math fundamentals for statistics (math 52) homework unit 1

Homework – Unit 1 –

Math Fundamentals for Statistics (Math 52)

Homework Unit 1: Problem Solving and

Patterns

By Scott Fallstrom and Brent Pickett

“The ‘How’ and ‘Whys’ Guys”


1.1: A First Puzzle to Play With Vocabulary and symbols – write out what the following mean:

Solve a Simpler Problem Concept questions: 1. In your own words, what does it mean to “solve a simpler problem?” Exercises: 2. Molly moves a couple blocks away from school, but still has the problem with the bully. Since

it’s further away she has to leave earlier to get to school on time. Determine the number of different shortest paths that are possible to get to school. From the picture, Molly is now 8 blocks south and 2 blocks west of the school.

3. Solve a similar problem where Molly is now 12 blocks south and 2 blocks west of the school.

4. Solve a similar problem where Molly is now 20 blocks south and 2 blocks west of the school.

5. If Molly lived 5 blocks south and 3 blocks west of the school, and you were asked to find the number of different shortest paths, how would you go about solving the problem? (don’t actually need to solve it, just describe your process.

6. Challenge ☼: Solve the problem for Molly being 5 blocks south and 3 blocks west!

School

Molly


The square above is 4-by-4. Answer some questions about other large squares. 7. How many 1-by-1 squares are in the first shape above?

8. How many 1-by-1 squares are in a square that is 8-by-8?

9. How many 1-by-1 squares are in a square that is 15-by-15?

10. Challenge ☼: How many total squares (of any size) are in the 4-by-4 square above?

Consider the triangles pictured below. 11. How many of the smallest triangle (1 unit per side) are in each of the first 4 shapes?

12. Fill in the table for the pattern above:

13. If the longest side of the triangle has length 37, how many of the smallest triangles will it

have? 14. Challenge ☼: How many total triangles (of any size) are in the triangle with 4 unit sides?

Wrap-up and look back: 15. Write in words what you learned from this first section. Did you have any questions remaining

that weren’t covered in class? Write them out and bring them back to class.

Length of the side of the large triangle

1 2 3 4 5 6 7 8 … n

Number of smallest triangles

1 4 …


1.2: Problem Solving Strategies Vocabulary and symbols – write out what the following mean:

Guess and Check Draw a Picture Logic and Computation

Make a List Write an Equation

Concept questions: 1. Should you use the same problem solving strategy for all problems? Why or why not? Exercises: 2. 20 children come to middle school, each bringing either a wagon (4 wheels) or a scooter (2

wheels). All together there are 76 wheels in the parking lot. How many children rode a scooter to school? Explain how you came up with and checked your answer. Solve this problem using two different problem solving strategies.

3. Elementary school parking lot. 20 children come to school, each bringing either a tricycle (3 wheels) or a bicycle (2 wheels). All together there are 53 wheels in the parking lot. How many children rode their bike to school? Explain how you came up with and checked your answer. Solve this problem using three different problem solving strategies.

4. Picture a high school parking lot. 30 high school students come to school, each bringing either a car, (4 wheels) or a bike (2 wheels), a skate board, (4 wheels), or walk (0 wheels). All together there are 74 wheels in the parking lot. How many children rode their bike to school? Explain how you came up with and checked your answer. Solve this problem using two different problem solving strategies.

5. There are chickens and cows in a pasture. The farmer counts 40 heads and 100 feet. How many cows are in the pasture, and how many chickens are in the pasture? Solve with an efficient method – show your work and explain why you picked the method.

6. At the Thursday Market! An apple and a chair cost $9, while an apple and a t-shirt cost $19. Another person sees that a chair and a t-shirt are $24. How much does each item cost? Solve with an efficient method – show your work and explain why you picked the method.


Problems: SIT DOWN, YOU’RE ROCKING THE BOAT! Picture a long canoe with many people inside. One such canoe is shown below that could hold 7 people (possibly). For this entire puzzle, you will assume that the middle seat begins open. For this problem, there are 3 people on the left (marked with L) and 3 people on the right (marked with R). Everyone must change sides – the people on the right must move to the left, and vice versa. However, since it’s a narrow canoe, only two moves are possible:

a) a person can move to an adjacent empty seat (seen below)

b) or they may step over one person into an empty seat.

7. Determine the smallest number of moves for a 3 person canoe. Solve with an efficient method –

show your work and explain why you picked the method.

8. Determine the smallest number of moves for a 5 person canoe. Solve with an efficient method – show your work and explain why you picked the method.

9. Determine the smallest number of moves for a 7 person canoe. Solve with an efficient method – show your work and explain why you picked the method.

10. Challenge ☼: Determine the smallest number of moves for a 9 person canoe. Solve with an efficient method – show your work and explain why you picked the method.

L L L R R R

L L L R R R

L L L R R R


Ending position

Additional Support Post (if needed)

Starting position

ACE OF CAKES!

There are layers of cake currently on a support post in the “Ace of Cakes” shop. You have been hired to move them to another support post for transportation to a wedding. The boss sets up one additional support post that you could temporarily move a cake layer to if needed. There are rules for moving the layers:

No larger layer can ever sit on top of a smaller layer as it would smash the smaller one. Moving a layer from any post to another counts as 1 move. For safety, you can only move one layer at a time.

