....An important idea is "writing equations of lines" 

• This site is from algebra lab. 
• This is a tutorial from College Algebra.

...Another concept is factoring algebraic expressions...you use the same patterning you used in prime factoriziation

• This is a site I have written.
• For a more complete explanation with sample problems go to http://regentsprep.org/Regents/math/math-topic.cfm?TopicCode=factor

..A new concept is solving quadratic equations...note the "rules" are not the same as solving linear equations

• Purple Math at http://www.purplemath.com/modules/solvquad.htm  gives an explanation.
• For a more complete explanation with sample problems go to http://regentsprep.org/Regents/math/math-topic.cfm?TopicCode=FacEq

..Solving literal equations or "algebraic symbol manipulation" can be challenging

• This site may help.

Beginning Algebra

 159 Objectives

Sample Problem

Worktext Section

I. Real Numbers

See Pie 1

II. Solving Linear Equations

See Pie 1

III. Graphs and Functions

B. Graphing lines

alge196: Graphing the line through a given point with a given slope

Graph the line with slope 9 passing through the point
(– 3, 5)

3.9

alge637: Determining the slope of a line given its graph

Find the slope of the line graphed below:

Answer:

The two points are (0,2) and
(1, -1).

C. Equations of lines

alge631: Finding the slope of a line given its equation

What is the slope of the line

Answer:
Solve for y.  The coefficient of the x- term is the slope.

alge070: Writing the equation of a line given the slope and the y-intercept

The slope of a line is – 2 and its y-intercept is – 9. Write an equation for this line, using
(x, y)-coordinates.

3.13

alge071: Writing the equation of a line given the slope and a point

A line passes through the point (9, 5) and has a slope of – 2. Write an equation for this line, using (x, y)-coordinates.

3.14

alge072: Writing the equation of a line through two given points

Find the equation of the line that passes through the points (-8, 3) and (1, -3) in (x,y)-coordinates.

3.15

alge073: Writing the equations of vertical and horizontal lines through a given point

Write equations for the vertical and the horizontal lines passing through the point (– 6, 9), using (x, y)-coordinates.

3.16

geom807: Slopes of parallel and perpendicular lines: Problem type 1

Write an equation for the line that is parallel to the line
  – 3x + 9y = 9 and passes through the point (1, 2).

3.17

geom808: Slopes of parallel and perpendicular lines: Problem type 2

Write an equation for the line that passes through the point (2, 3) and is perpendicular to the line
8x – 3y = – 12

3.18

D. Inequalities

alge018: Graphing a linear inequality in the plane: Problem type 1

Graph 2x + 3y < 4

3.19

alge225: Graphing a linear inequality in the plane: Problem type 2

Graph: y  > – 6

3.20

E. Sets
F. Functions

See Pie 1

IV. Systems of Linear Equations

V. Exponents and Polynomials

A. Properties of Exponents
B. Scientific Notation
C. Polynomials

See Pie 1

D. Factoring

alge041: Factoring a product of a quadratic trinomial and a monomial

Factor completely:

Answer:

6.17

alge042: Factoring with repeated use of the difference of squares

Factor completely:

Answer:

6.18, 6.19

alge044: Factoring the sum or difference of two cubes

Factor completely:

6.20

alge055: Least common multiple of two monomials

Find the least common multiple of the two expressions
 and

Simplify your answer as much as possible.

6.10

alge181: Factoring a multivariate polynomial by grouping: Problem type 2

Factor:

 

Answer:

6.12

E. Solving quadratic equations

alge045: Roots of a quadratic equation with leading coefficient 1

Find the roots of the quadratic equation:

6.24

alge048: Roots of a quadratic equation with leading coefficient greater than 1

Solve for x:

6.25

alge046: Roots of a product of polynomials

Find all values of which satisfy the equation

6.26

alge211: Solving a quadratic equation  needing simplification

Solve the equation for u:

6.27

VI. Rational expressions and functions

A. Simplifying expressions

Multiply and simplify:

Answer:

alge054: Dividing rational expressions

Divide:  and reduce the result to

 lowest terms.

5.10

alge058: Complex fraction: Problem type 1

Express the following compound fraction in lowest terms:

5.11

alge057: Adding rational expressions

Express as a single reduced fraction:

5.15

Subtract and simplify

Answer:

Simplify the following expression:

5.16

Reduce the following expression to its lowest terms

6.21

B. Solving equations

alge205: Solving a simple equation with rational expressions: Problem type 2

Solve the following equation for t:  

Simplify your answer as much as possible.

5.19

E. Direct and inverse variations

alge175: Word problem on direct variation

For a car moving at a constant speed, the distance covered by the car varies directly with the driving time. If the car covers 495 miles in 9 hours, how many miles does it cover in 7 hours?

5.24

alge176: Word problem on inverse variation

The time it takes to cover the distance between two cities by car is inversely proportional to the speed of that car. The ride takes 11 hours for a car moving at 65mph. How long is the ride, if the car moves at 55 mph?

5.25

James races his bicycle for 188 m, and a wheel of his bicycle turns 47 times over this distance. What is the diameter of the wheel?
Use the value 3.14 for and do not round intermediate steps. Round your final answer to one decimal place.

Answer:
Each time the wheel makes one complete turn, it moves forward a distance equal to its circumference.  Let's denote the circumference of the wheel by C and we know that C = d.  The wheel turns 47 times or travels a distance of 47C.

We know that James raced 188 m, so
   47C = 188
      C = 188/47 = 4

Since C = d, we have d = 4.
     3.14 d = 4
            d = 4/3.14 = 1.2738…
           d = 1.3 m

The diameter is 1.3 m, rounded one to decimal place.

VII. Radicals and rational exponents
 

A. Simplifying expressions
B. Solving equations
C. Higher roots

See Pie 1

D. Quadratic equations

alge094: Completion of the square

Find the value of c such that
    
is a perfect square.

6.16