MAT 1003C Highlights for Chapter 1
Be able to classify numbers using the fol lowing
categories : natural number, whole
number, integer, rational number , irrational number and real number. Many times
a
given number can fall under more than one category.
Know how to recognize and use the various properties of numbers such as the
distributive, associative, and commutative properties. Also, be able to find the
additive
and multiplicative inverses for a given number. Additive inverses add to a sum
of zero,
while multiplicative inverses yield a product of one. Zero is the additive
identity because
any number added to zero remains the same. One is the multiplicative identity
because
any number multiplied by one remains the same.
You need to be proficient at using the order of operations . You can remember
this order
using the acronym Parenthesis Exponents (Multiplication or
Division) (Addition or
Subtraction). Compute expressions in parenthesis first then compute
exponents second.
Next comes multiplication and division which carry equal weight in terms of
order. This
is true because division can be changed to a multiplication problem using the
reciprocal.
As a last step, you should add or subtract. Addition and subtraction also carry
equal
weight in terms of order because subtraction can be changed into addition by
changing
the subtraction sign into an equivalent form of “adding a negative”.
Remember that the product of numbers with like sign is always positive while the
product
of numbers with opposite sign is always negative.
Know how to add and subtract fractions using least common denominators. You
should
know how to multiply and divide fractions as well as be able to reduce fractions
by
canceling out common factors.
Be proficient at scientific notation. Know how to change numbers into scientific
notation
and vice versa.
You definitely need to know the rules of exponents. Look at problems #43 through
#54
on page 36 for practice test problems.
Be able to complete a table of values from a given formula involving exponents.
Also,
you should be able to, by inspection, come up with a simple formula that models
the data
in a table of values exactly.
Know how to plot points on the xy - coordinate plane . Remember anytime you graph
something to label the axes and indicate what scale you are using. When you are
using
the graphing calculator you will need to write down the appropriate viewing
window that
you are using for your graph. This, of course, means that you will need to first
decide on
an appropriate viewing window. Usually, this means a window in which you can
clearly
see all qualitative features of a graph including any intercepts.
Identify the domain and range of a relation in the form of a set of points.
When working with a table of values, know how to plot the
individual points associated
with the table on graph paper and connect the points using a line graph. Many
times
tables are used in real life situations to put data into an organized and
consolidated
format. You need to know how to interpret the significance of data and the
relationships
among the data in plain English within the context of a real world problem.
Please review examples 1, 4, and 8 in section 1.4 to be fully prepared for one
of the word
problems on the test.
MAT 1003C Highlights for Chapter 2
Know how to evaluate functions given their formulas OR graphs. For example, be
able
to evaluate f (2) where f (x) = 3x -1. You should be able to do these types of
problems
for a wide variety of functions with varying formulas. Alternatively, if you are
given the
graph of a function i.e. a visual representation, be able to, by inspection,
evaluate, f (2) .
Be able to sketch, on graph paper, the graph of a linear function in
slope- intercept form .
For example, the graph of y = 3x -1 has a slope of three and a y - intercept of
(0,-1). To
be able to graph this line successfully, you will need to be proficient with the
concept of
“rise over run” as it relates to line graphing. Conversely, if you are given the
graph of a
linear function be able to come up with the equation for it.
You should be familiar with the “input/output” view of functions. Know how to
transform a regular English sentence into a mathematical equation . For example,
“Subtract 9 from the input x to obtain the output y.” translates into y = x - 9.
Know how to produce a formula that converts one unit of measurement to another.
For
example, given that there are 12 inches in a foot, the equation f (x) = 12x will
convert
feet to inches. Try coming up with a formula that converts from inches to feet.
Be able to evaluate functions from a table of values and interpret the meaning
of the
results in a simple sentence or two. To do this, you will need to know what a
table of
values means in the context of a simple word problem. There are examples
scattered in
your text that touch on this.