11. With these rules, determine the smallest number of moves in order to move all the cake layers to

the final support post; start with 3 cake layers and work your way up to 8. Solve with an efficient method – show your work and explain why you picked the method.

WATER JUGS! You are given two unmarked jugs (large cups) – one will hold 3 units of water, and the other will hold 5 units. Here are the rules for this problem:

You have a virtually unlimited supply of water and may fill the jugs up as often as you like. You may pour one into the other until it is full, but may not partially empty one jug unless the

other is full. Examples:

a) If the 5-unit jug has 4 units inside, you could fill the 3-unit jug and pour it into the 5-unit jug which would leave exactly 2 units in the 3-unit jug.

b) If the 5-unit jug is empty and the 3-unit jug is full, you cannot pour 1 unit into the 5-unit jug leaving exactly 2 in the 3-unit jug, because the jugs are not marked so you wouldn’t know it was exactly 1 unit.

12. Find two different ways to obtain one jug with exactly 4 units of water. Solve with an efficient method – show your work and explain why you picked the method.

13. Find two different ways to obtain one jug with exactly 4 units of water, but this time start with a 7-unit jug and a 10-unit jug. Solve with an efficient method – show your work and explain why you picked the method.

1 2 3 1 2 3


14. Starting with a 7-unit jug and a 10-unit jug, is it possible to obtain one jug with exactly 1 unit? Explain your work (and if there is more than one way!) Solve with an efficient method – show your work and explain why you picked the method.

15. Challenge ☼: Find all the different amounts you could end with in a jug if you started with a 6-unit jug and a 7-unit jug. Solve with an efficient method – show your work and explain why you picked the method.

Wrap-up and look back: 16. Write in words what you learned from this first section.

17. What is the hardest part of problem solving for you?

18. Which of the problem solving methods is your favorite?

19. Did you have any questions remaining that weren’t covered in class? Write them out and bring

them back to class.

1.3: Number Patterns Vocabulary and symbols – write out what the following mean:

None Concept questions: 1. In your own words, could there be more than one answer to a number pattern? Try to explain why

this is the case.

Exercises: For the patterns in this section, try to fill in the next three items in the pattern. Be sure to explain your reasoning. 2. Days Patterns: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday

a. M, W, F, S,

b. T, W, Th, F,

c. O, U, E, H

d. 6, 7, 9,

3. Months Patterns

Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec a. A, E, A, P,

b. U, U, U, E,

c. B, R, R, Y,

d. J, J, A, S,

e. J, F, M, A,

f. M, A, M, J,

g. N, D, J, F,

h. Y, Y, H, L,


4. Letter Patterns using the alphabet: A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z

a. A, D, G, J,

b. K, I, G, E,

c. A, F, K, P,

d. A, C, F, J,

e. V, W, X, Y,

f. Z, V, R, N,

g. A, E, I, …

h. B, C, D, F, G,

5. Number and Symbol Patterns. a. 10, 12, 14,

b. 25, 30, 35,

c. 35, 30, 25,

d. 3, 6, 12,

e. – 1, – 2, – 3,

f. 2, 5, 8, 11,

g. 2, 4, 8,

h. 3, 6,

i. 16, 8, 4,

j. 1, 1, 1,

k. 1, 3, 6, 10,

l. 1, 4, 9, 16,

m. 8, 6, 4,

n.

Wrap-up and look back: 6. What part of this section was the most fun for you?

7. Which patterns are the easiest for you to spot quickly?

8. Were you able to come up with more than one answer for any of the patterns?


them back to class.

1.4: Arithmetic Sequences Vocabulary and symbols – write out what the following mean:

Arithmetic Sequence “a” “d”

Variables Common difference dnaan 1

Concept questions: 1. If a sequence of numbers goes up by 7 each time, would we be able to say that it is arithmetic?

Why or why not?

2. If a sequence of numbers goes up by 1, then up by 2, then up by 3, would we be able to say that it is arithmetic? Why or why not?

3. Do all arithmetic sequences increase in size? Explain.


Exercises: 4. Interpret the given information and then find the missing piece.

a. 201 a and 5d . Find 2a .

b. 701 a and 2d . Find 3a .

c. 541 a and 11d . Find 4a .

d. 1005 a and 50d . Find 7a .

e. 927 a and 9d . Find 26a .

f. 637 a and 11d . Find 6a .

g. 637 a and 11d . Find 5a .

h. 637 a and 11d . Find 4a .

i. 637 a and 11d . Find 3a .

j. 5597 a and 5d . Find 95a .

