DP Math AI Year 1: 8th Period-8th: M-Th: 2:25-3:16, F: 1:38-2:16 Assignments

Practice problems for the week of 5/17.

We will be working on slide 1 in class today (Friday, 5/7).

Good morning and happy Friday everyone!

I will be taking a religious day off today as it is Greek Orthodox Good Friday (Easter is this Sunday).  


During today's class, please watch the attached Objective 3 Guided Notes Video (sine rule) from the beginning until 22:00.  While watching the video, complete the Jamboard slides.  This assignment will be counted as a Criterion B quiz grade!

We will be working on these two problems in class on Wednesday, 4/28.  

Please upload a picture of your work from today's Kahoot review.

During today's class, please complete the following modeling practice. Now that you have had some time to work on these problems, here are some hints if needed:

a: c = 0

b: Find h(3)

c: 0 = -t^2 + 7t... can use Quadratic Formula to solve for the time.

d and e: 10 = -t^2 + 7t... You can use factoring, Quadratic Formula or GDC to solve for the two times.

f: x-coordinate of vertex. x = -b/2a

g: y-coordinate of vertex. Find h(-b/2a)

h: 5 = -t^2 + 7t (intersection points on GDC) --> Should be between two times

i: 8 = -t^2 + 7t (intersection points on GDC - but this time SUBTRACT the times)

Please try your best and finish as many problems as you can in the 50 minute class period. Show work for partial credit or for follow through (F/T) points.

Slide 6 the last one at the bottom... First put the equation in factored form and then use FOIL/box method to get the value of b, which the number before x.

Slide 7 the one on the left... Get your two solutions and then find the x-coordinate of the vertex using r1 + r2 / 2. Substitute that value for x into the equation given in order to get the y-value of the vertex or d in the problem.

Slide 7 the last one on the right... The easiest way is to FOIL the answer choices and see which one gives you the original equation. Keep in mind that the square root of a times the square root of a equals the square root of a squared which is just a (the square root and squared cancels).

We will complete #1 - #3 together as a class today, Tuesday, 2/9. #4-#6 is individual/small group practice. We will have class time on Wednesday, 2/10 to finish these. There will be a two question quiz on this material on Thursday, 2/11.

These are the problems you are going to work on in class on Monday. Feel free to get a head start if you'd like. Please write directly on this Jamboard and/or place a picture of your work on this Jamboard.

ANSWSERS:
1. B
2. D
3. A
4. B
5. x-int, y = 0
5/2 or 2.5
6.D
7. 9
8.A
9. 13
10. -14
11. D
12. A
13. A
14. 0.15($95.00) --> Discount amount
0.85($95.00) --> New sale price of the boots with the 15% off
15. 1,600
16. 2,048 - 1, 200 = 848
17. f(8) = 22
f(-5) = -17
= 22 - (-17)
= 39
18. B
19. 1.03
20. 600(1.03)^10 = 806.349
600(1.035)^10 = 846.359
= 846.359 - 806.349
= 40
21. 2 or 8 (pick one answer)
22. A
23. A
24. A

Please write your answers directly on the Jamboard.

Answers to Exponential Functions Practice:

1a-i: a = 4
1a-ii: b = 1
1b. y = 3 (make sure to include y = 3 because the horizontal asymptote is an equation)
1c: Domain: xER Range: y > 3

2a-i: (-1, 0) (x-int, y = 0)
2a-ii: (0, -1) (y-int, x = 0)
2b: Use the table to help you graph both graphs. Make sure you graph when x = -3 to see ALL intersection points)
2c: x = 1.34 or x = -2.96
2d: -2.96 < x < 1.34
2e: x < -2.96 or x > 1.34

3. At the beginning 840 fish were counted. t = time, N(t) = the number of fish.
a. t = 0, N(t) = 840
840 = a(b)^-0 + 40
840 = a(1) + 40 (b^-0 = 1)
800 = a

b. t = 4, N(t) = 90
N(t) = ab^-t + 40
90 = 800(b)^-4 + 40 (Use the table to solve this: Y1 = 90 and Y2 = 800(b)^-4 + 40)
b = 2

c. The asymptote is the value of p. p = 40

4.
a. At the start t = 0, N = ?
N = 2(1.81)^0.7t
t = 0
N = 2(1.81)^0.7(0)
N = 2(1)
N = 2

b. t = 5
N = 2(1.81)^0.7(5)
N = 15

c. t = ?
N = 150
150 = 2(1.81)^.7t (Use the table to solve this --> Go to 2nd Window and change the "Triangle Tbl = .1)
Y1 = 150 and Y2 = 2(1.81)^.7t)
t = 10.4

This week's practice problems.

