Gateway Quiz #1 Results:
• Average class score: xx.x%
• Number of students who passed: x
(Passing the Gateway requires a perfect score of 8/8, and
very few students score 100% on the first try…)
• Common errors on the Gateway:
• Not simplifying fractions.
• Misplaced negative signs.
• Not following the order of operations.
• The next Gateway will be given in class in about 2 weeks.
(Those who have scored 8/8 on the first one don’t have to
take it again.)
Next Gateway:
•
The next Gateway will be given in class about 2 weeks from now.
•
Before that day, each student who did not score 8/8 on the first
Gateway must go over that online quiz and the paper worksheet you
get back today one-on-one with a teacher or TA and get a signature
from them on the bottom of the second page of the quiz. This can be
done either in the open lab or in any class session after lecture.
•
After reviewing that worksheet, the TA or teacher will give you a paper
copy of another practice Gateway to take in the lab at that session. They’ll
grade it for you when you finish and then they’ll review with you any
questions you missed.
•
You must show your classroom teacher the signed quiz before you
will be allowed to take the next version.
•
You should also take the online practice Gateway again before the
next in-class Gateway. You can do this as many times as you want
to, so work on it until you can score 100%.
Online Quiz #1 Results:
• Average class score after partial credit: xx.x%
• Commonly missed questions: # x, x, x, x
Grade Scale
Grade
A
A-
B+
B
B-
C+
C
C-
F
Points
≥925
≥900
≥875
≥ 825
≥800
≥775
≥725
≥700
<700
% Score ≥ 92.5
≥ 90
≥ 87.5
≥ 82.5
≥ 780
≥ 77.5
≥ 72.5
≥70
< 70
Make sure you review all
problems you got wrong on
Quiz 1.
(Do this by clicking on Gradebook, then click Review,
and go over your quiz and your paper answer sheet.)
TAs in the open lab can help you understand how to
do any problems you got wrong.
These sections will be tested again on
Test 1 and on the final, and you’ll
need to continue using these skills
on upcoming homework sections.
NOW PLEASE
CLOSE
YOUR LAPTOPS
and prepare to
take notes.
Section 2.1
A term in an algebraic expression is
the product of a real number and variables
(or variables raised to powers) , or
 a real number by itself.

The number part at the front of the term is called a
coefficient.
Examples of Terms:
5x3
(coefficient is 5)
4xy2
(coefficient is 4)
z2
(coefficient is 1)
-10x
(coefficient is -10)
-y
(coefficient is -1)
7
(coefficient is 7)
NOTE: If a variable does not have a power after it, the power is
understood to be 1. Example:
In the term 4xy2, the coefficient is 4, the power (or exponent) of the
x term is 1 (x = x1), and the power of the y term is 2.
In the algebraic expression 7x5 + x2y2 – 4xy + 7,
there are 4 terms:
7x5, x2y2, -4xy and 7.
The coefficient of term 7x5 is 7,
The coefficient of term x2y2 is 1,
The coefficient of term –4xy is –4 and
The coefficient of term 7 is 7.
7 is called the constant term. (no variable part, like x or y)
Like terms are terms that contain exactly the
same variables raised to exactly the same
powers (i.e. the variable parts are “alike”.)
To combine like terms, add or subtract the numerical
coefficients (the numbers in front of the letters), then
put that combined number in front of the variable
(letter) part.
Examples:
3x + 5x = 8x
10y2 – 6y2 = 4y2
Note: The coefficients of unlike terms cannot be combined to make
one term. Examples:
3x + 3y (cannot be combined into one term)
10y2 – 6x2 (cannot be combined into one term)
Examples of Combining Terms:
Terms Before Combining:
6x2 + 7x2
19xy – 30xy
13xy2 – 7x2y
After Combining Terms:
13x2
-11xy
Can’t be combined (since
the terms are not like
terms)
Problem from today’s homework:
Example:
Simplify 4(2x + 3) – 2(3x – 1)
Solution: 4·2x + 4·3 – 2·3x – 2·(-1)
= 8x + 12 – 6x + 2
= 8x – 6x + 12 + 2
= 2x + 14
Example:
Subtract 4x – 7 from 8x + 10
Solution: 8x + 10 – (4x – 7)
= 8x + 10 – 4x + 7
= 8x – 4x + 10 + 7
= 4x + 17
Problem from today’s homework:
Note that this problem requires skills from
several different Gateway problems.
Make sure you combine like terms and
simplify all fractions in your final answer!
Example:
Simplify 0.4y – 6.7 + y – 0.3 – 2.6y
Solution: 0.4y + 1y – 2.6y – 6.7 – 0.3
= (0.4 + 1 – 2.6) y – 7.0
= -1.2y – 7.0 or -1.2y - 7
Example
Add or subtract each of the following, as indicated.
1) (3x – 8) + (4x2 – 3x +3) = 3x – 8 + 4x2 – 3x + 3
= 4x2 + 3x – 3x – 8 + 3
= 4x2 – 5
2) 4 – (-y – 4) = 4 + y + 4 = y + 4 + 4 = y + 8
3) (-a2 + 1) – (a2 – 3) + (5a2 – 6a + 7) =
-a2 + 1 – a2 + 3 + 5a2 – 6a + 7 =
-a2 – a2 + 5a2 – 6a + 1 + 3 + 7 = 3a2 – 6a + 11
Example:
Write the following phrase as an algebraic
expression, then simplify:
The sum of 2, three times a number, -9, and four
times a number
Solution: Let x stand for the number.
Then the sum is:
2 + 3x + (-9) + 4x Now simplify:
= 3x + 4x + 2 – 9
= 7x - 7
Problem from today’s homework:
Example:
Write and simplify an algebraic expression for the
perimeter of a rectangle whose length is 3x feet and
whose width is 2x + 1 feet.
NOTE: It always helps
to draw a picture!
Solution: Remember that the perimeter of a figure is
the sum of all the sides of the figure.
A rectangle has four sides: two sides equal to the
length and two sides equal to the width.
Therefore the perimeter is 2 lengths + 2 widths
= 2(3x) + 2(2x + 1)
= 6x + 4x + 2
= 10x + 2
Homework for Section 2.1
is due before the start
of the next class period.
Reminder: You should be doing this homework
without using a calculator,
because calculators can’t be used
for Quizzes 1 or 2, Test 1 ,
or the Gateway Quiz.
DON’T FORGET TO GO OVER YOUR
GATEWAY QUIZ WITH A TEACHER OR TA
AND HAVE THEM SIGN OFF ON PAGE 2.