5. Give the first 3 terms of the following arithmetic sequence and the nth term, na .

a. a = 4 and d = 2

b. a = 4 and d = 3

c. a = 3 and d = 5

d. a = 12 and d = – 2

e. a = 21 and d = – 3

f. a = 25 and d = – 5

g. a = 1 and d = 1

h. a = 10 and d = 10

i. a = 100 and d = 100

j. a = 37 and d = 0

6. Find the term that is requested using the formula dnaan 1 , and use your when this

symbol shows up.

a. Find 5a when a = 13 and d = 5.

b. Find 11a when a = 13 and d = 5.

c. Find 101a when a = 13 and d = 5.

d. Find 5a when a = 13 and d = – 5.

e. Find the 23rd term in a sequence with a = 7 and d = 3.

f. Find the 50th term in a sequence with a = 1 and d = 1.

g. Find 100a when a = 1 and d = 1.

h. Find 67a when a = 573 and d = – 7.

i. Find 25a when a = 37 and d = 11 .


7. Determine whether the sequence is arithmetic. For arithmetic sequences, identify a and d.

Sequence Arithmetic? a d a.

1 1 1 1 11, 1 , 2, 2 , 3, 3 , 4, 4 , 5, 5

2 2 2 2 2 Yes No

b. 2, 6, 12, 36, 72 Yes No

c. 1, 7, 4, 9, 2, 3, 12 Yes No

d. 155, 152, 149, 146, 143, 140 Yes No

e. 1, 8, 18, 818, 8818, Yes No

f. 1, 1, 2, 3, 5, 8, 13, 21 Yes No

g. 11, 11, 11, 11, 11, Yes No

h. 7, 12, 17, 22, 27 Yes No

i. – 21, – 23, – 25, – 27, – 29, – 31 Yes No

8. Let’s explore what happens when we add up terms in an arithmetic sequence. Consider the

arithmetic sequence 5, 6, 7, 8, 9, … a. Find the first 10 terms of a new sequence that is formed by the sums of these terms: the values

would be 5, 5 + 6, 5 + 6 + 7, 5 + 6 + 7 + 8, …

9. Challenge ☼: The sum of n terms in an arithmetic sequence in general is found with the formula:

2

Sum 1 naan . Use this formula to find the sum of the following:

a. 1 + 2 + 3 + 4 + 5 + 6

b. 1 + 3 + 5 + 7 + 9

c. 1 + 2 + 3 + 4 + … + 100

d. 2 + 5 + 8 + 11 + 14 + … + 299

e. Going back to Sections 1.1 and 1.2, do the sequence in the previous problems match any of

the problems done in class or in the homework? Explain.

Wrap-up and look back: 10. How can you quickly tell that a sequence is arithmetic?

11. Why do we find the nth term with a formula?

12. What would it mean if an arithmetic sequence had d = 0?

13. Could you explain how an arithmetic sequence is changing if d was negative? What about if d

was positive ?



them back to class.

1.5: Geometric Sequences Vocabulary and symbols – write out what the following mean:

Geometric Sequence “a” “r” Common ratio

Base Exponent

1 nn raa

Concept questions: 1. If a sequence of numbers goes up by 7 then 8 then 9, would we be able to say that it is geometric?

Why or why not?

2. If a sequence of numbers has the property that the next term is always 3 times the previous term, would we be able to say that it is geometric? Why or why not?

3. Do all geometric sequences increase in size? Explain.

Exercises: 4. Interpret the given information and then find the missing piece.

a. 91 a and 4r . Find 2a .

b. 151 a and 3r . Find 2a .

c. 61 a and 3r . Find 3a .

d. 405 a and 2r . Find 7a .

e. 205 a and 17r . Find 7a .

f. 1007 a and 100r . Find 6a .

g. 1007 a and 2r . Find 6a .

h. 647 a and 4r . Find 5a .

i. 102455 a and 8r . Find 53a .

j. 102463 a and 2r . Find 59a .

5. Give the first 3 terms of the following geometric sequence and the nth term, na .

a. a = 4 and r = 2

b. a = 4 and r = 1

c. a = 3 and r = 3

d. a = 5 and r = 0

e. a = 21 and r = 2

f. a = 73 and r = 2


6. Find the term that is requested using the formula 1 nn raa , and use your when this symbol

shows up.

a. Find 5a when a = 13 and r = 5.

b. Find 11a when a = 13 and r = 2.

c. Find 101a when a = 13 and r = 5. Just write the term out – no calculator needed.

d. Find 6a when a = 2 and r = 3.

e. Find 5a when a = 1 and r = 7.

7. Determine whether the sequence is geometric. For geometric sequences, identify a and r.

Sequence Geometric? a r a.

1 1 1 1 11, 1 , 2, 2 , 3, 3 , 4, 4 , 5, 5

2 2 2 2 2 Yes No

b. 3, 6, 12, 36, 72 Yes No

c. 1, – 3, 9, – 27, 81, Yes No

d. 155, 152, 149, 146, 143, 140 Yes No

e. 1, 8, 18, 818, 8818, Yes No

f. 1, 1, 2, 3, 5, 8, 13, 21 Yes No

g. 11, 11, 11, 11, 11, Yes No

h. 7, 12, 17, 22, 27 Yes No

i. – 21, – 23, – 25, – 27, – 29, – 31 Yes No

8. Challenge ☼: Let’s explore what happens when we add up terms in an geometric sequence.

Consider the geometric sequence 1, 2, 4, 8, … a. Find the first 10 terms of a new sequence that is formed by the sums of these terms: the values

would be 1, 1 + 2, 1 + 2 + 4, 1 + 2 + 4 + 8, …

b. Going back to Sections 1.1 and 1.2, does the new sequence in the previous problem match

any of the problems done in class or in the homework? Explain.

c. There is a formula that can be used for sums of n terms in a geometric sequences:

r

ra

n

1

1Sum . Let’s use this to find the sum of the first ten terms in 1, 2, 4, 8, …


Wrap-up and look back: 9. How can you quickly tell that a sequence is geometric?