From a table of values or from a graph, be able to identify the domain and range
using
interval notation.
Determine whether or not a table of values OR a graph could represent a linear
function.
Remember that for a relation to represent a linear function, the rate of change
must be
constant. For example, if the x -coordinates increase/decrease by some fixed
amount
then the y -coordinates must also increase/decrease by some fixed amount (not
necessarily the same amount).
Be prepared to select a graph that BEST models a situation in real life. See
problems #63
through #66 on page 100 of the text for an example of this.
Use the vertical line test to determine whether or not a
given graph represents a function.
Review the “Diagrammatic Representation” of functions given on page 76. Study
the
margin on this page closely for examples.
Know how to use the slope formula to calculate the slope between two points .
Know when the slope of a line is undefined and what all lines having an
undefined slope
have in common.
Know how to apply the special relationship that governs the slopes of
perpendicular lines.
The same goes for parallel lines. See the blue boxes on pages 123 and 124. Work
problems #49 through #52 for practice with this.
You need to know the point-slope form of a line by heart and be able to use it
freely in
specific problems on the test. Review problems #27 through #36 on page 128 for
extra
practice regarding this.
Be able to find x -intercepts and y -intercepts from a linear equation in
general form, and
be able to graph such a line using only the intercepts. Remember that whichever
intercept you are trying to find, you must set the opposite variable equal to
zero.
Make scatter plots from a table of values and be able to give a linear equation
that models
the data in the table.
IMPORTANT: Be able to give a “real life” interpretation of slopes and
intercepts for
given word problem. You will need to write your interpretations in complete
sentences.
See problems #75 through 77 on pages 129 and 130 for examples.
MAT 1033C Highlights for Chapters 3 and 4
For a given natural number, decided whether or not it satisfies a given linear
equation by
plugging it in to both sides of the equation and seeing if it yields a true or
false statement.
Be able to explain using plain English how you made your determination.
Be able to solve linear equations AND linear inequalities using only a table of
values and
be prepared to explain the process involved in this. Also, be able to solve
linear
equations and inequalities symbolically. Solving equations symbolically means to
solve
them using only the rules of algebra such as the distributive property.
Know how to solve the main two types of compound inequalities . The first
involves the
word ‘OR’ and the second involves the word ‘AND’. Be able to solve such
inequalities
graphically, numerically, and symbolically. Know how to determine whether or not
a
given numerical value is a solution to a given compound inequality.
You need to know how to write your solutions to compound inequalities in
interval
notation. This may involve using the infinity symbol at times as well as
appropriately
using brackets and parenthesis. Also, be able to graph your solutions to
compound
inequalities on a number line.
You need to know how to solve systems of linear equations in two variables using
the
substitution AND elimination methods . Please refer to your textbook to review
the
process for these methods. Also, you should be able to use a graph to determine
whether
such a system has a solution or not. For example, lines that intersect in
exactly one point
yield exactly one solution and lines that do not intersect at all yield no
solutions. What
would the graphs of two lines look like if their corresponding system of
equations has an
infinite number of solutions? What is such a system called? How would you
determine
whether a given point is a solution to a given system of linear equations?
Know how to interpret a distance versus time graph. In particular, be able to
interpret the
slope of a line for such a graph.
Practice on WORD problems involving linear equations. You will need to know how
to
set linear equations up from given information in a word problem. There will be
more
than one word problem on the test so be sure to review the various types of word
problems including those dealing with the perimeter of rectangles.
Know how to use the TRACE and ZOOM method or the INTERSECT method on your
graphing calculator to solve systems of linear equations. When using either
method, you
will need to indicate the WINDOW size on the test itself for full credit.
Lastly, be able to solve systems of linear inequalities by sketching graphs and
shading the
region in the xy-plane that corresponds to the solution of the linear
inequality. Remember
to use dotted lines for strict inequalities and solid lines otherwise. Also, be
able to write a
linear inequality given a picture of its graph.
