Thinking With Mathematical Models Problem 2.1 Answers
It Is In The System
4/25 Unit 6 Test Review Packet
4/13 Notes for solving systems
4/6
4/4 Quiz review
4/1 1.3 ACE Pg 15 # 23 WRKS Practice
3/31 1.3 ACE Pg 15 # 22
3/30 1.2 ACE Pg 14 # 9, 11, 15, 17 Investigation C-D
3/29 1.2 Investigation A
3/28 1.1 ACE Pg. 13 #1 Investigation B-D
Combining Like Terms, Distributions, and Solving Equations
3/9 - VOLUME RELATIONSHIPS
3/9 ACE 2.4 Pg 37 # 13
3/8 ACE 2.3 Pg 36 #10
3/7 ACE 3.2 Pg 57 # 10 - 17 odd
3/4 ACE 3.2 Pg. 57 #8 d-e
3/3 ACE 3.2 Pg. 57 #8 a-c
3/2 ACE 3.1 Pg 55 # 1,2
3/1 ACE 2.2 Part B-C, ACE 3.1 Part C
2/29 ACE 2.2 Pg. 35 # 6-8
2/25 ACE 2.1 Pg 34 #1
2/24 ACE 1.4 Pg. 17 #7
2/23 ACE 1.2 Pg 16 #6
2/22 ACE 1.2 Pg. 16 #3
2/19 ACE 1.1 Pg. 15 # 1, 2
Page 1 Page 2
2/16 Terms and Combining like terms Test Review
Page 1 Page 2
2/4 WRKS - Recognizing Parts of terms.
Growing, Growing, Growing
2/1 WRKS - Scientific Notation and Exponential Practice
1/29 Test Review
1/28 5.5 ACE Pg. 95 # 63, 65
1/27 5.4 ACE pg. 92# 39, 45, 51, 54
1/26 WRKS Exponential Rules Practice
1/25 5.2 ACE Pg. 88 # 2-5, 7, 9, 11, 15
1/22 5.1 ACE Pg. 88 #1
1/21 5.1 ACE Pg. 97 # 67-69
1/20 - WRKS - More Scientific Notation Practice
1) 2.9700987 X 1020 OR 3.0 X1020
2) i. 1.3X101 g ii. 1.4X10-2 lbs iii. 8.0X100 L iv. 6.072X104 ft
3) a. 7.1X104 b. 6.3X1012 c. 3.3X10-2 d. 1.5X10-22
4) 5.9 times bigger
5) 2.0126 times bigger
1/19 2.3 ACE Pg. 36 #14
1/15 1.3 ACE Pg. 20 #17-21
1/12 - 1.2 ACE Pg. 16 # 5-10
1/11 - 1.1 ACE Pg. 14 #2, Pg. 21 # 21, 22, 25, 26, 28, 31
Butterflies, Pinwheel and wallpaper 1/07 Unit Test Review
Page 1 Page 2 Page 3 Page 4
1/05 ACE 4.3 #16 - 18 ACE 4.4 #20, 21
12/16 ACE 4.2 #11 - 15 #26
12/14 WRKS - Dilation Practice
12/14 Mini Translation Project
12/11 WRKS - Transformation Rules
12/10 Parallel lines and transversal and triangle angle measure
12/7 Quiz 2 Review
Page 1 Page 2 Page 3
12/4 2.1 #3, 4 and 2.2 #13 - 18 Congruency and Transformations
12/4 - Properties of Transformations
1.4 Properties of transformations
Pg. 22 # 18 Pg. 27 #38
Pg. 27 # 39
1.3 Translations Pg. 21 #11, 13
1.2 Rotations not on the figure Pg. 20 # 9 Pg. 24 # 29
1.2. Rotations on the figure Pg. 20 # 8 and 10
Looking for Pythagoras
WRKS - Test Review
WRKS - Application 2D and 3D
sqrt = square root
1. 75 cm
2. 2 sqrt (589) m
3. 15 cm 2
4. 5 sqrt (114) m
5. 10 sqrt (2) ft
6. The shorter length is through the field. It is 2 miles shorter
7. 24 inches
8. the legs are 5 sqtr(2) inches long each