Extra Credit opportunity!

For those students that have finished the Geometric weekly practice problems

#1: A geometric sequence has 1,024 as its first term and 128 as its fourth term.
a. Find the value of the common ratio (hint: you can find the cube root of .125 using the MATH button and then hit "4" on your GDC).
b. Find the value of the eleventh term.
c. Find the sum of the first eight terms.
d. Find the number of terms in the sequence for which the sum first exceeds 2,047.968.


#2: a. Consider the geometric sequence u1= 18, u2 = 9, u3 = 4.5,...
a. Write down the common ratio of the sequence.
b. Find the value of u5.
c. Find the smallest value of n for which un is less than 10 ^-3 (.001)

CORRECTION: On slide 6, change the 12.6 answer to --> .957

Hints:
Slide 4: Un = 0 since the tank needs to empty. d = -183. You will need to round up your answer so that the tank is completely empty.
Slide 10: To get the r divide: 162/486: 486, 162, ...

#1
a: u11 = $160
b: S12 = $1,380
c: u11 = $155.62
d: S12 = $1,283.06
e: 17 weeks
The SUM formula from the tea shop (Y1) should be greater than the SUM formula from the cafe (Y2). So, 60(1.1^n - 1)/1.1-1 > x/2((2*60) + (x-1)10)
Y1 = 60(1.1^n - 1)/1.1-1
Y2 = x/2(2*60 + (x-1)10)
Then use the TABLE to find the value of x where Y1>Y2.

#2:
a: 21 = u1 + 6d
b: 29 = u1 + 10d
c: d = 2, u1 = 9
d: S30 = 1,140 mg
e: u5 = 1.25 mg
f: k = 10 20(.5)^(x-1) < .06
Y1 = 20(.5)^(x-1)
Y2 = .06
Then use the TABLE to find the value of x where Y1g: S10 = 40 (n = 10, from part f)

Answers: Check your answers before submitting... of course show all work - don't just copy the answers! Let me know if you are stuck on any of this!)

1) a: u18 = 475
b: S18 = 4,725

2) a: 79,0000
b: 55,000 + (n-1)6000
c: 335,000

3) a: 12 = u1 + (3-1)d
27 = u1 + (8-1)
b: u1 = 6, d = 3
c: S48 = 3,672

4) a: 100 = u1 + (6-1)d
b:124 = u1 + (10-1)d
c: d = 6, u1 = 70
d: S20 = 2,540

5) a: d = 3
b: S10 = 245

6) a: u5 = 1,212
b: 1064 + (n-1) < 2014 (this is the inequality you need since the problem states UP TO the year 2014)
n < 26 (need to round down since you won't see the comet 27 times)

7) a: S10 = 200 (use the SUM formula since the question is asking for the TOTAL saved)
b: n =15 (see work below)
450 = n/2[2(2) + (n-1)4] (distribute the 4)
450 = n/2[(4 + 4n - 4)] (combine like terms)
450 = n/2(4n) (multiply)
450 = 2n^2 (divide both sides by 2)
225 = n^2 (square root of both sides)
15 = n

Directions: After reading the Summer Jobs text below and attached...
1.) Add at least one in either or both columns
2.) Add your name in parentheses at the end of your answer

Summer Jobs:
You are looking for a summer job with McDonalds or Burger King. McDonalds employees will receive $0.01 for the first day’s labor and then McDonalds agrees that each additional day you stay on the job, your daily wage will be doubled. So, if you work at McDonalds you will get $0.02 on the second day, $0.04 on the third day, and so on. On the other hand, Burger King offers employees $150 for the first day’s wage and an increase of a $100 raise every day you stay on the job. So if you work at Burger King, you will get $250 on the second day, $350 on the third day, and so on.

