Question: Simplify: (log210)(log48-log3)
Solution: (log10/log2)(log16)
=(1/log2)(log2^4)
=4log2/log2
=4
Wednesday, November 25, 2009
Test Question
1st question (2 marks)
Convert expression into a single expression logarithm:
½ln(x) - 2 ln(x-1) - 1/3 ln (x²+1)
=ln √(x) - ln(x-1)² - ln ³√(x²+1)
= ln (√x)/ [ (x-1)² * ³√(x²+1) ] <--- Log Law #2.
surprisingly, thats all you have to do for that question (simplify)
2nd question (1 mark)
Express log 6 1/216= -3 in exponential form
6^-3= 1/216
3rd question (1 mark)
Evaluate ln ( 1/ 4√e)
*multiple choice here guys..
a) ¼
b) -¼
c) -4
d) 4
Convert expression into a single expression logarithm:
½ln(x) - 2 ln(x-1) - 1/3 ln (x²+1)
=ln √(x) - ln(x-1)² - ln ³√(x²+1)
= ln (√x)/ [ (x-1)² * ³√(x²+1) ] <--- Log Law #2.
surprisingly, thats all you have to do for that question (simplify)
2nd question (1 mark)
Express log 6 1/216= -3 in exponential form
6^-3= 1/216
3rd question (1 mark)
Evaluate ln ( 1/ 4√e)
*multiple choice here guys..
a) ¼
b) -¼
c) -4
d) 4
Thursday Test Question
This is my test question:
Solve for x: ln6+ln(x−2)=−2
(Express your answer correct to 3 decimal places.)
This question is worth 3 marks as well
Here is the method I used to get the answer:
ln[6(x-2)]=-2
ln(6x-12)=-2 (1 mark here)
(e^-2)=6x-12
6x=(e^-2)+12
x=(e^-2)+12/6 (1 mark here)
x=2.022 556
x=2.023 (1 mark here)
(that's where the marking guide said the marks should be awarded)
I would suggest to everyone that you go over all the test questions mentioned on here. This way you know what you will have to answer and how to do it. Good Luck to everyone!
Solve for x: ln6+ln(x−2)=−2
(Express your answer correct to 3 decimal places.)
This question is worth 3 marks as well
Here is the method I used to get the answer:
ln[6(x-2)]=-2
ln(6x-12)=-2 (1 mark here)
(e^-2)=6x-12
6x=(e^-2)+12
x=(e^-2)+12/6 (1 mark here)
x=2.022 556
x=2.023 (1 mark here)
(that's where the marking guide said the marks should be awarded)
I would suggest to everyone that you go over all the test questions mentioned on here. This way you know what you will have to answer and how to do it. Good Luck to everyone!
Transformations Questions
Questions: #13 - 2 marks (1 per letter)
#14 - 3 marks (1 per letter)
http://www.bmlc.ca/Math40S/Pre-Calculus%20Math%2040s%20Standards%20Test%20-%20Transformations%20QUESTIONS.pdf
Answers Link:
http://www.bmlc.ca/Math40S/Pre-Calculus%20Math%2040s%20Standards%20Test%20-%20Transformations%20ANSWERS.pdf
#14 - 3 marks (1 per letter)
http://www.bmlc.ca/Math40S/Pre-Calculus%20Math%2040s%20Standards%20Test%20-%20Transformations%20QUESTIONS.pdf
Answers Link:
http://www.bmlc.ca/Math40S/Pre-Calculus%20Math%2040s%20Standards%20Test%20-%20Transformations%20ANSWERS.pdf
Test Questions
Here are my questions for our test tomorrow:
1) Point P is a point on the terminal arm of an angle Θ in standard position. If cscΘ<0 and sin theta=-15/17, deterine the value of the other five trigometric functions.