10. What would it mean if an geometric sequence had r = 1?

11. Could you explain how an geometric sequence is changing if r was greater than 1? What about if

r was between 0 and 1?

12. What would it mean if a geometric sequence had a = 0? What about r = 0?

13. A popular application for cell phones is Boom Beach. In the game, players can collect stone fragments. Using one of the buildings in the game, players can use 7 fragments to build a statue (Idol) that can be traded for one shard. 7 shards will build a statue (Guardian) that can be traded for one crystal. 7 crystals will build the highest statue (Masterpiece).

a. How many crystals are needed to build a Masterpiece statue? How many shards? How many

fragments?

b. Do these numbers fall into a geometric sequence? Explain.

c. How many fragments are needed to build a Guardian statue?

14. A popular application for cell phones is 2048, a game where tiles with 2 or 4 are randomly put

on the screen. The user will drag a direction (left, right, up, or down) and any tiles that are exactly the same would be added together. Two “2” tiles would combine to be 4. Two “4” tiles would combine to be 8. a. Write out the possible tiles in the game.

b. If you wrote the tiles in order, would it form a sequence we are familiar with? Explain.

c. How many different number tiles are created on the way to making the tile “2048”?

15. Did you have any questions remaining that weren’t covered in class? Write them out and bring them back to class.


1.6: Connections and Other Patterns Vocabulary and symbols – write out what the following mean:

None Concept questions: 1. What is an arithmetic sequence and how can you tell it is arithmetic quickly?

2. What is a geometric sequence and how can you tell it is geometric quickly?

3. Is every sequence arithmetic or geometric?

4. With a sequence like 2, 4, 2, 4, 2, 4, 2, 4, … would it be classified as arithmetic or geometric?

5. With a sequence like 5, 5, 5, 5, 5, 5, … would it be classified as arithmetic or geometric? Exercises: 6. Write the nth term for the following patterns, then answer the questions: could this pattern be

arithmetic (A), geometric (G), or maybe neither (N)? Circle the answer.

Start of the Sequence nth Term Type of Sequence a.

9, 10, 11, 12, A G N

b. 1, 8, 27, 64 A G N

c. 11, 18, 25, 32, 39, A G N

d. 40, 20, 10, 5 A G N

e. 8, 2, 10, 12, 22, 34, A G N

f. 22, 22, 22, 22, 22, A G N

g. 2, 8, 32, 128, A G N

h. 1, 7 A G N

i. 5, 7, 5, 7, 5, 7, A G N


7. Determine the next 3 possible terms of these patterns, and explain your rationale.

a. 1 2 3

, , ,4 4 4

b. 15, 16, 17, 18,

c. 1, 5, 9, 13,

d. 3, 9, 27, 81,

e. 5, 15, 25, 35,

f. 10; 100; 1,000; 10,000;

g. 2, 10, 50,

h. 3, 5, 7, 9,

i. 4, 12, 36,

j. 7, 28, 35,

k. 3, 6, 12, 24,

l. 3, 6, 9, 12,

m. 2, 6, 12, 20,

n. 9, 81, 729,

o. 256, 64, 4,


a. 0.1, 0.2, 0.3,

b. 11, 12, 13,

c. 1.1, 1.2, 1.3,

d. 0.11, 0.22, 0.33,

e. 3.4, 3.5, 3.6,

f. 4, 5, 4,

g. 3.2, 3.4, 3.6,

h. 1.005, 1.006, 1.007

i. ,53

12 ,

53

10 ,

53

8

j. ,28

19 ,

28

18 ,

28

17

k. ,23

49 ,

23

45 ,

23

41

l. ,5

25 ,

3

25 ,

1

25

m. ,16

25 ,

4

25 ,

1

25

n. 1, 4, 9,

o. 1, 2, 3,

p. – 1, – 2, – 3,

q. – 2, – 1, 0, 1, 2,

r. 1, 4, 9,

s. 1π, 2π, 4π,

t. 3π, 5π, 7π,

u. 1 2 3 4 5

, , , , ,3 5 7 9 11

v. 1 2 3 4 5

, , , , ,3 5 7 9 11

w. 1 2 3 4 5

, , , , ,3 5 7 9 11e e e e e


9. A popular cell-phone application is “1010” and is played similar to the game of Tetris. Pieces are placed into the 10-by-10 puzzle and points are scored. Different shaped pieces are worth different points based on how many filled in squares for the shape:

is worth 9 points is worth 5 points is worth 3 points.

If a player fills in an entire row or column, that line will disappear and bonus points are awarded.

