The document discusses various online tasks completed by Bianca Pilar including: 1) A task on adding and subtracting fractions with dissimilar denominators which explained the process of finding the least common denominator. 2) Evaluating functions at given values and determining if binomials are factors of polynomials. 3) A reflection on the tasks noting difficulties with carelessness when solving problems multiple times and with fractions with dissimilar denominators. Strengths included note-taking and meeting deadlines while weaknesses involved math topics like linear programming and word problems.

2. Online Tasks

3. Task 1:

4. Task 3: Fractions Task 4 :
Task 5:
Bianca Marie Z. Pilar J une 3, 2013
DFM8 A lgebra-X Task 3
How to Add or Subtract Fractions with Dissimilar Denominators:
Adding fractions with dissimilar fractions:
First we need to find the Least Common Denominator (LCD) which is the Least
Common Multiple of the denominators.
Ex.
1/4 + 3/2= ?
(To get the LCM, we can list down the multiples of 4 and 2)
The multiples of 4 are 4, 8, 12, 16, 20….
The multiples of 2 are 2, 4, 6, 8, 10….
The LCM of the denominators 4 and 2 is 4. So the LCD is 4.
Now change ¼ by multiplying both their numerator and denominator of the other fraction
which is 2.
1 x 2 = 2
4 x 2 8
Now change 3/2 by multiplying both their numerator and denominator of the other
fraction, which is 4.
3 x 4 = 12
2 x 4 8
So now both the fractions have the same denominator, we can add them.
1/4 + 3/2
= 2/8 + 12/8
= 2 +12/8
= 14/8
Now we can still simplify 12/8, using the LCM of both the numerator and the
denominator, which is 4. So we divide 12 and 8 by 4.
12/ 4 = 3
8/4 = 2
3/2 is now the final answer.
Subtracting fractions with dissimilar fractions:
Same process as addition:
4/3 - 4/9 = ?

5. Task 6 Task 7:
Task 8:

6. Task 9: Task 10:Bianca Pilar
DFM8
Task 11:

7. Task 12:
Task 13:

8. Task 14:
Task 15: Task 16:
Bianca Marie Z. Pilar
DFM8
Evaluate each function at the given value.
f(x) = -x^3 + 6x – 7 at x =2
=-(2)^3 + 6(2) – 7
= -8 + 36 – 7
= 21
f(2) = 21
f(x) = x^3 + x^2 – 5x – 6 at x=2
= (2)^3 + (2)^2 – 5(2) – 6
= 8 + 4 – 10 – 6
= -4
f(2) = -4
State if the given binomials is a factor of the given polynomial
(k^3 – k^2 – k – 2) / (k-2)
Yes, it is a factor
(b^4 – 8b^3 – b^2 + 62b – 34) / (b-7)
No, it is not a factor.

9. Task 17
Task 18:
Task 19:

10. Task 20:
Task 21:
Task 22:

11. Task 23:
Page 1 Page 2

12. Page 3 Page 4

13. Page 5 Page 6

14. Task 24:

15. Task 25

16. Reflection/Learning Gained/ Difficulties
encountered for online tasks
 Reflection - I should be more careful and watchful of my problem
solving and plotting the points. I’ll try harder next time not to get
confused with for example, which part to shade or should it be a
straight line or dashed.
Its hard to answer a test if both you and your partner don’t know the
answers, so we had to really think deeper thank our stock knowledge
because we weren’t prepared. We just shared answers in each number
then discussed.
I realized how even though the article I’ve just read has been repeated
to me numerous times, it doesn’t change the fact that it is true, I
should learn to be more responsible when it comes to school works or
preparing for an exam.
I learned how to think thoroughly when it comes to math, not just to
answer without thinking. I was able to reflect on what I generally
think of algebra and how I react to it or affects me.

17.  Learning Gained
I learned how to think thoroughly when it comes to math, not
just to answer without thinking. I was able to reflect on what I
generally think of algebra and how I react to it or affects me. I
should also be more careful in plotting the points. I should be
prepared more, broaden my studying range. Also maybe
reviewing with my partner. Though we still worked together
with a strategy. I also was able to review about operations of
fractions. And from what I’ve learned from the article regarding
studying habits, that its best if I don’t wait til the last minute to
cram, and avoid procrastination. Always keep a schedule and
follow it so you’d know when to start doing tasks orderly.

18.  Difficulties
I had a difficult time solving the problems correctly 3 times in a
row. My carelessness would be the reason why I’d make such a
small mistake in my solutions. I also had a hard time answering
the test, because I was prepared for word problems when it
didn’t appear on the test so basically the whole long quiz I had a
hard time. Answering fractions with dissimilar denominators
weren’t my strong points in Math. Lastly, I had a hard time
trying to remember the basic algebra topic that I’ve already
encountered in highschool. Algebra was never really one of my
best subjects.

19. Notes

50. Reflection/Learning Gained/ Difficulties
encountered for online tasks
 Reflection – I take down notes while listening to the teacher
discussing. It helps me to understand the topic easier. I also
can’t stand just listening to the topic while not doing
anything at the same time, that’s why I take anything down
that’s written on the board or powerpoint if necessary. Plus
at least if I don’t understand the topic, it helps for me to look
at my notes, and I’ll be able to remember the topic.
 Learning – I learned that taking down notes is essential.
Very useful when it comes to reviewing.
 Difficulties – I sometimes have difficulties when it comes to
graphing graphs on my notebook since my notebook only
has straight lines and no graphs.

51. Short and Long Quizzes

66. Reflection/Learning Gained/ Difficulties
encountered for online tasks
 Reflection – I’ve noticed that I’ve been getting better at the
recent short quizzes than the ones before.
 Learning – I learned that in order to get a high grade for the
daily short quiz, I have to study the day before. It gets me to
review the last topics and not forget, which is very useful
since even when people say that its good to review the
lessons even though there’s no test, I still don’t do it.
 Difficulties – I have difficulties with remembering all the
topics especially if we have a long quiz about a topic that
was discussed a month ago, I would have a harder time
trying to review the topic.

67. Midterm Exam

69. Reflection/Learning Gained/ Difficulties
encountered for online tasks
 Reflection – I was relieved, because 25 items was already
little for me and it gives me ample time to answer them all.
There were some items I wasn’t able to answer, so I just left
them blank first then come back for it later.
 Learning – I learned to take my time, don’t just guess the
answers when you see your blockmates already finished
and getting out of the classroom. I shouldn’t be in a hurry to
join them because the test is very important.
 Difficulties - there were a few numbers that I didn’t really
know how to solve so I tried my best to think hard about the
question, analyzing it, see if I can remember any details
from the book or my notebook.

70. Strengths and Weaknesses
 Strengths:
Listening to the professor and copying notes at the same time
Last minute cramming
Answering moodle tasks before the said deadline
 Weaknesses:
Getting all the moodle tasks answers correct
Linear Programming
Completing the square and square root property
Word problems; everything except number relations and work
Fractions