2)P(Θ) is a point on the unit circle. If secΘ<0 and tan(theta)<0, and the coordinates for P are (x, 2root6/7)
a. Find the value of x
b.State the coordinates of P(Θ+pi)
Solutions:
1)step 1: Determine quadrat-(quadrat III)
step2: Find sinΘ=1-(-8/17)squared=-15/17
Step3: Determine other 4 trig. values
sec=-17/8
csc=-17/15
tan=15/8
cot=8/15
2) a.
step1: determine quadrat-(quadrat 2)
step 2:1-(2√6/7)²=-5/7
b.step1: determine quadrat-(quadrat 4)
step 2: determine integer values for x and y: (5/7, -2root6)
1) Point P is a point on the terminal arm of an angle Θ in standard position. If cscΘ<0 and sin theta=-15/17, deterine the value of the other five trigometric functions.
2)P(Θ) is a point on the unit circle. If secΘ<0 and tan(theta)<0, and the coordinates for P are (x, 2root6/7)
a. Find the value of x
b.State the coordinates of P(Θ+pi)
Solutions:
1)step 1: Determine quadrat-(quadrat III)
step2: Find sinΘ=1-(-8/17)squared=-15/17
Step3: Determine other 4 trig. values
sec=-17/8
csc=-17/15
tan=15/8
cot=8/15
2) a.
step1: determine quadrat-(quadrat 2)
step 2:1-(2√6/7)²=-5/7
b.step1: determine quadrat-(quadrat 4)
step 2: determine integer values for x and y: (5/7, -2root6)
My question.
These questions are pulled from the Mickelson book.The solutions can be found on pages 198 and 199.
Page: 179
Number:16)
Letter: c)
Evaluate(worth one mark):
10! 4! / 8! 6!
= (1*2*3*4*5*6*7*8*9*10)(1*2*3*4) /
(1*2*3*4*5*6*7*8) (1*2*3*4*5*6)
= 9 * 10 /
5 * 6
90 / 30
= 3
Second question (page 180, number 23) (worth two marks):
How many different groups of four letters can be made from the letters A, B, C, D, E, and F if the letters can only be used once?
P(6, 4) = 6! / (6 - 4)! = 6! / 2! =
1 * 2 * 3 * 4 * 5 * 6 /
1 * 2
= 3 * 4* 5 * 6
= 360
We can create 360 groups of four letters from A, B, C, D, E, and F if the letters can only be used once.
Tuesday, November 24, 2009
TEST QUESTION!
HERE WE GO GUYS...QUESTION ON THE FUNDAMENTAL COUNTING PRINCIPLE (FCP)
This is out of the Mickelson (hmm i always thought it was nickleson) book. pg 176.
There are 4 roads between cities A and B, and 3 roads between cities B and C.
a) How many ways can a person travel from A to C through city B??
(4)(3) = 12
b) How many ways can a person make a round trip from A to C and back to A, through city B?
(4)(3)(3)(4) = 144
c) How many ways can a person make a round trip from A to C and back to A through city B, without using any road twice?
(4)(3)(2)(3) = 72
Alright, hope that helped and you all do great
This is out of the Mickelson (hmm i always thought it was nickleson) book. pg 176.
There are 4 roads between cities A and B, and 3 roads between cities B and C.
a) How many ways can a person travel from A to C through city B??
(4)(3) = 12
b) How many ways can a person make a round trip from A to C and back to A, through city B?
(4)(3)(3)(4) = 144
c) How many ways can a person make a round trip from A to C and back to A through city B, without using any road twice?
(4)(3)(2)(3) = 72
Alright, hope that helped and you all do great
Brett's Test Question
Question:
1. a) How many 6 letter arrangements can be made using the letters M A T T E R ? Give your answer as a whole number. (1 mark)
b) How many 6 letter arrangements end with T T? Give your answer as a whole number. (1 mark)
c) How many 6 letter arrangements can be made if the letters M T T R must be together? Give your answer as a whole number. (2 marks)
Solutions:
1. a) 6!/2!= 360
b) _ _ _ _ T T
4!= 24
c) (3!) (4!/2!) = 72
**3 groups, 4 consonants, 2 t's
GOOD LUCK THURSDAY!
