AS PRINCIPAIS FÓRMULAS DE MATEMÁTICA DO ENEM EM 15 MINUTOS | GUIA RÁPIDO [PARTE 2]

10 Formulas for ENEM: Part 2

Introduction to Key Formulas

• The video presents the top 5 formulas most frequently tested in the ENEM exam, following a previous part that covered formulas ranked from 10th to 6th.

• Emphasis on the importance of specific methodologies tailored for ENEM preparation to achieve faster results.

Importance of Methodology

• A structured approach allows students to prioritize their study areas effectively, enhancing understanding across subjects like chemistry and physics.

• The speaker shares success stories of students who significantly improved their scores, highlighting the effectiveness of targeted study methods.

Formula #5: Median

• The fifth most tested formula is the median, which represents a typical annual number of earthquakes based on data from 2000 to 2011.

• To find the median, data must be arranged in ascending order; if there’s an even number of terms, average the two middle values.

Calculating Median Example

• An example illustrates how to calculate the median with a dataset containing 12 terms by identifying and averaging the sixth and seventh terms.

• The calculation shows that when averaging these two numbers (15 and 16), you arrive at a median value of 15.5.

Transitioning to Formula #4: Pythagorean Theorem

• Moving on to the fourth most common formula, which is the Pythagorean theorem used in right triangles.

• An origami example is introduced where dimensions are manipulated through folding paper, leading into a practical application of geometry.

Applying Pythagorean Theorem

• In this scenario, one segment measures 12 cm while another measures 6 cm; using these dimensions helps set up for applying Pythagoras' theorem.

• A triangle setup is described where calculations will determine an unknown length (x), reinforcing understanding through visual representation.

Conclusion on Geometry Application

• The speaker outlines how to apply Pythagorean theorem principles by squaring both known sides and summing them up to solve for x.

Solving for x and Area Calculations

Finding the Value of x

• The speaker discusses solving for x, indicating that x = 180 is a potential solution, but notes that this option is not available.

• The speaker suggests two methods to solve the problem: factoring or squaring an alternative. They demonstrate using option D, where calculations confirm it yields 180.

Factoring and Simplifying

• The speaker factors 180 by dividing it by prime numbers (2, 3, and 5), ultimately rewriting it as sqrt2 times 3 times 5.

• After simplification, they conclude that the expression becomes 6 times sqrt5.

Area of Rectangles in Real-Life Context

• Transitioning to practical applications, the speaker introduces a scenario involving a rectangular park requested by residents due to limited leisure spaces.

• They mention budget constraints limiting fencing material to a maximum of 180 meters.

Evaluating Land Options

• The speaker emphasizes eliminating land options exceeding the fencing limit. For example, they quickly dismiss one plot based on its perimeter calculation.

• They calculate perimeters for various plots, confirming which ones meet the criteria while noting specific dimensions.

Comparing Areas of Selected Plots

• The area calculations are performed for two selected plots: Plot C (60m x 30m = 1000 m²) and Plot D (70m x 20m = 1400 m²).

• Ultimately, Plot C is determined to have a larger area despite initial confusion about which plot was superior.

Key Formulas in Mathematics

Importance of Scale in Geometry

• The discussion shifts towards essential mathematical formulas with emphasis on scale as one of the most frequently tested concepts in exams like ENEM.

Application of Scale in Practical Scenarios

• An example is provided where students must create a scaled model of a sports court measuring 28m by 12m, using a scale factor of 1:250.

Converting Measurements for Scaling

• The speaker explains how to convert real measurements into centimeters for accurate scaling representation.

Utilizing Proportions for Calculation

• A rule-of-three method is suggested instead of relying solely on formulaic approaches. This involves setting up proportions based on known values.

Finalizing Dimensions from Calculations

• By applying conversions correctly (e.g., converting meters to centimeters), they derive necessary dimensions needed for constructing the model accurately.

This structured approach provides clarity on key mathematical concepts discussed throughout the transcript while ensuring easy navigation through timestamps linked directly to relevant sections.

Understanding Arithmetic Mean in ENEM

Key Concepts of Arithmetic Mean

• The arithmetic mean is highlighted as the most frequently tested formula in the ENEM exam, emphasizing its importance for students.

• Contracts for various online services often contain excessive information, leading to lengthy reading times; understanding average reading time is crucial.

• To calculate the arithmetic mean, one must sum all terms and divide by the number of terms, illustrating a straightforward mathematical process.

• An example calculation is provided: summing specific values (e.g., 13 + 27 + 40...) to demonstrate how to arrive at an average effectively.

• The video concludes with a recap of key formulas discussed, reinforcing their relevance for exam preparation and practical application.