Correlation of ALEKS objectives, Pie 4, and ALEKS Online Worktext

 

  • Pie 4 includes the following topics in ALEKS and material on Relations and Functions.  You do not send any homework to me from the Relations and Functions mini-module.  There will be a 3-4 questions on Test 4 and a couple on the final about relations and functions.  Some, but not all, of what you are to learn is in this course is in ALEKS.  Thus, the reason for writing this material for you.

...Solving more difficult absolute value equations and solving absolute value inequalities are covered

...A main focus of this Pie is working with radicals: simplifying; adding, subtracting, multiplying and dividing; and solving equations

...Having learned to work with radicals, you can now solve quadratic equations which do not factor...you will use the quadratic formula

  • Purplemath has an explanation.
  • This site explains how the quadratic formula is derived and how to use it.  You do not need to know how it is derived but you may find it helps you understand the concept.
  • Mathematics has a nice review of "all" the methods of solving quadratic equations.
  • This part of the Purplemath website shows rational expressions simplifying to quadratic equations: go the bottom half of the page, and to the next page.

...Another concept is graphing parabolas

  • Purplemath has an explanation: only do pages 1-3.
  • This site has a conversational flow to it as it explains graphing a parabola.
  • I authored this site.

 

 

Beginning Algebra

219 Objectives

Sample Problem

Worktext Section

I. Real Numbers

See Pie 1 and 3

 

 

II. Solving Linear Equations

 

 

 

E. Absolute value

alge167: Solving an equation involving absolute value: Basic

 Solve the following equation for z:

 

2.24

III. Graphs and Functions

 

 

 

E. Sets

set004: Set builder and interval notation

Site to help you

Another one

 

 
  set005: Union and intersection of sets    
F. Functions

fun016: Domain and range: Problem type 1

Specify the domain and the range of the relation:

Answer:
Domain  {u, b, 8}
Range: {m, f, k, 5}

 

  

 

fun004: Domain and range: Problem type 2

  

 

 

fun010: Vertical line test

  

 

IV. Systems of Linear Equations

See Pies 1, 2, and 3

 

 

V. Exponents and Polynomials

See Pies 1 and 2

 

 
C. Manipulating polynomial expressions alge708: Polynomial long division: Linear divisor    
E. Solving quadratic equations alge163: Writing a quadratic equation given the roots and the leading coefficient

Write the quadratic equation whose roots are -6 and 2, and whose leading coefficient is 3.
(Use the letter x to represent the unknown variable)
Answer:
  

 

 6.30

VI. Rational expressions and functions

See Pies 1, 2 and 3

 

 

VII. Radicals and rational exponents

 

 

 

A. Simplifying expressions

 alge275: Simplifying a radical expression: Problem type 2    
 

alge082: Simplifying a product of radical expressions: Problem type 3

Simplify 
Assume that all variables represent positive real numbers.

7.5

 

alge084: Simplifying a sum of radical expressions

Simplify the following expression as much as possible:
 
Assume that all variables represent positive real numbers

7.2

 

alge640: Simplifying a product of radical expressions

Simplify. 

Answer:

 

 

 

 

alge276: Simplifying a product of radical expressions using the distributive property

Perform the following multiplication and simplify:

7.4

 

alge088: Rationalizing the denominator of a radical expression using conjugates

 Write in simplified radical form by rationalizing the denominator.

Answer:

 

 

 

 

7.7

B. Solving equations

alge090: Solving an equation with radicals: Problem type 2

 

7.11

 

alge091: Solving an equation with radicals: Problem type 3

 

7.12

 

 alge182: Solving an equation with radicals: Problem type 4    

D. Solving quadratic equations

alge095: Quadratic formula

Solve the following equation for by using the quadratic formula

6.31

 

alge214: Discriminant of a quadratic equation

 Compute the value of the discriminant and give the number of real solutions to the quadratic equation
.
Answer:
 Discriminant = b2 – 4ac
Discriminant = 42 – 4(3)(4)
                    = 16 – 48 = - 32

Since the discriminant is negative (and is the value inside the square root and you cannot take the square root of a negative number), there are no real solutions.

6.32
  alge193: Discriminant of a quadratic equation with parameter

 

    

 

alge524: Solving a word problem using a quadratic equation with irrational roots

When a ball is thrown, its height in meters h after t seconds is given by the equation , where v is the initial upwards velocity in meters per second. If v = 10 meters per second, find all values of t for which h = 4 meters. Do not round any intermediate steps. Round your answer to 2 decimal places.

Answer:

 

 

 

 

 

E. Graphing parabolas

alge252: Graphing a parabola: Problem type 1

Graph the parabola

Answer:

This is the form .  The vertex is (0,0) and a = 2.

 

 

 

6.35

 

alge253: Graphing a parabola: Problem type 2

Graph the parabola

Answer:

This is the form .  The vertex is (h,k), or (1, -3) and a = 1

 

 

 

 

 

alge254: Graphing a parabola: Problem type 3

 Graph the parabola:

To graph the parabola, plot the vertex, the x-intercept and y-intercept.

6.35
  alge277: Finding the x-intercept and vertex of a parabola    
VIII. Other alge185: Vertical translation of the graph of a function    
  alge191: Midpoint of a line segment in a plane    
  alge132: Distance between two points in a plane    

IX. Relations and Functions

 

Additional information on relations and functions
 RELATIONS AND FUNCTIONS