The document provides a review for a final exam, including the following:
1) It reviews rational expressions and equations, as well as radicals.
2) Sample exam questions are presented in various math topics.
3) Notes are provided about the schedule, including the date of the final exam on rational expressions and equations, due dates for Khan Academy topics and class work, and upcoming STAR math testing.
4) The final part states that all of the sample questions were taken from versions of the upcoming final exam.
Suppose you are sitting in algebra class and a funny thing happens - your teacher catches your attention! This happens when she says that she will cut class short by 5 minutes if anyone in the class can find two numbers, x and y, such that both of the following equations are true:
For a system involving two variables (x and y), each linear equation determines a line on the xy-plane. Because a solution to a linear system must satisfy all of the equations, the solution set is the intersection of these lines, and is hence either a line, a single point, or the empty set
This presentation will be very helpful to learn about system of linear equations, and solving the system.It includes common terms related with the lesson and using of Cramer's rule.
Please download the PPT first and then navigate through slide with mouse clicks.
Suppose you are sitting in algebra class and a funny thing happens - your teacher catches your attention! This happens when she says that she will cut class short by 5 minutes if anyone in the class can find two numbers, x and y, such that both of the following equations are true:
For a system involving two variables (x and y), each linear equation determines a line on the xy-plane. Because a solution to a linear system must satisfy all of the equations, the solution set is the intersection of these lines, and is hence either a line, a single point, or the empty set
This presentation will be very helpful to learn about system of linear equations, and solving the system.It includes common terms related with the lesson and using of Cramer's rule.
Please download the PPT first and then navigate through slide with mouse clicks.
Quadratic equations are explained in simple steps to meet your level of understanding. Please provide feedback so we improve our program for your learning benefit.
1. Review for Final Exam
Review Rational Expressions & Equations
Final Class Work Distributed
2. Jeanette bought 2 scoops of ice cream and 3 brownies for
$4.40. Nanette bought 3 scoops of ice cream and one brownie
for $5.20. How much was each item?
20% of what number is 80?
A) 40 B) 16 C) 1600 D) 400 E) 160
3.
4.
5. A 40" piece of wood was cut into three pieces. The lengths of
the three pieces were: 2x -5, x + 7, and x + 6.
What was the length of the longest piece?
6. Bonus Question: 10 pts.
(Submit answers before the end of class)
Hint: You can call the middle number 'two spoons and a fork'
if you want, but the relationship between any three
consecutive numbers is always the same.
8. Notes
1. Our last test before the final exam will
be on Wednesday, June 3rd.
2. Last Khan Academy topics are due this
weekend.
3. The Last day to submit class work is
Friday, June 5th.
4. STAR Math Testing still to come before
end of year.
Warm-Up Section of notebook
9. All of today's questions were taken from the 4
versions of the final exam
Final Exam Review: Radicals
10. Find the LCD of the following
rational expression. 124
3
,
6
1
y
x
y
yy 326 )3(2)3(4124 2
yyy
)3(12)3(32isLCDtheSo 2
yyyy
Find the LCD of the following rational expressions.
xx 3
2
,
3
1
Both of the denominators are already factored.
Since each is the opposite of the other, you can
use either x – 3 or 3 – x as the LCD.
Adding & Subtracting Rational Expressions
12. Multiply the 1st fraction by an equivalent form of
the number 1 so the denominators are the same.
95
729
3
yy
5
9
3
y 4
4
5
8
8
9
3
y
y
y 9
4
72
24
y
y
Multiplying & Dividing Rational Expressions
13. Multiplying & Dividing with Polynomials
Factor numerators and denominators first.
Then, multiply (don’t FOIL, keep in factored form)
Simplify. Divide: (Factor by Grouping)
Simplify:
14. Solve the following
rational equation.
What is the LCD?
2613 xx 2633 xx 233 x
13 x
3
1x
Solving Rational Equations: Last Practice Problem