SAT Math Week 10: More Equation Solving Strategies

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SAT Math Week 10: More Equation Solving Strategies

Lesson Review:
Today we discussed Chapter 8 Exercise and went through Chapter 9: More Equation Solving Strategies.

1) Matching coefficients
2) Clearing denominators

*Note that a lot of SAT problems will include some conditions such as x>0 or x<0, to eliminate one of the solutions. Read the questions carefully.

*For some long questions, you do not need to read every single word. Catch the keywords, focus on the formula or equations, you will save time and reduce the working load of your brain!

Homework:
1)Page 66-67, Ex 1-12
2)Bonus Problem 13-17

bonus questions

Extra Resource:
https://www.math.utah.edu/~macarthu/fall08/math1010/EquationSolvingStrategies.pdf

https://blog.prepscholar.com/single-variable-equations-algebra-act-math-strategies

Next week we are going to solve systems of equations! See you soon!

AoPS_CP Week 10: Probability with Dependent/Independent Events

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Lesson review:
Today we have finished the second half of Chapter 8: Basic Probability Techniques and Chapter 9: Think about it!

  1. Addition or Multiplication
    We add probabilities of exclusive events: P(A or B) = P(A) + P(B);
    and multiply probabilities of independent events: P(A and B) = P(A) X P(B)
  2. Independent VS Dependent Events
    Independent Events: the probability that one event occurs in no way affects the probability of the other event occurring.
    Dependent Events: the probability of one event occurring influences the likelihood of the other event.
  3. Avoid unnecessary computation:
    1) take advantage of symmetry
    2) ignore the irrelevant information
    3) consider multiple events at once instead of dealing with them separately
    4) be flexible, think out of the box!

Homework:
Page 135: Ex 8.4.1, 8.4.4, 8.5.1, 8.5.4, 8.5.6
Page 151: Ex 9.8, 9.10, 9.12, 9.14

Additional Resource:
https://www.siyavula.com/read/maths/grade-11/probability/10-probability-02

https://www.wyzant.com/resources/lessons/math/statistics_and_probability/probability/further_concepts_in_probability

https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:prob-comb/x9e81a4f98389efdf:dependent-events-precalc/v/independent-events-1

https://www.khanacademy.org/math/ap-statistics/probability-ap/probability-multiplication-rule/v/compound-probability-of-independent-events

See you next Sunday and I look forward to exploring the geometric probability with you! Have fun!

SAT Math Week 9: Manipulating & Solving Equations

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Welcome our new friend, Tina!

Flexibility Assessment:
Thanks to everyone for participating in the pilot Flexibility Assessment from Harvard Graduate School of Education. Your feedback will help to revise this assessment. This study will be carried out in Finland, Sweden, Spain, America, and China. We learned that for some problems, there are some “innovative strategies”. Be familiar with the properties and principles in math, you can solve problems faster, and better:)

I was deeply impressed that several of you can solve many (even all) of the problems in an innovative way in Part I (the first trial). Good job! Please remember to apply these strategies in your SAT tests to save time 😛

Responding to the feedback from Emma’s mom, in the following lessons, I would love to share some strategies to 1) read long questions 2) reduce the workload of calculating during the SAT test.

Lesson Review:
We discussed Page 57: Ex(3n +1) and went through the 12 example problems in Chapter 8. Some useful techniques in dealing with equations include but not limited to:
1) combine like terms
2) square and square root
3) cross-multiply (fractions)
4) factoring
5) treat complicated expressions as one unit
6) solve for expressions, rather than any one variable
7) Guess and check

Image result for equation solving strategies

Homework:
Page 58-62, Ex 1-24
(everyone picks 2 problems that you feel most challenged and would like us to explain in class, and label them on your textbook)
(everyone prepares to explain on board in class!We will do the shuffling cards again:P)

We will explore more equation solving strategies (Chapter 9) next week. See you then!

AoPS_CP Week 9: Probability & Addition, Complementary Probabilities

lilijia Post in AOPS_Counting_Probability
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Flexibility Assessment:

Thanks to everyone for participating in the pilot Flexibility Assessment from Harvard Graduate School of Education. Your feedback will help to revise this assessment. This study will be carried out in Finland, Sweden, Spain, America, and China.

It’s interesting to see that most of the students in this class solved the problems in a traditional way in Part I, but developed better (more innovative) methods in Part II for the same set of problems. Perhaps because of the time constraint, or being used to the more traditional ways. We learned that for some problems, there are some “innovative strategies”. Be familiar with the properties and principles in math, you can solve problems faster, and better:)

Lesson Review:

8.2 Probabilities and Addition
If events A and B are mutually exclusive, then P(A or B) = P(A) + P(B)
More generally, if A1, A2, …, An are mutually exclusive, then P(A1 or A2 or A3 … or An) = P(A1) + P(A2) + … + P(An)

If the events are not mutually exclusive, you have to correct for the overcounting:
P(A or B) = (P(A)+P(B)-P(A and B)
(think about the Venn Diagram)

Image result for probabilities of mutually exclusive events

8.3 Complementary Probabilities
P (A does not occur) = 1 – P(A occurs)

Sometimes it is easier to calculate the “opposite” events, so the complementary method can work better than the constructive method. (Refer to Example Problem 8.6)

Homework:
Page 128: 8.2.1-8.2.3, 8.2.6
Page 130: 8.3.1-8.3.4

Next week we are going to finish Chapters 8 and 9. Please be prepared and look forward to seeing you soon!

