Download semester exam 2007

SEMESTER EXAM 2007
THE SEMESTER EXAM WILL BE COMPOSED OF MULTIPLE CHOICE AND
SHORT ANSWER QUESTIONS, BUT NO ESSAY. THE QUESTIONS ARE NOT
MEANT TO TRICK YOU, BUT WILL REQUIRE THAT YOU HAVE AN INDEPTH UNDERSTANDING OF THE MATERIAL AS WE HAVE DISCUSSED
IT IN CLASS. BE PREPARED TO ANSWER THE QUESTIONS WITH A
COMPLETE THOUGHT. (See bottom for examples.)
Sec. 1.7
What does x-4> 5 mean? Be able to solve this.
Sec. 2.5
In what form are the solutions of 3x-5y < 15? How do you know
algebraically and graphically that (3,1) is a solution?
Sec. 3.1
When solving a system of linear equations, you may obtain a
solution (x,y). What does this ordered pair represent graphically?
Sec. 3.1, 3.2
State 3 methods for solving a system of linear equations.
Sec. 3.6
How does adding 5z to the equation –4x – 3y = 1 change the
equation’s graph?
Sec. 4.1
What is the stipulation placed on matrices so that they may be
added?
Sec. 4.1
Given matrix A of order m x n. What do m and n represent
respectively?
Sec. 4.1, 4.2
Is matrix addition commutative? Is matrix multiplication
commutative? Be able to state your reasoning.
Sec. 4.2
Given matrix A of order m x n and matrix B of order n x p, can you
multiply them? If so, what is the new order?
Sec. 4.3
State 2 methods for evaluating the determinant of a 3x3 matrix.
Sec. 4.4, 4.5
What does it means when the determinant for a matrix equation is
equal to 0? (Include something regarding the solution and what
kind of lines you have.)
Sec. 4.4
How are matrix determinants and inverses related?
Sec. 4.5
What is represented by the solution to a matrix equation?
Sec. 4.5, 4.6, 4.7
State 3 methods that use matrices that would be useful in finding a
solution to a system of linear equations.
Sec. 5.1
Given x2 = d, state some generalizations regarding the solutions.
(There are 4 possible statements you could make if you include
complex number solutions.)
Sec. 5.2
What do the solutions to the quadratic equation represent
graphically?
Sec. 5.4
Given any quadratic equation, without solving it, how can you
determine how many solutions it has?
Sec. 5.2, 5.3, 5.4
State 3 methods for solving a quadratic equation.
Sec. 5.4
Be able to derive the quadratic formula from standard form by
completing the square.
Sec. 5.5
On what kind of plane are complex numbers graphed? What are its
axes? What geometric application of graphing (or rather mapping)
such complex numbers did we discuss in class?
Sec. 5.4
If the discriminant of a quadratic equation is 0, what does the
remaining portion of the quadratic formula represent?
Sec. 5.4, 5.6
Using the quadratic formula to solve a quadratic equation, you get
two complex number solutions. What significance does this have
regarding its graph?
Sec. 6.1
Define the domain and range of a function.
Sec. 6.1
Define a function. Is every relation a function? Is every function a
relation?
Sec. 6.1
What is the graphic check that determines whether a relation is a
function? What is the graphic check that determines whether an
inverse is a function?
Sec. 6.3
If two functions are inverses of each other, they will be reflected
about which axis or line? How can you tell algebraically if two
functions are inverses of each other?
Sec. 6.6
How do the domains differ of a function f(x) and a recursive
function f(n)? Give an example (or name) of a recursive function.
Sec. 6.6
How does one determine whether a set of values follows a linear or
quadratic model?
Sec. 6.7
Describe the 1st, 2nd and 3rd quartiles.
SAMPLE QUESTIONS – As you look through these, please pick through them for
the actual answers before you “freak out” as to how long they are. Very little of
what I have here is the answer that I am looking for from you; most of it is
“discussion” that is meant to help you better understand how I have arrived at
the answer.
SHORT ANSWER
A) Of what form are the solutions of the inequality 3x-5y < 15?
GOOD answer: They are ordered pairs.
B) How do you know algebraically (3,1) (Hopefully, seeing this would clue you in as to
how to answer the above question if you had forgotten – always look for clues to other
questions throughout any test.) is a solution to the above inequality?
BAD answer: Plug it in.
Problem: This says nothing about how to conclude whether or not it is a
solution.
A “GETTING THERE” answer: Plug it in and see if it is a true statement.
Problem: If it is a true statement, then what? Is it a solution or not?
Let’s think about our English skills here for a second – or possibly what you learned
about if/then statements in geometry last year. Any time you begin a sentence with “if”
(an insubordinate clause), you must finish it off with a “then” statement (a subordinate
clause).
So, a GOOD ANSWER would look like this: Substitute the values for “x” and
“y” into the inequality. If you get a true statement, then it is a solution.
C) How do you know graphically if (3,1) is a solution to the inequality 3x-5y<15?
BAD answer: If it lies in the shaded area.
Problem: If it lies in the shaded area, then what? Is it a solution or not?
GOOD answer: Graph the inequality. If the point (3,1) falls in the shaded area,
then it is a solution.
Another GOOD answer: Graph the inequality. If the point (3,1) falls outside the
shaded area or on the curve (since this is not a less than or equal to
inequality – so think about how you would answer this question if it was),
then it is not a solution.
MULTIPLE CHOICE
D) If the discriminant of a parabola is less than zero and the leading coefficient of the
corresponding quadratic equation is positive, what are the two possible quadrants
in which this parabola could be graphed? (Choose the best answer.)
a)
b)
c)
d)
Quadrants III and IV because this parabola opens down and has two x-intercepts.
Quadrants III and IV because this parabola opens up and has two x-intercepts.
Quadrants I and II because this parabola opens up and has no x-intercepts.
Quadrants I and II because this parabola opens down and has no x-intercepts.
The correct answer here is “c”. Because the discriminant (b2 – 4ac) is < 0, there are not
solutions to this quadratic equation – and consequently no x-intercepts, let’s remember.
Because the leading coefficient is positive, this parabola opens up. Therefore, the
parabola must be graphed in the quadrants I and II if it is going to open up and never
cross the x-axis.
My advice when answering the multiple choice questions is to first answer the
questions in your head and look for the answer that matches up with what you have
already decided. Do not read through the options as a means to figure out which one
it is, unless of course, you have absolutely no idea as to what the answer might be.