5=20

1.3 Solving Equation with Variables on Both Sides- Example: 5 x+6=3 x+20

−3 x −3 x

2 x+6=20

−6 −6

2 x=14

Last step…

2x2

=142

x=7

Algebra 1A Midterm Topics 2015-2016

1.4 Rewriting Formulas- Example: Solve for x:

y=mx+b

−b −b

y and −b are not “like” terms so…

y−b=mx

m and x are connected by multiplication so we need to divide to separate them

y−bm

=mxm

mm

=1 so…

y−bm

=x

Unit 2

Note: When solving inequalities it can also be expected that you graph the solution (i.e. plot the inequality on the number line) to communicate your answer after solving the inequality algebraically.

2.1 Writing and Graphing Inequalities

- Example: Write the sentence as an inequality

w−3.5≤−2

Algebra 1A Midterm Topics 2015-2016

- Example: Graph 2<x

2.2 Solving Inequalities using addition and subtraction

Examples:

Algebra 1A Midterm Topics 2015-2016

2.3 Solving Inequalities using multiplication and addition

Examples:

4 ≥ x4

4 ∙4≥ x4∙4

16≥ x

Multiplying and Dividing by a NEGATIVE Number to Solve Inequalities:

Algebra 1A Midterm Topics 2015-2016

2.4 Solving Multi-step Inequalities

2.5 Compound Inequalities (“AND”/”OR”)

Algebra 1A Midterm Topics 2015-2016

Solve −4<x−2<3

Solve each inequality separately

2 x+6←2 Subtract 6 from each side of the inequality so…

−6−6

2x2

<−82 Divide each side of the inequality by 2 so…

x←4

4 x−5>3 Add 5 to each side of the inequality so…

+5 +5

4 x4

> 84 Divide each side of the inequality by 2 so…

x>2

Answer: x←4 OR x>2

Algebra 1A Midterm Topics 2015-2016

3.1 Functions

Be able to:

- Determine if a relation is a function by looking at:Graph (Vertical Line Test)

Ordered Pairs

Table

Mapping Diagram

Algebra 1A Midterm Topics 2015-2016

- Find the domain (inputs) and the range (outputs) of a function

The domain of f ( x )=|x| is all real numbers

The range of f ( x )=|x| is y ≥0

Algebra 1A Midterm Topics 2015-2016

3.2 Linear Functions

Algebra 1A Midterm Topics 2015-2016

Looking at the exponent to determine if a function is linear or nonlinear:

y=3 x+5 has an exponent of 1 so it is linear.

y=x2has an exponent that is not equal to 1 so it is nonlinear*

*Examples of linear equations without an exponent of 1 would be y=5 (horizontal) and x=3 (vertical) lines

Continuous and Discrete Domain

Discrete Continuous

Algebra 1A Midterm Topics 2015-2016

3.3 Linear Functions

Evaluate f ( x )=3 x+5 when x=2

f (2 )=3 (2 )+5

f (2 )=6+5

f (2 )=11

For h ( x )=2 x−6 find x so that h ( x )=8

Since h ( x )=8

8=2x−6

+6 +6

14=2 x

Divide both sides of the equation by 2

142

=2 x2

7=x

Be able to identify the independent and dependent variables of a function

Given, C (t )=2 t+180, where C represents costs and t represents number of t-shirts purchased. Identify the independent and dependent variables.

Cost C is the dependent variable because the cost depends on the number of t-shirts purchased.

T-shirts, t, is the independent variable because a consumer chooses the amount of t-shirts purchased.

Algebra 1A Midterm Topics 2015-2016

3.4 Graphing Linear Equations in Standard Form

After graphing one should be able to identify the coordinates of the x-intercept (4, 0) and the coordinates of the y-intercept (0, 3) of the graph.

3.5 Graphing Linear Equations in Slope-Intercept Form

Be able to find the slope of a line by using the formula:

m=y2− y1x2−x1

Algebra 1A Midterm Topics 2015-2016

3.6 Transformations of Graphs of Linear Equations

Algebra 1A Midterm Topics 2015-2016

Algebra 1A Midterm Topics 2015-2016

Algebra 1A Midterm Topics 2015-2016

3.7 Graphing Absolute Value Functions

Be able to apply the transformations of 3.6 to the Absolute Value Function (pgs. 156-159 in the textbook)

Be able to determine the domain and range of an Absolute Value Function

Other:

Classification of numbers (integers, rational numbers, etc…) Properties of numbers (distributive, identity, inverse, etc…) Word Problems involving the above topics Word Problems involving perimeter and area of rectangles and

squares

Algebra 1A Midterm Topics 2015-2016