1. a) How many 6 letter arrangements can be made using the letters M A T T E R ? Give your answer as a whole number. (1 mark)
b) How many 6 letter arrangements end with T T? Give your answer as a whole number. (1 mark)
c) How many 6 letter arrangements can be made if the letters M T T R must be together? Give your answer as a whole number. (2 marks)
Solutions:
1. a) 6!/2!= 360
b) _ _ _ _ T T
4!= 24
c) (3!) (4!/2!) = 72
**3 groups, 4 consonants, 2 t's
GOOD LUCK THURSDAY!
My test question!
I just got this from accelerated math, so i'll write it out for you as opposed to posting a link!
(Worth 2 marks)
Write as a logarithm of a single expression:
2log5x + 3log5(x+6)
Answer:
= log5x^2 + log5(x+6)^3
= log5x^2(x+6)^3
Taaa Daaaa!
(Worth 2 marks)
Write as a logarithm of a single expression:
2log5x + 3log5(x+6)
Answer:
= log5x^2 + log5(x+6)^3
= log5x^2(x+6)^3
Taaa Daaaa!
Test Question for Nov 26 2009
http://www.bmlc.ca/Math40S/Pre-Calculus%20Math%2040s%20Standards%20Test%20-%20Transformations%20QUESTIONS.pdf
Question #2
a) Worth 2 marks
b) Worth 2 marks
c) Worth 2 marks
Question #11 Part A, B, C and D
Answers can be found here...
http://www.bmlc.ca/Math40S/Pre-Calculus%20Math%2040s%20Standards%20Test%20-%20Transformations%20ANSWERS.pdf
Question #2
a) Worth 2 marks
b) Worth 2 marks
c) Worth 2 marks
Question #11 Part A, B, C and D
Answers can be found here...
http://www.bmlc.ca/Math40S/Pre-Calculus%20Math%2040s%20Standards%20Test%20-%20Transformations%20ANSWERS.pdf
my test questions
HEYYYYYYYY YOUUUUUUU GUYYYYYYYY'S
If you would like the advanced edge on tomorrows upcoming test, here it is.
I Picked two questions, one from exercise 3 and one from exercise 5.
from exercise 3, I picked question 1, part e), which was
find the exact value of tan(7pi/4), show work, ie. unit circle
from exercise 5, question 1
Solve for thaeta where the domain is the set of all reals.
sin thaeta=1/2
answer is pi/6+2kpi where k is an integer
and
5 pi/6 + 2kpi where k is an integer
dont forget to show how you got those answers. ie unit circle
If you would like the advanced edge on tomorrows upcoming test, here it is.
I Picked two questions, one from exercise 3 and one from exercise 5.
from exercise 3, I picked question 1, part e), which was
find the exact value of tan(7pi/4), show work, ie. unit circle
from exercise 5, question 1
Solve for thaeta where the domain is the set of all reals.
sin thaeta=1/2
answer is pi/6+2kpi where k is an integer
and
5 pi/6 + 2kpi where k is an integer
dont forget to show how you got those answers. ie unit circle
In class today Mr. Max gave us more examples on Perms and coms. The first example that we were given showed us how to create possible cases for one question, but after creating the possible cases you combine them together to get the final answer.
Next, we were given the term and definition: Sample Space- some display, rendition, showing all probability outcomes. "has everything" Scrabble was used as the example to explain sample space, which is shown below.
Test has now been moved to Thursday everyone, and there is tutoring today after school with Mr.Max. The Test questions should be posted on to the blog by wither today or tomorrow, where we will be able to see the problems and solutions. Good luck everyone!
Next, we were given the term and definition: Sample Space- some display, rendition, showing all probability outcomes. "has everything" Scrabble was used as the example to explain sample space, which is shown below.
Test has now been moved to Thursday everyone, and there is tutoring today after school with Mr.Max. The Test questions should be posted on to the blog by wither today or tomorrow, where we will be able to see the problems and solutions. Good luck everyone!