1 row/column gives 10 bonus points 2 rows/columns done at one time gives 30 bonus points 3 rows/columns done at one time gives 60 bonus points 4 rows/columns done at one time gives 100 bonus points

a. Based on this pattern, how many bonus points would a player score for 5 rows done at one

time?

b. Based on the pattern, how many bonus points would be a player score for 6 rows done at one

time?

c. Is this sequence of bonus points considered arithmetic, geometric, or neither?

Wrap-up and look back: 10. Does knowing the first three terms of a sequence mean that we’ll know all the terms in the

sequence?

11. Is there always one correct answer?

12. Does knowing the first three terms of an arithmetic sequence mean that we’ll know all the terms

in the sequence?

13. Does knowing the first three terms of a geometric sequence mean that we’ll know all the terms in

the sequence?


them back to class.

1.7: Inputs and Outputs Vocabulary and symbols – write out what the following mean:

Ordered pairs Coordinates

Input Output


Concept questions: 1. Use the terms “ordered pairs” and “coordinates” correctly when thinking of (2, 5).

2. Use the terms “input” and “output” correctly when thinking of (2, 5).

3. Which coordinate in an ordered pair is the input and which is the output?

Exercises: 4. Fill in the blank spaces of the table following the pattern given.

a. Input: 0 5 10 15 20 25 30

Output: 2 4 6

Ordered pairs:

b.

Input: 1 3 5 7 9 11 13

Output: 3 5 7

Ordered pairs:

c.

Input: 1 3 5 7 9 11 13

Output: 2 4 6

Ordered pairs:

d.

Input: 1 3 5 7 9 11 13

Output: 2 4 8

Ordered pairs:

e.

Input: 1 2 3 4 5 6 7

Output: 2 4 6

Ordered pairs:


f.

Input: 1 2 3 4 5 6 7

Output: 2 4 8

Ordered pairs:

g.

Input: – 2 – 1 0 1 2 3 4

Output: 4 1 0 16

Ordered pairs:

h.

Input: – 3 – 2 – 1 0 1 2 3

Output: – 11 – 9 – 7

Ordered pairs:

Wrap-up and look back: 5. Did you have any questions remaining that weren’t covered in class? Write them out and bring

them back to class.

1.8: Graphing Patterns Vocabulary and symbols – write out what the following mean:

Number line Horizontal

Vertical Point

Origin Between

Concept questions: 1. How do the words “point” and “ordered pair” relate?

2. In an ordered pair, which coordinate is the horizontal and which coordinate is the vertical?

3. Is 7 between 5 and 12? Is 7 between 9 and 20? Is 7 between 7 and 13?

4. Is the origin a point, and if so, what are the coordinates for this ordered pair?

Exercises: 5. Describe (5, 11) in words using: coordinate, input, output, point, and ordered pair.

6. Describe (– 67, – 3) in words using: coordinate, input, output, point, and ordered pair.


7. Complete the following table by filling in the missing pieces.

Ordered Pair First Coordinate

Second Coordinate

Input Output

a. (51, – 3)

b. – 3 17

c. – 42 – 8

d. 23 400

8. Fill out the missing parts of the table including the letter of the point.

Input: 4 8 20 12 16 24

Output: 6 5 2 4 3 1

Ordered pairs:

Letter of the point: A

0 0 28

2

14

6

Input

Output A

D

E

C

F

B

4


9. Use the graph to answer the following questions.

a. Find the letter that corresponds to the given point.

Ordered pair Letter (Point) Ordered pair Letter (Point)

a) (9, 1) b) (5, 5)

c) (2, 8) d) (4, 6)

e) (8, 2) f) (10, 8)

b. Now backwards: Find the coordinates of the following points:

Letter (Point) Ordered pair Letter (Point) Ordered pair

B C

G F

c. List all the labels (letters) for points that have their first coordinate greater than 3.

d. List all the labels (letters) for points that have their second coordinate less than 4.

e. List all the labels (letters) for points that have their first coordinate between 3 and 9.

f. List all the labels (letters) for points that have their second coordinate between 3 and 9.

g. List all the labels (letters) for points that have 7 as their second coordinate.

h. List all the labels (letters) for points that have 8 as their second coordinate.

i. List all the labels (letters) for points that have 5 as their first coordinate.

j. List all the labels (letters) for points that have 2 as their first coordinate.

k. List all the labels (letters) for points that have 0 as their first coordinate.

l. Challenge ☼: List all the labels (letters) for points that have their first coordinate between 4

and 8 while having their second coordinate less than 8.

10

15

A K

B

C

H

D

A

J F

E G

I



a. Find the ordered pairs for the points:


a) A b) D

c) M d) P

e) F f) H

b. If possible, determine which point is represented by the ordered pair.

Ordered pair Letter (Point)


a) (– 8, 0) b) (– 5, – 3)

c) (1, – 7) d) (0, 3)

c. Draw in these points on a graph:

U (2, 10) V (– 9, – 2)

W (– 3, 6) X (– 4, – 6)

Y (0, – 4) Z (6, 5)

H

A

M

B

F

C

D

Q

G

E

N

P

Homework Unit 1 –

11. Graph the patterns on the same graph. When finished graphing the points, connect the dots! a. Consider the arithmetic pattern given by a = – 5 and d = 2. Graph and label these points.

