Your Algebra Homework Can Now Be Easier Than Ever!

Summary for Math 120 Midterm Two

Here are some thoughts I was having while considering what to put on the second midterm.
The core of your studying should be the assigned homework problems: make sure you really
understand those well before moving on to other things ( like the old midterms on the test

• Chapter 7 - Quadratic Modeling

– The quadratic function is introduced. You should know the significance of the vertex
and how to find it. You should be able to sketch the graph of a given quadratic

– You should be able to determine the maximum and minimum value of a quadratic
function on a specified interval.

– You should be able find the maximum or minimum possible value of a quantity by
expressing it as a quadratic function of some other quantity (e.g., area of a rectangular
enclosure as a function of the width of the enclosure, etc.). Problem 7.10-7.14 all
involve this idea.

• Chapter 8 - Composition

– In addition to combining two functions into a new function via arithmetic (the way
we can combine two numbers into a new number), we can also combine two functions
via composition.

– You should understand what f(g(x)) means, and how to express a rule for f (g(x))
given rules for f(x) and g(x).

– I especially like problems 8.3, 8.4, 8.5.

• Chapter 9 - Three Construction Tools

– You should understand horizontal and vertical shifting, and horizontal and vertical
scaling (aka dilating)

– You should understand how to derive the graph of g(x) = af(bx + c) + d from the
graph of f(x) (see, e.g., problem 9.2)

– I especially like problems 9.2, 9.3, 9.4, and 9.7

• Chapter 11 - Inverse Functions

– Another very short chapter.

– You should understand what an inverse function is, what conditions a function
must satisfy in order to have an inverse (do all functions have inverses? can you tell
if a function has an inverse by looking at its graph?), and how to find the inverse of
a given function

You should understand what a one-to-one function is, and what is special about the
graph of a one-to-one function

– Problems 11.2, 11.6, and 11.8 are particularly good.

• Chapter 12 - Rational Functions

– An important chapter, it introduced a new class of functions for modeling.

– You should be able to find the asymptotes (horizontal and vertical) of a linear-to-linear
rational function, and be able to sketch the graph of a rational function like
those in problem 12.1(a) or (b).

– You should be able to model with linear-to- linear rational functions. This comes
down to finding a rational function of the form

whose graph
1. passes through three given points
2. has a given asymptote and passes through two given points
3. has two given asymptotes and passes throuh one given point
You will need to translate the language of the modeling problem. Take a look at old
midterm 2 exams from the archive for examples to work on.
Pay particularly close attention to the words “linear-to-linear”.
Note that a linear-to- linear function is not a linear function.
– I especially like problems 12.6, 12.7, 12.8, 12.10, and 12.11.

• Chapter 13 - Measuring an Angle

– You should understand how to convert between degrees and radians

– You should understand and be able to use the relationships between radii, angle,
arc length and area

– I like problems 13.8 and 13.9 (check the electronic version of the text at the 120 Materials
Website if your copy of the text doesn’t show the shading well).

• Chapter 14 - Measuring Circular Motion

– You should understand the various measures of angular speed (aka angular velocity),
like rpm, radians per second, or degrees per hour

– You should understand the relationship between radius, angular speed and linear

– You should know how to solve a belt -and-pulley problem (e.g., the bicycle example
from lecture, example 14.4.1, problems 14.8, 14.9 and 14.11)

– I also like problems 14.5 and 14.7.

• Chapter 15 - The Circular Functions

– This chapter introduces the trigonometric functions .

– You should be able to solve problems using the idea of trigonometric functions as
ratios of sides of right triangles (e.g., problems 15.4, 15.7, 15.8) and some algebra

– You should understand the definitions of sin x and cos x using the unit circle ; you
should be able to determine certain simple properties of the functions sin x and cos x
from this definition (e.g., the range, the domain, the graph, the values at certain
value of x, like x = 5π /2)

– You should be able to determine the location of an object moving circularly given information
about its speed and starting location (e.g., problems 15.2, 15.5, 15.9, 15.15,
and the three non-textbook Chapter 15 problems)

• Chapter 16 - Trigonometric Functions

– This is a short chapter which adds some final touches to our knowledge of the functions
sin x and cos x and related functions.

– I like problems 16.3 and 16.4.

• Chapters 17 - Sinusoidal Functions

– You should understand the notion of a sinusoidal function as a shifted/stretch/squished
version of the function sin x.

– You should understand the effect of the four parameters A,B,C and D on the graph

– You should be able to model with sinusoidal functions. In particular, you should
be able to determine the parameters A,B,C, and D from a verbal description of a
quantity that varies sinusoidally with time (see problems 17.2, 17.3, 17.4,17.6)

Prev Next

Start solving your Algebra Problems in next 5 minutes!

Algebra Helper
Download (and optional CD)

Only $39.99

Click to Buy Now:

OR is an authorized reseller
of goods provided by Sofmath

Attention: We are currently running a special promotional offer for visitors -- if you order Algebra Helper by midnight of August 15th you will pay only $39.99 instead of our regular price of $74.99 -- this is $35 in savings ! In order to take advantage of this offer, you need to order by clicking on one of the buttons on the left, not through our regular order page.

If you order now you will also receive 30 minute live session from for a 1$!

You Will Learn Algebra Better - Guaranteed!

Just take a look how incredibly simple Algebra Helper is:

Step 1 : Enter your homework problem in an easy WYSIWYG (What you see is what you get) algebra editor:

Step 2 : Let Algebra Helper solve it:

Step 3 : Ask for an explanation for the steps you don't understand:

Algebra Helper can solve problems in all the following areas:

  • simplification of algebraic expressions (operations with polynomials (simplifying, degree, synthetic division...), exponential expressions, fractions and roots (radicals), absolute values)
  • factoring and expanding expressions
  • finding LCM and GCF
  • (simplifying, rationalizing complex denominators...)
  • solving linear, quadratic and many other equations and inequalities (including basic logarithmic and exponential equations)
  • solving a system of two and three linear equations (including Cramer's rule)
  • graphing curves (lines, parabolas, hyperbolas, circles, ellipses, equation and inequality solutions)
  • graphing general functions
  • operations with functions (composition, inverse, range, domain...)
  • simplifying logarithms
  • basic geometry and trigonometry (similarity, calculating trig functions, right triangle...)
  • arithmetic and other pre-algebra topics (ratios, proportions, measurements...)


Algebra Helper
Download (and optional CD)

Only $39.99

Click to Buy Now:

OR is an authorized reseller
of goods provided by Sofmath
Check out our demo!
"It really helped me with my homework.  I was stuck on some problems and your software walked me step by step through the process..."
C. Sievert, KY
19179 Blanco #105-234
San Antonio, TX 78258
Phone: (512) 788-5675
Fax: (512) 519-1805

Home   : :   Features   : :   Demo   : :   FAQ   : :   Order

Copyright © 2004-2022, Algebra-Answer.Com.  All rights reserved.