Matemática | Gráficos e Tabelas para o ENEM | Semana da matemática

Summary

This video tutorial focuses on analyzing different types of graphs and calculating percentages, growth rates, and probabilities, particularly in relation to the ENEM exam. The presenter discusses methods to interpret pie charts, bar graphs, and tables, using examples such as percentage increases, salary increments, and symptom statistics. Emphasizing multiple approaches like the rule of three and fraction simplifications, the video aims to simplify complex concepts. Viewers are encouraged to engage with the content, helping them efficiently solve graph-related problems and probability questions commonly found in exams.

Takeaways

• 😀 The ENEM exam often includes questions on graphs, such as bar charts and sector graphs, which can test understanding of percentage changes and rates of increase or decrease.
• 😀 Sector graphs are common in the exam, where understanding the change in percentages over time (e.g., from 40% to 52%) is essential to solving questions about growth or decline.
• 😀 A simple rule of three can be applied to calculate percentage increases, such as when comparing a percentage change from 40% to 52%.
• 😀 Another method to calculate percentage increase involves dividing the final value by the initial value (e.g., 1300 / 1000) and converting the result into a percentage.
• 😀 To calculate percentage reductions, subtract the new percentage from the original, and use the rule of three to find the corresponding reduction rate.
• 😀 When given a situation with a series of values (e.g., number of subscribers over months), it’s important to identify the total increase and calculate percentage growth accurately.
• 😀 The rule of three is particularly helpful in scenarios where you need to calculate the percentage increase or decrease between two data points, such as monthly or yearly changes.
• 😀 For bar charts, the total value for each category is derived from the length of the bars, and this information can be used to answer probability-based questions (e.g., what’s the probability of a patient having either cough or fever).
• 😀 Probability questions related to bar charts often involve summing up categories (e.g., patients with cough or fever) and dividing by the total number of observations to find the likelihood of a specific event.
• 😀 In tasks that involve comparing unit prices, converting all products to the same volume (e.g., per liter) helps determine which item offers the best value, as demonstrated in the example with different types of soda bottles.

Q & A

What is the main focus of the transcript in terms of graphical analysis?

The main focus is on analyzing different types of graphs, particularly sector graphs and bar graphs, and understanding percentage changes, such as growth or reduction in values.

How can the percentage increase from 40% to 52% in the sector graph be calculated?

The percentage increase can be calculated using the rule of three or through division. First, find the difference (52% - 40% = 12%), then calculate the percentage increase by dividing the increase (12%) by the original value (40%), resulting in a 30% increase.

What method does the video suggest for calculating percentage increases, and which is considered more efficient?

The video suggests two methods: using the rule of three and dividing the final value by the initial value. The division method is considered quicker and more efficient.

How do you calculate the percentage reduction from 60% to 48% in the sector graph?

The percentage reduction is found by subtracting the final percentage (48%) from the initial percentage (60%), resulting in a 12% reduction. Then, using the rule of three, you can find the percentage reduction.

How do you calculate the percentage increase in the number of subscriptions from January to February?

The percentage increase can be calculated by dividing the increase (1000 new subscriptions) by the initial value (5000 subscriptions in January), which gives a result of 20%. Alternatively, you can use the rule of three.

What is the probability question related to the bar graph about symptoms?

The probability question asks for the likelihood that a patient has either a cough or a fever. The solution involves adding the number of patients with these symptoms (45 with cough and 35 with fever) and dividing by the total number of patients (100), resulting in an 80% probability.

How do you solve the probability question using fractions?

To solve the probability question with fractions, you add the quantities of patients with the symptoms (45 for cough, 35 for fever) and calculate the total (80 out of 100), which simplifies to 8/10 or 80%.

What strategy is recommended for calculating the price per liter in a table of drink prices?

The strategy involves calculating the price per liter by dividing the price by the quantity. For example, for a 1.5 liter drink, the price per liter can be calculated by multiplying the price by 2 to find the equivalent price for one liter.

How can you determine the most economical drink from a price table?

To find the most economical drink, calculate the price per liter for each option. The drink with the lowest price per liter is the most economical.

What is the final conclusion regarding the most economical drink in the provided example?

The most economical drink in the example is the type 3 drink, which has a price of 72 cents per liter.