A B C D E F G

Input 1 2 3 4 5 6 7

Output – 5 – 3 – 1

b. Also, on the same grid graph the arithmetic pattern given by a = 6 and d = – 2.

H I J K L M N

Input 1 2 3 4 5 6 7

Output 6 0 – 4

When creating your graphs, be sure you label the axes so the graph will fit!

Homework Unit 1 –

12. Graph the patterns on the same graph. When finished graphing the points, connect the dots! a. Consider the arithmetic pattern given by a = 2 and d = 2.

Input 1 2 3 4 5 6 7

Output 2

b. Also, on the same grid graph the arithmetic pattern given by a = 7 and d = – 1.

Input 1 2 3 4 5 6 7

Output 7


13. Graph the patterns on the same graph. When finished graphing the points, connect the dots!

a. Consider the geometric pattern given by a = 2 and r = 2.

Input 1 2 3 4 5 6 7

Output 2

b. Also, on the same grid graph the geometric pattern given by a = 64 and r = 2

1.

Input 1 2 3 4 5 6 7

Output 64


Homework Unit 1 –

14. Graph the patterns on the same graph. When finished graphing the points, connect the dots! a. Consider the arithmetic pattern given by a = 1 and r = 3.

Input 1 2 3 4 5 6 7

Output 1

b. Also, on the same grid graph the geometric pattern given by a = 1 and r = 3.

Input 1 2 3 4 5 6 7

Output 1

15. One author, Scott Fallstrom, spoke with his kids on the first of the month of April about

allowances. He gave each of his kids two options for allowances that would be paid for the entire month of April. Think about what you would choose and be able to explain your result. If you’d like, you can also graph the values once you find them.

a. Option 1: paid $5 on the first day, $10 on the second day, $15 on the third day, and so on

(arithmetic sequence). Find how much was paid in allowance on the last day of April.

b. Option 2: paid 1¢ on the first day, 2¢ on the second day, 4¢ on the third day, and so on (geometric sequence). Find how much was paid in allowance on the last day of April.

c. Challenge ☼: Find the total amount of money that would be paid out for the whole month

using “Option 1” with the formula:

2Sum 1 naan .

d. Challenge ☼: Find the total amount of money that would be paid out for the whole month

using “Option 2” with the formula: r

ra

n

1

1Sum .

e. Is it possible for Scott to be able to make this claim and back it up?

f. Does the day of the discussion change your answer to part (c)? Why or why not?

16. The population of the world is growing with a geometric pattern. Food production in the world is growing with an arithmetic pattern. Describe what this could mean for the world.

Homework Unit 1 –

Wrap-up and look back: 17. What type of a graph is created by arithmetic patterns?

18. What type of a graph is created by geometric patterns?

19. What are the visual differences between arithmetic and geometric graphs?

20. With the geometric patterns, explain the visual change in the graph when the common ratio was

greater than 1 and when the common ratio was between 0 and 1.

21. With the arithmetic patterns, explain the visual change in the graph when the common difference was greater than 0 and when it was less than 0.

22. With an arithmetic pattern, what do you predict would happen visually when d = 0?


1.9: Functions Vocabulary and symbols – write out what the following mean: Function

Function notation

xF

Concept questions: 1. Is it possible that a function has both of these points: (2, 5) and (5, 5)? Link your response to the

definition of a function.

2. Is it possible that a function has both of these points: (2, 7) and (2, 11)? Link your response to the definition of a function.

3. Is it possible that a function has both of these points: (2, 5) and (11, – 5)? Link your response to the definition of a function.

4. If we wrote Pxg , what are the input, output, and name of the function.

Homework Unit 1 –

Exercises: 5. Identify the following information from function notation.

Function Notation Function Name Input Output

a. xxC 4150

b. 2575 ttR

c. 53 kkg

d. rrS 327

e. 43zW

f. w

wK36

g. xxA 2

h. 677 Jpm

6. For the functions listed above, find the following:

a. xC for x = 10, 20, 30, 40

b. tR for t = 0, 1, 2

c. kg for k = 3, 4, 5, 6

d. rS for r = 6, 7, 8, 9

e. zW for z = 3, 5, 11, 25

f. wK for w = 2, 4, 5, 12, 18

g. xA for x = 2, 8, 18, 32

h. xJpm for x = 7

7. Challenge ☼: If rprS 327 , what is 10S ?

8. If the point (6, 15) is on the function f, how could we write the point using function notation?

9. If the point (– 5, 7) is on the function g, how could we write the point using function notation?

10. If 611 J , what point does this notation represent?

11. If 457227 P , what point does this notation represent?

12. Challenge ☼: If 53 kkg , what point does this notation represent?

Homework Unit 1 –

Using the table for areas of a circle (based on radius), answer the following questions. Area of a Circle (rounded to 2 decimal places):

r Area r Area r Area 0.5 0.79 5 78.54 9.5 283.53

1 3.14 5.5 95.03 10 314.16

1.5 7.07 6 113.10 10.5 346.36

2 12.57 6.5 132.73 11 380.13

2.5 19.63 7 153.94 11.5 415.48

3 28.27 7.5 176.71 12 452.39

3.5 38.48 8 201.06 12.5 490.87

4 50.27 8.5 226.98 13 530.93

4.5 63.62 9 254.47 13.5 572.56 13. Find the area of a circle with …

a. Radius of 4

b. Radius of 6.5

c. Radius of 8

d. Radius of 11

e. Radius of 12.5

f. Radius of 0.5

14. Find the radius of the circle if the circle has area of …

a. 95.03

b. 314.16

c. 415.48

d. 7.07

e. 153.94

f. 283.53

15. Using the table, estimate the information requested.

a. Example: Area is 15, estimate the radius. Answer: The radius is between 2 and 2.5.