Tuesday November 24, 2009- More Perms and Coms!
First of all, TEST MOVEMENT! Instead of Wednesday, we're moving this to Thursday.
What happens if the orderings of perms/coms are circular? i.e) people around a table; bracelets; necklaces; basically things that require objects in sequence on a round form of something.
ex) How many ways can you sit 4 people around a table?
*moving to the cafeteria to do some shananigans around the tables.
-How many things are actually moving?
ANSWER- 3 things are actually moving, which makes the equation 3!
Final answer- 3!= 6 ways
FORMULA: (n-1)!, where n= number of things to order in a circular way.
ex) Regarding this necklace, how many ways can we make this thing unique?
Thinking the same as the previous example? If so, that is incorrect. The 3D object can be flipped around, as shown in the picture. FORMULA: (n-1)!/2
ex) 5 people around a circular table
a) if person A and person B have to sit together?
{(n-1)!} *2 <--- because they can switch around (A-B, B-A) b) if person A and person B can not sit together? FORMULA: (All ways)-(undesired ways)= Answer.
4! - 3!2! = 12 ways
c) person A and person B together; person C and person D together.
2! (from the n-1 ! formula); 2! ways to organize A/B; 2! ways to organize C/D
2! * 2! *2!= 8 ways.
Ordering identical things-
ex) "How many different 'words' are possible with these letters?"
Z O O M
*thinking the answer is 4! ? 24 ways? Wrong, again!
MOZO* is the same as MO*ZO..
FORMULA: total number of ways / "total number of identicals"! = desired ways
ex) S T A T I S T I C S
10 !/ {(3!)(3!)(2!) = 50400 UNIQUE words
What happens if the orderings of perms/coms are circular? i.e) people around a table; bracelets; necklaces; basically things that require objects in sequence on a round form of something.
ex) How many ways can you sit 4 people around a table?
*moving to the cafeteria to do some shananigans around the tables.
-How many things are actually moving?
ANSWER- 3 things are actually moving, which makes the equation 3!
Final answer- 3!= 6 ways
FORMULA: (n-1)!, where n= number of things to order in a circular way.
ex) Regarding this necklace, how many ways can we make this thing unique?
Thinking the same as the previous example? If so, that is incorrect. The 3D object can be flipped around, as shown in the picture. FORMULA: (n-1)!/2
ex) 5 people around a circular table
a) if person A and person B have to sit together?
{(n-1)!} *2 <--- because they can switch around (A-B, B-A) b) if person A and person B can not sit together? FORMULA: (All ways)-(undesired ways)= Answer.
4! - 3!2! = 12 ways
c) person A and person B together; person C and person D together.
2! (from the n-1 ! formula); 2! ways to organize A/B; 2! ways to organize C/D
2! * 2! *2!= 8 ways.
Ordering identical things-
ex) "How many different 'words' are possible with these letters?"
Z O O M
*thinking the answer is 4! ? 24 ways? Wrong, again!
MOZO* is the same as MO*ZO..
FORMULA: total number of ways / "total number of identicals"! = desired ways
ex) S T A T I S T I C S
10 !/ {(3!)(3!)(2!) = 50400 UNIQUE words
Sunday, November 22, 2009
Friday Nov 20. Work Period.
Friday we had a work period to catch up on Accelerated Math, Cumulative Exercises and to work on our 2 questions of our choice picked from Old exams, Cummulitave Excercises, Accel Math, ect to be submit for the test on Wednesday.
It would be wise to be into the Probility on Acell Math and have the following Cummulative Exercises completed prior to Wednesdays test...
