Bahas 40 SOAL TES MATEMATIKA SPMB POLSTAT STIS | Part 2 No 11-20

Summary

In this video, Riri Afrianti continues the discussion of 40 math test preparation questions for the 2024 Poltastis SPMB. The second part covers questions 11 to 20, aligned with the latest Poltastis SPM standards and includes formulas and quick problem-solving methods. Topics include probability, trigonometry, derivatives, logic, and integrals. Riri explains solutions in a step-by-step manner, helping students improve their skills with clear explanations and practical tips. Viewers are encouraged to join the Telegram channel for direct interaction and further learning.

Takeaways

• 😀 The video focuses on preparing for the 2024 Poltastis SPMB math test with 40 questions split into multiple parts.
• 😀 The presenter, Riri Afrianti, explains questions 11 to 20, using formulas and quick methods to solve them.
• 😀 Question 11 discusses probability involving fake and real coins, calculating the probability of selecting one real and one fake coin.
• 😀 Question 12 involves using trigonometry to calculate the height of a coconut tree based on the angle of elevation and distance from the observer.
• 😀 In Question 13, the presenter solves for the values of m and n in a derivative equation involving a cubic function.
• 😀 Question 14 addresses integrating a rational function using trigonometric substitution to simplify the integral.
• 😀 Question 15 focuses on expressing logical statements using logical operators and negations, specifically about Azizah’s skills and enrollment in a polytechnic.
• 😀 Question 16 explains how to use integration to find the area under a curve, providing a clear example with functions.
• 😀 In Question 17, the teacher calculates the number of ways to choose students for a math competition, ensuring a mix of male and female students.
• 😀 Question 18 involves solving exponential equations to find the value of 2^(x * y * z) based on given powers of 4 and 3.
• 😀 Question 19 presents a data analysis problem to calculate the number of residents in a certain age group, based on population averages.
• 😀 In Question 20, the video teaches how to find the maximum value of a function by first deriving it and then substituting possible values for x.

Q & A

What is the probability of drawing one real coin and one fake coin from a mix of 8 real coins and 4 fake coins?

The probability can be calculated using combinations. The number of favorable outcomes (choosing one real and one fake coin) is 32, and the total number of possible outcomes (choosing two coins from 12) is 66. The simplified probability is 16/33.

How do we calculate the height of the coconut tree when Farhan is 160 cm tall, the tree is 20 dm away, and the elevation angle is 45 degrees?

First, we convert 20 dm to 200 cm. Then, we apply the formula tan(45) = height of the tree / 200, where tan(45) = 1. The height of the tree is 200 cm above Farhan’s eye level, so the total height is 200 + 160 = 360 cm or 3.6 meters.

What is the value of m * n if f'(1) = 0 and f'(-5) = 0 for the function f(x) = mx^3 + 2x² - nx + 5?

By taking the derivative of f(x), we obtain the equation f'(x) = 3mx² + 4x - n. Substituting x = 1 and x = -5 into this, we solve the system of equations and find m = 1/3 and n = 5. Therefore, m * n = (1/3) * 5 = 5/3.

How do you solve the integral ∫(1 / (-2x + 5)) dx?

This integral is solved by using the trigonometric substitution method. By completing the square for the quadratic expression, we transform it into a form suitable for using the formula 1/a * tan⁻¹(u/a) + C. The final result is 1/2 * tan⁻¹((x - 1)/2) + C.

How can we express the logical operation 'Azizah is good at mathematics and not a student of the Polytechnic of Statistics'?

The correct logical operation is A ∧ ¬B, where A represents 'Azizah is good at mathematics' and B represents 'Azizah is a student of the Polytechnic of Statistics'. The negation of B (¬B) indicates Azizah is not a student at the Polytechnic.

What is the formula for calculating the area of a building using integrals?

To calculate the area of a building with an integral, use the formula ∫(fx - gx) dx, where fx is the upper boundary function and gx is the lower boundary function. For example, for the interval from 0 to 3, if fx = 2x and gx = 0, the integral becomes ∫(2x) dx, which gives the area.

How many ways can a teacher select five students from 10 male and 15 female students, with the condition that at least three male students must be chosen?

There are two possible combinations: 3 males and 2 females, or 4 males and 1 female. Using combinations, the total number of ways to select the students is 12,600 + 3,150 = 15,750.

If 4^x = 9, 3^y = 4, and 4^z = 2, what is the value of 2^(x * y * z)?

By manipulating the equations, we replace 4^x with 2^(2x), 3^y with 4, and 4^z with 2. After substitutions, the value of 2^(x * y * z) simplifies to 2.

How do we calculate the average age of a population when the frequency of different age groups is known?

To calculate the average age, we multiply the midpoint of each age group by its corresponding frequency, sum these products, and then divide by the total frequency. For the unknown frequency in the 20-24 age group, we solve for it by setting up an equation using the average age formula.

How do we determine whether a point is a maximum or minimum for the function f(x) = 2x³ - 9x² + 12x?

First, find the derivative of the function, f'(x) = 6x² - 18x + 12. Then solve f'(x) = 0 to find critical points. For x = 1 and x = 2, substitute these values into f(x) to determine which gives the larger value. The larger value corresponds to the maximum.