Explanation: while this area isn’t listed in the table, it is between 12.57 and 19.63, so the

radius must be between 2 and 2.5.

b. Area is 10, estimate the radius.

c. Area is 50, estimate the radius.

d. Area is 100, estimate the radius.

e. Area is 200, estimate the radius.

f. Area is 300, estimate the radius.

g. Area is 400, estimate the radius.

h. Radius of 6.3, estimate the area.

i. Radius of 11.8, estimate the area.

Homework Unit 1 –

Using the table for areas of a rectangle (based on width and length), answer the following questions.

Area of a Rectangle: W

idth

Length 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 2 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 3 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 4 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 5 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 6 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 7 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 8 8 16 24 32 40 48 56 64 72 80 88 96 104 112 120 9 9 18 27 36 45 54 63 72 81 90 99 108 117 126 135

10 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 11 11 22 33 44 55 66 77 88 99 110 121 132 143 154 165 12 12 24 36 48 60 72 84 96 108 120 132 144 156 168 180 13 13 26 39 52 65 78 91 104 117 130 143 156 169 182 195 14 14 28 42 56 70 84 98 112 126 140 154 168 182 196 210 15 15 30 45 60 75 90 105 120 135 150 165 180 195 210 225

16. Find the area of a rectangle with …

a. length 6, width 9

b. length 3, width 12

c. width 11, length 3

d. length 14, width 14

e. width 4, length 4

f. length 2, width 2

g. length 3, width 3

h. length 2, width 3

i. width 4, length 3

j. width 3, length 4

k. width 13, length 14

l. length 15, width 14

17. Find the length and width of a rectangle if the rectangle has area of…

a. 48

b. 117

c. 225

d. 36

e. 99

f. 121

18. Using the table, estimate the information requested.

a. Example: Area is 23 and length is 4, estimate the width. Answer: The width is between 5

and 6. Explanation: while this area isn’t listed in the table, we can use a length of 4 and

estimate what width would put the area at around 23.

b. Area is 57 and width is 6, estimate the length.

c. Area is 159 and length is 11, estimate the width.

d. Length is 12 and width is 6.7, estimate the area.

e. Length is 7.2 and width is 14, estimate the area.

Homework Unit 1 –

Using the table for a t-distribution (based on level, degrees of freedom and number of tails), answer the following questions.

t Distribution: Critical t values

Area in one tail

0.005 0.01 0.025 0.05 0.10

Degrees of Freedom

Area in two tail

0.01 0.02 0.05 0.10 0.20

1 63.657 31.821 12.706 6.314 3.078

2 9.925 6.965 4.303 2.920 1.886

3 5.841 4.541 3.182 2.353 1.628

4 4.604 3.747 2.776 2.132 1.533

5 4.032 3.365 2.571 2.015 1.476

6 3.707 3.143 2.447 1.943 1.440

7 3.499 2.998 2.365 1.895 1.415

8 3.355 2.896 2.306 1.860 1.397

9 3.250 2.821 2.262 1.833 1.383

10 3.169 2.764 2.228 1.812 1.372

19. Find the t-critical value using the table above if … a. Area in one tail at a 0.05 level with 7 degrees of freedom.

b. Area in one tail at a 0.05 level with 9 degree of freedom.

c. Area in two tails at a 0.01 level with 7 degrees of freedom.

d. Area in two tails at a 0.05 level with 7 degrees of freedom.

e. Area in two tails at a 0.01 level with 9 degrees of freedom.

f. Area in two tails at a 0.05 level with 9 degree of freedom.

g. Area in one tail at a 0.01 level with 3 degrees of freedom.

h. Area in two tails at a 0.01 level with 3 degrees of freedom.

i. Area in one tail at a 0.05 level with 4 degree of freedom.

j. Area in two tails at a 0.05 level with 4 degree of freedom.

Homework Unit 1 –

20. Based on the previous problem, explain what happens when… a. Everything else is the same, but the degrees of freedom increases.

b. Everything else is the same, but the level increases.

c. Everything else is the same, but we move from one tail to two tails.

d. Everything else is the same, but we move from two tails to one tail.

21. Here, you’ll be given a critical t-value. Find whether there is only one way or more than one way

to get this value, and explain how it is obtained? a. 2.132

b. 3.707

c. 1.886

d. 2.228

22. Using the table, estimate the information requested. a. 7 degrees of freedom, one tail, critical value of 2. Estimate the level.

b. 9 degrees of freedom, two tails, critical value of 2.63. Estimate the level.

c. 4 degrees of freedom, two tails, critical value of 3.97. Estimate the level.

d. 10 degrees of freedom, one tail, critical value of 1.66. Estimate the level.

