INTERMEDIATE ALGEBRA STUDY GUIDE -- CH 3 and
4
3-1 Solve for c: 4ac -3a = 2c + 8
3-2 Graph equations of the forms (some
solving may be required to get to the form):
y
= mx+b Ex: y =
-2/3 x + 4, Ex:
x = –3y (solve for y)
ax + by = c Ex: 2x - 5y = -10 , Ex: 3(x–2) + 4(y+1) = 10
x
= h Ex: x = –3, Ex: –(x+3) = 5
y = k Ex: y = 4, Ex: 2(3y+4) = 5y
3-3 Find
the slopes of lines, given their equations (See examples above)
3-4 Find the slope of a line (and write an
equation of the line), given
a. Two points
Ex: (4,-3) and (-2,5)
Ex: (–5,3) and (–5,–6)
b. Graph of the line (hint: find two points where the line crosses a
"grid point")
c. Table of values
|
x |
y |
|
-3 |
15 |
|
2 |
17 |
d. Data in a word problem.
Example: The average major league
baseball player salary in 1967 was $25,000, and in 1976 it was $40,000.
3-5 Be able to write the equations of the lines above in
a. Slope intercept
form
b. Point-slope form
c. General form
And
be able to convert from one form to another
Point-slope
to slope-intercept
Slope-intercept
to standard
Standard
to slope-intercept
3-6 Find the slope of any line:
a. Parallel to a given line (Examples from above)
b. Perpendicular to a given line
3-7 Solve for a variable "a" given the slope and two points, one with a coordinate in terms of "a" Ex: slope is -1, line passes through (a,3) and (2,6).
3-8 Graph
linear inequalities in 2 variables.
Know:
Solid vs. dotted line?
Which
side to shade (true side)? Ex: y < 2/3 x -4:
3-9 Given a graph, determine whether or not it is the graph of a
function.
(Use
vertical line test)
3-10 If
f(x) = 4x-1 and g(x) = x2
+ 2, find and simplify:
(clear
parentheses and combine like terms)
a. g(-3)
b. f(k)
c. g(z) -1
d. f(x+1)
4-1 Solve
a system of equations:
a. Graphically Ex: y = 1/2 x - 2, 2x - y = -1
b. By
substitution Ex: x + y = 2,
y = x2
c. By
addition/elimination Ex: 9x - 8y = 4, 2x + 3y = 6
d. By Cramer's rule (Expect one or two coefficients or constants to be letters)
Ex: 4x - 7y =a, bx + 2y = -3
For each method, be able to
recognize the no-solution and infinite-solution cases
("inconsistent" and "dependent", respectively)
In
both cases, the variable terms drop out completely
In
the no-solution case, the result is impossible (for example, 0=1)
In
the infinite-solution case, the result is true (for example, 0=0)
4-2 Be able to deal with fractional
coefficients (I strongly recommend that you start by clearing fractions).
Ex: 
and 
4-3 Solve
a 3X3 system of
equations with fractions (take-home question)
(I strongly recommend that
you start by clearing fractions).
4-4 Calculate
a 2X2 determinant
Ex: 
4-5 Calculate a 3X3 determinant.
You may use either short-cut
"criss-cross" method or expansion by minors
2 3 -2 1 4 1 1 5 -1
Example 5 from
textbook:
4-6 Applications: Selection of two from:
a. Interest problems
Typical example: Jill has a total of $15000 invested in two
investments, one earning 6% interest and the other earning 9% interest. If the total earned in the first year is
$1140, how much is invested at each rate?
b. Mixture problems
Typical example: May needs to prepare 500 mL
of a 36% acid solution for students in a chemistry lab. She must mix a 50%
solution and a 10% solution. How much of
each should she use?
c. Upstream-downstream problems
Typical example: It takes a boat 6 hours to travel 60 miles downstream, but 10
hours to return to its starting point (notice, on the return trip it is also
traveling 60 miles, but now it is traveling upstream). Find the speed of the boat and the speed of
the river.
4-7 Systems of linear inequalities in 2 variables.
Know:
Solid vs. dotted line?
Which
region to shade (true region for both inequalities)?
The
double-cross-hatched area is the solution:
Ex: y < 3/5 x
2x
+ 5y = -8
Examples
of cases where the lines are parallel:
Ex:
y < 2/3 x -4 y > 2/3 x -4 (direction is reversed)
2x
-3y £ 6 2x -3y £ 6
No
solution Solution
is the upper region
4-8 Add (–4) times the first row to the third row of the matrix below.
Answer: 
Return to: Merced College; Don Power
Updated 09/25/07 by Don Power