SAT math Week 8: Constructing models

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Lesson Review:

  1. Midterm Exam Paper Review
  2. Page 57, Problem 3n: Isolate the variables
  3. Chapter 7: Constructing Models
    Note the difference between linear function, quadratic function, and exponential functions;
    Note the increasing/decreasing (the slopes, the trend of lines)
    Note the rate of change (quickly: steeper lines, |slope|is greater; slowly: |slope| is smaller). || means absolute values.

Homework:

  1. Midterm Exam Paper Correction (Use different colors)
  2. Page 57, Problem 3n+1: Isolate the variables
  3. Chapter 7: Constructing Models Chapter Exercise (Page 47-49)

Look forward to seeing you on 11/10.

Image result for constructing models in math

AoPS_CP Week 8: Introduction to probability

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Lesson review:

  1. Midterm Exam Paper Correction
  2. Chapter 7: Introduction to probability
    1)P(A) = Number of outcomes for A / Number of possible outcomes
    or P(A) = Number of successful outcomes/Number of possible outcomes
    2). The range of P(A) is [0,1]

Homework:
Page 114: Ex 7.2.1-7.2.2
Page 117: Ex 7.3.1 -7.3.3
Page 120: Ex 7.4.1- 7.4.5
Page 121: Ex 7.12 (Classwork)

Annabelle gave a close guess to the “Shooting star” warm-up exercise: around 80%. The accurate probability is 84%. We will discuss it in class next Sunday.

See you next week!

Entering the second half of semester

lilijia Post in AOPS_Counting_Probability, SAT math
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Dear all,

Daylight saving time ends this Sunday. Your clocks are moved an hour back at 2AM on 11/3.

For my AoPS Counting & Probabilities class: In the first half of the fall semester, we have learned Countings. Since tomorrow, students are going to explore the strategies in finding Probabilities.

Here is one “warm-up exercise”: On Friday night, there is a 60% chance that Becky will see a shooting star in any given hour. If Becky watches the sky for 2 hours, what is the probability that she’ll see a shooting star?

For my SAT Math class, we are going to deep dive into the model construction and equation solving in the following weeks. Please be prepared!

Enjoy and see you soon!

Best,
Lijia

Daylight Savings: fall back with a clock and pumpkin

AoPS_CP Week 7: Midterm Exam

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Summary:

We took the midterm exam today, covering Chapters 1 to 6 (Countings). Congratulations to Annabelle, Jason, and Susan for being Top 3 this time! (Max is absent because of his contest). Keep up the good work!

If you feel upset about the score, do not give it up. What more important is to learn from the mistakes, and find the area of improvement. Look ahead. I am looking forward to your progress in the following months!

Here is the link to the answer key.

Here are some pictures of the board-writings in our second period (解题课), to help you make corrections.

Midterm Q15

The first picture is for Question 15. Thanks a lot to Annabelle for explaining it very clear to the class!!

Midterm Q18

The second picture is for Bonus Question 2. The star represents women, and the dot represents men. Please feel free to reach out if you have any questions.

Homework:

1. Make corrections to the test (Use a different color).

2. Preview Chapter 7: Introduction to Probability

 

See you next week!

SAT Math Week 8: Midterm Exam

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Summary:

We took the Midterm Exam today — another practice SAT test.

Congratulations to Austin, Marina, Danielle, and Irene for making 700+ this time! (Kevin and Sarah were not here today). Also, it is so nice to see each student’s progress compared to their pre-test!

 

Homework:

1. Please make corrections to section 1 (we will hand out section 2 when we meet next week).

2. Finish #multiples of 3 on Page 57.

3. Preview Chapter 7: Constructing Models.

 

Errata (SAT Math: The Advanced Guide and Workbook)

Chapter 3 Exponential vs. Linear Growth, #3 (pg. 26): The answer explanation on page 260 has a typo. The rate should be 1 – 0.06 = 0.9410.06=0.94.

Chapter 7 Constructing Models, #1 (pg. 47): The question should read “… and then lays \dfrac{x}{2}2x bricks per hour for 2y2y more hours.”

Chapter 21 Triangles, #14 (pg. 184): The diagram is drawn incorrectly, though it’s hard to tell. The diagram should be drawn so that triangle ABCABC is similar to triangle DEFDEF (and the sides should correspond).

Chapter 23 Trigonometry, #12 (pg. 207): The answer explanation on page 310 has a typo. In quadrant III, sine and cosine are both negatives (not positive).

Chapter 25 Probability, #10 (pg. 223): The first sentence of the question should read “A manufacturer uses two assembly lines to produce refrigerators.”

 

Please make those changes in the textbook 🙂 Thank you! See you all next week!

 

SAT Math Week 7

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I am glad to see that each of our students is working hard in this class!! Proud of you!

Lesson review_Chapter 6 Expressions

1. Combine like terms

2. Expansion and factoring

fb

3. Combining fractions (find the common denominator)

4. Flipping (dividing) fractions

5. Splitting fractions

Homework:

1. Chapter Exercise: Page 44 Ex 1-13

2. Bonus Question

3. Make corrections to previous work, review, and get ready for the Midterm Exam on 10/27. We will have another practice test. Please bring your calculator (for section 2).

See you soon! Stay on the right track, and keep up the good work!