Wrap-up and look back: 23. Is everything a function?

24. Does a function need to have only one input, or could there be more than one?

25. When using a table of function values, can estimate values in the chart or only use the exact

values?

26. Does every function look like xf ? Why is xf used so often?

27. Could we have different outputs for the same inputs in a function?


Homework Unit 1 –

1.10: Unit Review and Test Prep Vocabulary and symbols: All the terms and new symbols from each unit; you should have a working knowledge of each term (knowing what it means and how to use it). These are jumbled up and not in any order.

Solve a Simpler Problem Function Function notation xF

Guess and Check Draw a Picture Logic and Computation Make a List Geometric Sequence “a” “r” Common ratio Base Exponent

1 nn raa

Ordered pairs

Coordinates Input Output Number line Horizontal Vertical Point Origin Between Write an Equation Arithmetic Sequence “a” “d” Variables Common difference dnaan 1

Concept questions: 1. When you encounter a problem you’ve never seen before, what do you do? 2. What do you look for when you see a list of numbers that seem to be a pattern?

3. What are the main types of patterns that we’ve encountered?

4. What type of sequence forms a list of numbers that never changes?

5. With functions, could there be 2 outputs for one input?

6. When graphing points, which coordinate corresponds to the horizontal?

7. Where is the starting point when graphing all points?

Exercises: 8. A classroom has 15 rows of curved stadium seating – each row has 3 more seats than the last.

With 20 seats in the first row and 23 seats in the second, determine how many seats are in the back row.

Homework Unit 1 –

9. A farmer has three items to get across a river: a fox, a goose, and a bag of grain. There is a boat which will hold the farmer (who will row) and one extra item. Determine how to get the three items across if you have to follow these rules: a. None can swim.

b. Each trip can carry a maximum of one item.

c. None will run away while rowing across the river.

d. If you leave the fox with the goose, the fox will eat the goose.

e. If you leave the goose with the grain, then the goose will eat the grain.

10. With the patterns listed, determine if the sequence is arithmetic, geometric, or neither. For each,

try to find the nth term.

Start of the Sequence Type of Sequence a d or r nth Term a. 7, 10, 13, 16, 19, A G N

b. 2, 5, 7, 12, 19, A G N

c. 9, 9, 9, 9, 9, A G N

d. ,

3

1 ,1 ,3 ,9 ,27 ,81 A G N

e. 47, 39, 31, 23, 15, A G N

f. 1, 3, 6, 10, 15, 21, A G N

g. 1, 9, A G N


a. 1.1, 1.7, 2.3,

b. 3.4, 3.0, 2.6,

c. 43, 51, 43, 51,

d. 3.2, 3.4, 3.6,

e. 1, 10, 100, 1000,

f. 10, 2, 12, 2, 14, 2, 16, 2,

g. ,65

44 ,

65

22 ,

65

11

h. ,9

73 ,

6

74 ,

3

75

i. ,16

8999 ,

4

899 ,

1

89

j. ,27 ,20 ,13 ,6

k. 16, 6, – 4, – 14,

l. 100, 10, 1, 0.1,

m. 4π, 12π, 36π,

n. ,9

8 ,

8

4 ,

7

2 ,

6

1

AAAA

o. 800, 400, 200, 100,



a. Find the ordered pairs for the points:


a) B b) N

c) C d) A

b. Which point is represented by the ordered pair?

Ordered pair

Letter (Point)


e) (0, 7) f) (8, – 9)

g) (2, 4) h) (4, 2)

i) (– 9, 8) j) (7, 8)

c. Draw in these points on a graph:

T (4, –5) S (7, 0)

Q (– 3, 6) $ (– 4, 10)

J (– 4, 0) K (0, –5)

H

A

M

B

F

C

D

Q

G

E

N

P


13. Fill out the table below:

Function Notation Function Name Input Output

a) 23 xxM

b) ttR 2511

c) 44Ag

d) wwF 327

e) zzW 28

14. For the functions listed above, find the following:

a. xM for x = 11, 22, 3, 70

b. tR for t = 0, 1, 2, – 5,

c. Ag for A = 46, 17, – 304, π

d. wF for r = 6, 7, 8, 9

e. zW for z = 3, 5, 11, 25

15. Give the first 4 terms of the following arithmetic sequence and the nth term, na .

a. a = 38 and d = – 2 na =

b. a = – 9 and d = 7 na =

16. Find the term in the arithmetic sequence using the formula: dnaan 1 .

a. Find 17a when a = 31 and d = 1.

b. Find 11a when a = 75 and d = 2.

c. Find 68a when a = 371 and d = – 191.

17. Give the first 4 terms of the following geometric sequence and the nth term, na .

a. a = 7 and r = 3 na =

b. a = – 5 and r = 2 na =

Wrap-up and look back: 18. What was the most interesting part of this unit for you? 19. What concepts in this unit were the most challenging for you?

20. Do you have any additional questions?

math fundamentals for statistics (math 52) homework unit 1

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