WRKS - Rational Irrational 4.4 ACE Pg. # 20, 21 4.4 ACE Pg. 72 #13-15 4.3 ACE Pg. 71 # 6 - 7, 8, 9
4.2 ACE Pg. #71 3-5, 31
4.1 ACE Pg. 71 # ! and Pg. 73 # 24
4.1 Theodorus Spiral
WRKS - Review Operations with Roots
1 a. √ 28 = 2 √7 b. √32 = 4√2 c. √8 = 2√2
2.a. 3 √6 b. 2√15 c. 4√3
3.a. 3 √8 = 6√2 b. 2 +√2 + √5order does not matter c. 2√3
WRKS - Review Unit Test
Page 2
Page 1
Lesson 3.3
ACE Pg. 51 # 14, Pg. 53 #22, 23 and 25
Lesson 3.2
ACE Pg. 50 5, 6
Lesson 3.1
ACE Pg. 49 # 3, 4
ACE Pg. 49 # 1, 2
WRKS - Lesson 2.1 - 2.4
Page 1 Page 2
Lesson 2.4 Pg. #50-52 choose 2, #53-55 choose 2
WRKS - Practice 2.1 - 2.3
Page 3 Page 2 Page 1
Lesson 2.3 Pg. 32 44, 46
Lesson 2.3 Pg. 31 40, 41
Lesson 2.2 Pg.30 # 30 = 37
Lesson 2.2 #4
Lesson 2.1
Lesson 1.3
Lesson 1.2
Lesson 1.2
Lesson 1.1
Thinking with Mathematical Models Review Pg. 3 and 4
18. m = 4, b = -3 below
19. m = -2, b = -3 below
20. y = 15x + 240
21. y = x + 1
22. y = -3x - 2
23. y = 5/3x + 6
24. y = 9/5 x + 184
25. below 26. below
27. a 28. b 29. c 30. a 31. c
Graphs
Thinking with Mathematical Models Review Pg. 1 and 2
1. m = 40; It cost $40 a ski package per (1) person
2. m = 51; They drove 51 miles each (1) hr
3. m = -1/2 4. m = 3/4 5. 2/3 6. m=0 7. m= undefined
8. m= -4, b = 2 9. m= -8/9, b= -10/3 10. m= 1.9, b = 2.5
11. y = -5x -3 12. y = 3/5x + 1/3 13. y = -4.4x + 6.8
14. y = 5/8x + 1/2 15. y = -5/8x + 1 16. y = 4/3x + 3/4
17. y = -3/7x + 5 6/7 or y = -3/7x + 39/7
WRKS - Linear - Direct Variation, Inverse Variation
y = mx + b, (0, 0), y = mx, divide, x
y = k/x, No
1a. linear, direct b. Inverse c. linear
2a. y = 4x b. y = 2/x c. y = 2x + 3
3.
4.
5.
6.
7a. inverse b. linear c. Linear, direct
WRKS - Finding the Equation of a Line
1. y = -3x -1 2. y = 3x + 1 3. y = -2x + 2
Practice Problems:
1) y = 2x + 7 2) y = x - 4 3) -1/2x + 7
4) y = 2x 5) x = 0 6) y = -2x + 2
7) y = -3/2x + 3 8) x = -1 9) y = -x + 12
10) y = 2x = -1
Investigation 3
Problem 3.3
Problem 3.2
Problem 3.1
Investigation 2
WRKS - Practice Investigation 2 Problems
ANSWERS:
1.a. y = 2/ 3 x - 2 b. y = -2/ 3 x - 3 c. y = x d. x = -3
2. a. y = 4x - 8 b. y = 2 x + 1 c. y = 9 x - 1
3. a. y = 5/3 x + 15 b. y = -1/10 x + 35
4.
| Cans Recycled | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Cans Sold (actual) | 10 | 15 | 19 | 24 | 22 | 25 | 30 | 30 | 33 | 36 |
| Prediction Model y = 3x + 8 | 11 | 14 | 17 | 20 | 23 | 26 | 29 | 32 | 35 | 38 |
| Residual | -1 | 1 | 2 | 4 | -1 | -1 | 1 | -2 | -2 | -2 |
| Total Error -1 | ||||||||||
5. -1; The model is a very good model for the data.