Answers:
5a: (1, -2)
5b: -3/4
5c: 0 = -3x - 4y - 5

6: y = 4/3x - 5/2

Answers:
3a: y = 1/2x + 7/2
3b: (3, 5)
3c: -2x - y - 4 = 0
3d: k = -4
3e: 2.24
3f: (5/3, 13/3)

4a: -3
4b: y = -3x + 12
4c: x = 4

Answers:
1ai: -2
1aii: 10
1b: y = -2x + 3
1c: (3/2, 0)
1e: No solution
1f: (-2, 7)

2a: 0.0390625 (make sure calculator is in DEGREE mode and not radian)
2bi: 0.04
2bii: 0.0391
2c: 28.0%

On Monday we will be starting our 5th and final objective for this unit - "I can determine the equation of a perpendicular bisector and use perpendicular bisectors to complete a Voronoi Diagram." This is the week's practice problems focusing on perpendicular bisectors and Voronoi Diagrams. We will have workday Wednesday to work on these problems.

Take a picture of your work and upload.

1.) Find the equation of the perpendicular bisector of the line segment whose endpoints are A(-2, -3) and B(2, 7). Give your answer in the form ax + by + d = 0 where a, b, and d are integers.

2.) Write any questions you may have about perpendicular bisectors.

This week's practice problems - not due until Friday, but feel free to get a head start if you'd like. We will use Workday Tuesday of this week to work on this.

We will be looking at system of equations problems this upcoming week. This is the weekly assignment that will be due on Friday. We will have Workday Wednesday to work on this in class (for those not taking the PSAT). Feel free to get a head start on this if you'd like!

Please show all work, either on a physical copy of this assignment, or on a blank sheet of paper. Make sure to LABEL all work, and CIRCLE answers. When you are finished, submit a picture here.

Upload a picture of today's warm-up problems here.
Line L1 passes through the points A(-2, 4) and B(2, 7).
a. [2 marks] Write the equation of L1 in gradient-intercept form.
b. [2 marks] Write the equation of L1 in the form ax + by + d = 0 where a, b, and d ϵ Ζ .
c. [4 marks] Find the x-and y-intercepts of L1
d. [2 marks] Line L2 has equation x + 4y - 2 = 0. Find the point of intersection between L1 and L2.

You will have an opportunity to do quiz corrections and earn 1/2 the points back on your quiz! Here's what you need to do to earn 1/2 points back:
1.) For the problems you got wrong, show your work and get the correct answer
2.) If you can't show your work, EXPLAIN how you got the correct answer (answers only without work or an explanation will NOT be given credit back)
3.) Take a picture of your work and answers or explanations and upload it here

Due: Sunday, 10/4 --> If you want to go over anything, let me know! I'm available during 4th, 6th and after school.

These are the linear functions practice problems that we will be working on in class on Friday's workday.

ALL students will upload their answers/work to ALL 5 problems on the Google Classroom assignment.

Groups will be responsible for posting the following problems in class on Friday on the Jamboard.
Group 1: Problems 1
Group 2: Problems 2
Group 3: Problems 3
Group 4: Problems 4 & 5

You will have all period to work on this Gradient Investigation. Please show all work, either on a physical copy of this assignment, or on a blank sheet of paper. Make sure to LABEL all work, and CIRCLE final answers. When you are finished, submit a picture of your work/answers on the Google Classroom assignment.

This will be graded as a Criterion B: Investigating Patterns so take your time and answer each question to the best of your ability.

Please start working on the midpoint and distance Jamboard problems in your notebook. On Friday, 9/18 we will get into small groups to discuss and work on these problems. ALL students should upload their work/answers to all 4 slides (8 problems total by Tuesday, 9/22)

Please take a picture and upload your notes/practice problems from this week for the significant figures & percent error practice problems. We will have class time today to upload this.

What better way to learn about Jamboard then to create a Jamboard! This is a technology tool that we will be using throughout the school year which is great for presenting math problems. I thought it would be nice for us to introduce ourselves to one another by creating a Jamboard slide. Please read the directions on slide 1 and then create your own slide that you will then share with our class on Wednesday, 9/9. I thought I'd post this assignment early, in case anybody wants a head start. Have fun with this one - I can't wait to see your slides!