Many B2 compound interest problems boil down to sequentially solving ordinary interest problems. The main thing is to learn how to make this transition and, of course, to work correctly with simple interest. Today we will see how such problems can be solved using the simple percentage formula - one of the most effective tricks in this topic.
In this video tutorial, we continue to study complex percentage problems. But if last time we solved them using coefficients, then this time we will work according to the standard simple percentage formula. Many students will immediately have a question: how can compound interest be calculated using the simple interest formula? However, there is nothing complicated in this, and now we will see this together.
So let's go! Task:
Task B2. In June, 1 kg of tomatoes costs 240 rubles. In July, the price of tomatoes decreased by 50%, and in August - by another 40% compared to July. How many rubles did 1 kg of tomatoes cost after the price reduction in August?
Applying the simple interest formula
So, let's decide. What's happening? There was a certain price x, then, according to the condition of the problem, it decreased by 50%, and then this new value decreased by another 40%. Just for such situations, when we know the initial value of the value and the percentage by which it changes, it is perfect simple interest formula. Namely: let the original value be x, the percentage by which it changes is k, and the final value will be y. We can write the formula:
That's the whole formula. How to apply it in our case? Let's first find out how much tomatoes will cost after a 50% price reduction. It will be equal to:
y 1 \u003d x (100 - 50) / 100 \u003d 240 50/100;
Then we take into account the second decrease that occurred in August, namely, by 40% compared to July. Those. already the value of y 1 that we received, decreases another 40%. Let us denote the value again obtained after the next decrease as y 2 . It will be expressed according to the same formula:
y 2 \u003d y 1 (100 - 40) / 100 \u003d y 1 60/100;
Note that we have again applied the simple interest formula. And since we just found the expression for y 1, we substitute it into our formula and get:
And we got that after all the reductions in the cost of tomatoes, the total cost was 72 rubles per 1 kg. This is the answer to the problem.
Common mistakes when working with percentages
In conclusion, I would like to draw your attention to one subtlety related specifically to compound interest. Let's go back to the problem statement. Take a look: from the original cost of 240 rubles, it first decreased by 50%, and then by another 40%.
Many students are tempted to add 50% and 40% and instead of two consecutive actions, as we did, to do one single action, namely, reduce the value of 240 at once by 90%. Under no circumstances should this be done. Let's see what happens. Let's try to count as these students think:
It turns out that with this approach, the final cost, i.e. the answer, will not be 72, but 24. As you can see, an error occurs: answers differ by 3 times. In this case, the first answer will be correct, i.e. 72 rubles.
When calculating compound interest, never add interest directly! This will lead to offensive errors that are extremely difficult to detect when checking.
The reason for the discrepancy between these answers lies in the fact that we counted 50% from 240 rubles, but the further 40% - not from 240 rubles, but already from the value that resulted from a decrease in 240 rubles by 50%. In other words, we considered 50% and 40% from different values. That is why in the problem we got a larger answer than if we immediately took 50% and 40% of the original value of 240 rubles.
Be careful! At this point, a lot of people got burned. Don't make such mistakes. And that's all for me. Pavel Berdov was with you. See you soon!
Task B2 is aimed at reading graphical functions (the graph characterizes the change depending on the time of a certain value), usually, in the task it is required to find the largest or smallest value of this value.
In this task, the student demonstrates the use of mathematical knowledge and skills in practical activities and everyday life.
To successfully complete task B2, the student must be able to:
Determine the value of a function in various ways of specifying functions,
Find the largest and smallest values of given values, their ratios, according to the function graph, diagram,
Describe various dependencies using functions and read their graphs,
Use information presented in the form of tables, graphs and diagrams.
Typical mistakes:
1. Students confuse the abscissa and ordinate axes;
2. Find the value of the quantity without taking into account the specified interval;
3. The scale is calculated incorrectly: they do not take into account that one division does not always correspond to one unit;
4. When finding the number of days (hours, months, etc.) that meet the given conditions, they simply subtract the earlier date from the later date and lose one day (hour, month, etc.). Recommendations:
1. Analyze the solutions of typical tasks proposed below;
2. Solve the problems placed at the end of the section.
You can also find information of interest in the scientific search engine Otvety.Online. Use the search form:
More on the topic Task B2:
- ! Task 3.1. Make a diagram illustrating the structure of the social environment of the organization! Task 3.2. Make a diagram illustrating the relationship between the concepts of social environment and the social sphere
The level of English B2 is the fourth level of English in the Common European CEFR system, a system for identifying different language levels compiled by the Council of Europe. In everyday speech, this level can be called "confident", for example "I speak English confidently." The official description of the level is "above average". At this level, students can work independently in a variety of academic and professional environments while communicating in English, but their range of topics is limited and speech does not convey all the nuances.
How to determine if you know English at level B2
The best way to determine if your English language skills are B2 level is to take a quality standardized test. Below is a list of the main internationally recognized tests and their respective B2 scores:
What can you do with knowledge of English at level B2
English level B2 will be enough to work in an international company in English, moreover, most professionals who use English at work as a non-native speak it at this level. However, the B2 level may not be sufficient to ensure that nuances are not overlooked when discussing broad topics.
According to official CEFR guidelines, a student with a B2 English proficiency:
- Understands the main ideas of concrete and abstract messages, including discussion of technical details in his professional field.
- Can practically freely and without prior preparation discuss various topics with native speakers, without creating additional inconvenience for them.
- Can produce clear and detailed text on topics unfamiliar to him.
- Can describe experiences, events, dreams, hopes and aspirations, state and justify opinions and plans.
More about knowledge of English at Level B2
The formal conclusions about the student's knowledge are broken down into smaller sub-points for educational purposes. Such a detailed classification will help you evaluate your own level of English proficiency or help the teacher assess the level of students. For example, a student who is proficient in English at level B1 will be able to do everything that a student at level A2 can do, plus the following:
- participate in workshops, answering questions within their competence, enlisting the support of colleagues.
- discuss attitudes, cultural norms and deviations from them.
- talk about personal and professional life.
- discuss their education, the pros and cons of different educational systems.
- talk about favorite books and give recommendations for reading.
- talk about financial planning, give and receive advice on personal budgeting.
- talk about relationships and acquaintances, including communication with people on social networks.
- visit a restaurant, order food, engage in small talk at dinner, and pay the bill.
- participate in negotiations in their area of expertise, enlisting help in understanding some issues.
- Discuss workplace safety issues, report injuries and explain rules and regulations.
- Discuss the norms of polite behavior and adequately respond to impolite behavior.
Of course, progress will depend on the type of course and the individual student, however, a student can be expected to achieve a B2 level of English proficiency in 600 hours of instruction (total).