**Up to and including**
Ex 1 #1-12
Ex 2 # 1-12
Ex 3 # 1-7
Ex 4 #1-8
Ex 5 #1-12
Ex 6 #1-16
Ex 7 # 1-10
Ex 8 #1-10
Ex 9 # 1-14
Ex 10 # 1-6
Ex 11 # 1-12
Ex 12 # 1-10
Ex 13 #1-10
Ex 14 #1-11
Ex 15 # 1-14
Ex 16 # 1, 2, 4, 6-13
Ex 17 # 1-12
Ex 18 # 1-18
Ex 19 # 1-10
Ex 20 # 1-13
Ex 21 # 1-12
Ex 22 #1-10
Ex 23 # 1-12
Ex 24 # 1-10
Ex 25 # 1-15
Ex 26 # 1-16
Ex 27 # 1-10
Ex 28 # 1-10
Ex 29 # 1-10
It would be wise to be into the Probility on Acell Math and have the following Cummulative Exercises completed prior to Wednesdays test...
**Up to and including**
Ex 1 #1-12
Ex 2 # 1-12
Ex 3 # 1-7
Ex 4 #1-8
Ex 5 #1-12
Ex 6 #1-16
Ex 7 # 1-10
Ex 8 #1-10
Ex 9 # 1-14
Ex 10 # 1-6
Ex 11 # 1-12
Ex 12 # 1-10
Ex 13 #1-10
Ex 14 #1-11
Ex 15 # 1-14
Ex 16 # 1, 2, 4, 6-13
Ex 17 # 1-12
Ex 18 # 1-18
Ex 19 # 1-10
Ex 20 # 1-13
Ex 21 # 1-12
Ex 22 #1-10
Ex 23 # 1-12
Ex 24 # 1-10
Ex 25 # 1-15
Ex 26 # 1-16
Ex 27 # 1-10
Ex 28 # 1-10
Ex 29 # 1-10
Friday, November 20, 2009
Deeper Thinking...
Yesterday in class Mr. Max had us do a different style of assignment. We were to read an article online (link is below in his post) and write our own blog post based on our thoughts on the topic. It was about an agreement made between 2 students and a teacher about having a No Homework agreement where the 2 students would get, well, no homework. Ever.
So, your homework is to write a blog post on what you think about having no homework. Ironic?
We spent the rest of the block working on accelerated math. Try to get that done guys, I know I myself am super far behind and its just taking me ages to get caught up, but once I complete an objective I really do feel like I know what I'm doing for the most part.
REMINDER: Test is next Wednesday, so lets get our study on guys!
So, your homework is to write a blog post on what you think about having no homework. Ironic?
We spent the rest of the block working on accelerated math. Try to get that done guys, I know I myself am super far behind and its just taking me ages to get caught up, but once I complete an objective I really do feel like I know what I'm doing for the most part.
REMINDER: Test is next Wednesday, so lets get our study on guys!
Pilot Exam
I forgot to post this when I scribed for the class on Monday. For anyone who missed Monday's class, we were told that there is going to be a pilot exam (practice exam) for our Grade 12 Pre-Calculus exam after holiday break. This takes place at 12:30 on January 14th. I think this is a great opportunity to get a feel for what the real exam is like as well as to find find out where we need to improve before the actual exam. It is going to take place in Mr. Maksymchuk's room.
Thursday, November 19, 2009
Perms and Coms
Yesterdays class, we learned more about perms and coms. Permulations are the number of possible orderings of a set, provided that the order of set elements matters. An example would be 281-0563 218-0563 560-3812 or books on a shelf, locker combos. The BEST EXAMPLE EVER of a perm, is create 5 letter words from the alphabet no repeats. So you pick any 5 letters, and then you would times 26(because there is 26 letters in the alphabet) then 25 because you used a letter, then 24 b/c you used another letter...etc. you get 7893 600. At that point we learned the formula : 26!/21!=n!/(n-r)! n being the number of items to select from and r being selecting items r at 2 time. "n things, permulated 5 at a time". The second part of THE BEST EXAMPLE EVER is: pizzas. you have peperoni pinapple and ham, either order you put it in, its still the same pizza.
To Homework or Not? That is the question?
http://www.cbc.ca/canada/calgary/story/2009/11/18/calgary-homework-school-students.html
So what do you think? As young adults enrolled in the final year of public education, specifically in mathematics, which side of this 'argument' do you line up on?