6. 62 = 3(x) + 8, First subtract 8 then divide by 3. There were 62 cans sold.
7. The slope tells us that for every 3 cans sold 1 can will be recycled.
8. a. y = -1/4 x + 5 b. y = 2/3 x + 12 2 /3
c. y = x + 5 d. y = -13/7 x + 6 2 /3
Problem 2.4
Pg. 49 #11, 12, 13
ACE Pg 48 #8
ACE PgG 47 #6
Investigation 1
ACE #3
Problem 1.3
ACE #4
Your answers will be different. I am only giving you an example with these numbers. Your data and graph will be different.
A.
B. As length increases, breaking weight decreases, but the relationship is not linear. In the table, the breaking weights decrease as the lengths increase, but not at a constant rate. In the graph, the pattern of points is a curve that decreases at a slower and slower rate.
C. Predictions and explanations will vary.
For the graph on A you may predict breaking weights are 58, 34, 15, 13. The do not match the actual breaking point because the breaking points may not be exact pennies. Pennies may not be accurate enough to measure strength.
D. They are similar in that breaking weight depends on another variable - either number of layers or bridge length. The relationship are very different. As thickness increases, breaking weight increases. As length increases, breaking weight decreases. The thickness and weight is a linear relationship, while the length and weight is not.
ACE problem #1
1.
a. As distance increases, weight decreases. The decrease is sharper at shorter distances. (The product of distance and weight is always 90,000)
b. The graph shows that as distance increases, weight decreases - sharply at first, and then more gradually.
c. ≈5,000 lb ; ≈3,000 lb ; ≈1,250 lb
d. The graph's shape is similar to that of the bridge-length experiment because the values of the dependent variable decrease at a decreasing rate.
Experiment 1.1
A. This is a sample solution based on your experimental results.
Here is a POSSIBLE solution
B. The relationship is approximately linear. In the table, this is shown by the near-constant differences in breaking weights for consecutive numbers of layers.
In the graph, this is shown by the near straight-line pattern of points. The relationship is also increasing. That is, as the thickness increases, the breaking weight increases.
C. Bases on the given data, one possible prediction is 20 pennies. As thickness increases by 1 layer, the breaking weight increases by about 8 pennies. So as thickness increases by half a layer, breaking weight would increase by about 4 pennies.
D. Based on the given data, one possible prediction is 50 pennies. As thickness increases by 1 layer, the breaking weight increases by about 8 pennies. Therefore, 6 layers would probably have a breaking weight of 42 + 8 = 52 pennies.
E. We did not run the experiment.
ACE Problem 2
Problems 7 and 8
7. D
8. H
Problem 11 and 12.
11.
| Total Price | $1.00 | $1.50 | $2.00 | $2.50 | $3.00 | $3.50 | $4.00 | $4.50 |
| Probable Sales | 400 | 400 | 360 | 300 | 240 | 200 | 160 | 160 |
| Probable Income | $400 | $600 | $720 | $750 | $720 | $700 | $640 | $630 |
a. Use the "Probable Sales" row in the table.
b. Use the "Probable Income" row in the table.
c. $2.50
12.
Answers will vary according to your choice of babysitting rates.
a. Use a rate of $5 per hour, and mark axes for perhaps 20 hours and $100.
b. y =5 x
c. Jake would earn more per hour, for example, $6 per hour. The equation would then be y =6 x .
Thinking With Mathematical Models Problem 2.1 Answers
Source: https://sites.google.com/a/iteach.org/diazhomsi/math-scholars-class/homework-math-8
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