LATIHAN SOAL OSN KSN BAGI PEMULA MATERI ALJABAR MATEMATIKA OLIMPIADE SAINS NASIONAL 2024

Summary

In this video, the presenter discusses a series of mathematical problems from the OSN (National Science Olympiad) exams, focusing on algebra for beginners. The problems range from solving equations involving powers and fractions to simplifying complex algebraic expressions. Through step-by-step explanations, viewers are guided on how to simplify and solve each problem, ultimately finding the correct values for variables and expressions. The video encourages students to practice, subscribe, and share their learning experiences on social media, providing a valuable resource for both junior and senior high school students preparing for these exams.

Takeaways

• 😀 Problem 1 involves simplifying powers of 3 and solving for x in the equation 4x * 3^2006 + 1 = 3^2009 - 3^2007 + 24, resulting in x = 6.
• 😀 Problem 2 discusses a linear function F(z) = Az + b and asks to find (F(b) - F(a)) / (b - a), which simplifies to A.
• 😀 Problem 3 involves the fractional equation 173/61 = a + 1/b + 1/c + 1/d. By simplifying the terms, the final value of 25a + 5b + 100c + 500d is 5555.
• 😀 Problem 4 requires solving for (a + b) / (a - b) given that a² + b² = 6ab. Simplifying this leads to the final result of 2.
• 😀 Problem 5 focuses on simplifying expressions involving square roots: P = 1/√14 - √13 and Q = 1/√14 + √13. The final answer for P² + PQ + Q² is 55.
• 😀 Problem 6 involves simplifying the complex expression with exponents, ultimately reducing the given terms to 2017^2017.
• 😀 The solution for Problem 1 uses power manipulation and factoring, leading to a clear value for x.
• 😀 Problem 2 emphasizes the importance of substitution in linear functions to simplify expressions.
• 😀 For Problem 3, recognizing the pattern of continued fractions and simplifying them into separate variables (a, b, c, d) was key to solving it.
• 😀 Problem 4 showcases the technique of working with squared terms to simplify algebraic ratios.
• 😀 Problem 5 demonstrates how to handle algebraic fractions and square root terms efficiently using rationalization and simplification techniques.

Q & A

What is the main topic discussed in the video?

The video discusses practice problems related to algebra for beginners, specifically for the OSN (Olympiade Sains Nasional) competition, which includes both middle school (SMP) and high school (SMA) level math questions.

How do we solve the equation in Problem 1: 4x * 3^2006 + 1 = 3^2009 - 3^2007 + 24?

To solve this equation, we first simplify the terms with exponents and factor out common terms. The right side simplifies to 3^2007 * (3^2 - 1) + 24, and after simplifying and isolating x, the solution is found to be x = 6.

In Problem 2, what does the expression (f(b) - f(a)) / (b - a) represent?

In Problem 2, (f(b) - f(a)) / (b - a) represents the average rate of change of the function f(z) = Az + B between the points a and b. The solution simplifies to just the constant A, as the terms involving B cancel out.

How can we simplify the expression 173/61 = a + 1/b + 1/c + 1/d in Problem 3?

We simplify 173/61 by decomposing it into a sum of fractions with denominators corresponding to b, c, and d. After expressing it as a continued fraction, we find that a = 2, b = 1, c = 5, and d = 10, and the final answer to the expression 25a + 5b + 100c + 500d is 5555.

In Problem 4, what approach is used to solve the equation a^2 + b^2 = 6ab?

In Problem 4, the equation a^2 + b^2 = 6ab is used to find the value of (a + b) / (a - b). By substituting the given equation into the formula and simplifying, we obtain x^2 = 2, which means x = sqrt(2), and the answer is A.

What is the significance of the expression P * Q in Problem 5?

In Problem 5, P * Q represents the product of two fractions involving square roots. By using the difference of squares formula, we simplify P * Q to 1. This step is necessary for further calculations to find the value of P^2 + PQ + Q^2.

What is the solution to Problem 5 after calculating P^2 + PQ + Q^2?

After calculating P^2, PQ, and Q^2, we obtain the result 54. Adding PQ (which is 1) gives the final answer of 55.

How do we simplify the expression in Problem 6 involving powers of 2017?

In Problem 6, the expression involves manipulating the powers of 2017 to match the correct exponents. After simplifying, the result is 2017 raised to the power of 2017, which gives the final simplified answer.

What strategy is used to simplify the fraction in Problem 1 with exponents of 3?

In Problem 1, the strategy involves simplifying the exponents on both sides, factoring out common terms, and making sure that the powers of 3 match to simplify the equation, ultimately leading to a solution for x.

Why do we use the difference of squares formula in Problem 5?

The difference of squares formula is used in Problem 5 to simplify the product of two fractions involving square roots. This allows for easier calculation of P * Q, which is necessary to find the final result for P^2 + PQ + Q^2.