Discussion prompts?
Would you like a no-homework agreement?
Would you benefit from a no-homework agreement?
Would you learn enough with no homework?
Do you have enough time in school to both learn and practice?
Is the subject area a consideration when discussing such agreements?
I really don't know the answers, but inspirationally, I know you do. I look forward to reading your responses. Thank you in advance for informing both public education practice generally and specific decisions made in room 204 at the SVRSS.
So what do you think? As young adults enrolled in the final year of public education, specifically in mathematics, which side of this 'argument' do you line up on?
Discussion prompts?
Would you like a no-homework agreement?
Would you benefit from a no-homework agreement?
Would you learn enough with no homework?
Do you have enough time in school to both learn and practice?
Is the subject area a consideration when discussing such agreements?
I really don't know the answers, but inspirationally, I know you do. I look forward to reading your responses. Thank you in advance for informing both public education practice generally and specific decisions made in room 204 at the SVRSS.
Monday, November 16, 2009
Logarithmic Word Problems
Today in class we did logarithmic word problems. For the most part, it is just review from Grade 11 Pre-Calc. The first two images are a little small because of the formatting.
The first thing we did dealt with was radioactive decay and half lives. The first question had to do with finding the amount of substance left after a determined amount of time; In our case, it was 3 years. So, all you have to do is substitute your X value for 3 and from there it becomes calculator work.
The next section had to do with population increase. However, this formula can be used for anything that has to do with exponential growth. In this case, it ts used to show growth rates of bacteria. Also for this one, you just substitute in your values and solve.
Again, we are asked to find the half life of a substance. This question is just like the last one other than it is a different formula. You use natural logarithms to get rid of your e value, use the logarithmic laws, get x by itself, and solve with your calculator.
The first thing we did dealt with was radioactive decay and half lives. The first question had to do with finding the amount of substance left after a determined amount of time; In our case, it was 3 years. So, all you have to do is substitute your X value for 3 and from there it becomes calculator work.
The next question involves a little more work and use of the logarithmic laws. We were asked to find the half life of the substance. What is asked here is what amount of time does it take for the substance to decay to half its original mass. So, we're solving for X. We know that the original mass was 80g so the mass at its half life would be 40g. Our Y value is now 40. Next, you multiply everything by ln. This is usually beneficial because out original question has the variable e in it so there is a good chance that we can get rid of it by using ln. Remember, the ln(80e^-0.2x) is actually ln80+ln(e)^-0.2x since it is a law. Next, we bring down the x value (another law) so we can factor it and get x by itself. From here, it becomes calculator work.
Out next section had to do with compound interest. Our first question had to do with finding the value of the investment after 1 year. All you have to do is substitute 1 in for the t value. From there it becomes calculator work.
The next question had to do with finding the value of the investment after 10 years. Again, just substitute 10 in for the t value and take it from there.
The last question had to do with finding the interest after 10 years. All you have to do for this is find the value of the investment after 10 years and subtract it from the original investment ($5000)
This formula shows what the interest would be if it was compounded all the time as opposed to just monthly or annually. How this formula was derived is that when the interest reaches a very high number, it gets very close to the value e. So the formula (1+r/n)^n simply becomes e^r. The reason why banks don't use this way of compounding interest is because it means more money for the consumer. The use of this formula is strait forward; You just substitute in your values and solve with your calculator.
The next section had to do with population increase. However, this formula can be used for anything that has to do with exponential growth. In this case, it ts used to show growth rates of bacteria. Also for this one, you just substitute in your values and solve.
Again, we are asked to find the half life of a substance. This question is just like the last one other than it is a different formula. You use natural logarithms to get rid of your e value, use the logarithmic laws, get x by itself, and solve with your calculator.
We were assigned 1-16 on exercise 26 and 1-10 on exercise 27.
I think we're assigned up to objective 31 on our accelerated math to be done before our test next Wednesday.
Subscribe to:
Posts (Atom)
