{NEW 2024} Bahas 40 SOAL TES MATEMATIKA SPMB POLSTAT STIS | Part 1 No 1-10

Summary

In this educational video, Riri Afril provides a detailed walkthrough of 40 mathematical preparation questions for the 2024 Poltastis SPMB exam. The content covers various topics, including logarithms, geometric figures, inequalities, and vector operations. Riri breaks down complex problems with clear explanations, focusing on both the formulas and fast-solving techniques. Viewers are guided through each question step by step, including essential strategies like taking derivatives for optimization and applying logarithmic identities. The video is designed to help students strengthen their math skills and improve their chances for success in the upcoming exams.

Takeaways

• 😀 The video discusses 40 math problems as part of preparation for the 2024 SPMB Poltastis exam, with a focus on problems from the first 10 questions.
• 😀 Problems are aligned with SPMB Poltastis exam guidelines and standards from the last 5 years, providing solutions with formulas and shortcuts.
• 😀 For problem 1, the solution to an equation involving square roots and logarithms is found by squaring both sides to simplify the expression.
• 😀 In problem 2, the goal is to find the height of a box with maximum volume, solved by deriving the volume formula and finding its maximum using calculus.
• 😀 Problem 3 involves solving a quadratic inequality by identifying the regions where the expression under the square root is positive.
• 😀 In problem 4, composite functions are explored, where the value of F(g(x)) is determined by substituting g(x) into the function F.
• 😀 Problem 5 covers average calculations with a twist: after adding 5 to each student’s grade and increasing by 125%, the new average is calculated.
• 😀 Problem 6 discusses a football team’s performance over 10 matches, calculating the different ways the team can win at least 7 games using combinations.
• 😀 Problem 7 involves calculating the probability of drawing two cards of the same color from an envelope with four differently colored cards.
• 😀 In problem 8, logical reasoning is applied, with the conclusion that a whale does not breathe through gills based on a given premise about fish.
• 😀 Problem 9 deals with simplifying a rational series and using the properties of square roots to evaluate the sum.
• 😀 Problem 10 involves vector operations, where the value of x is found by ensuring that the sum of vectors a and bx is perpendicular to vector a.

Q & A

How do you solve the equation with the infinite square root expression, 1 + 2 log x + √(1 + 2 log x) + √(1 + 2 log x) + ... = 3?

To solve this equation, we first square both sides to eliminate the square root. This gives us 1 + 2 log x + 3 = 9. Simplifying this, we get 2 log x = 5, and using the properties of logarithms, x = 2^5. Therefore, the answer to 2 * x log 8 is 1/2.

What is the height of the box that gives the maximum volume when constructing an open-top box from a 10x10 dm square cardboard by cutting equal squares from each corner?

To maximize the volume, we first write the volume equation V = (10 - 2T) * (10 - 2T) * T, where T is the height of the cut. After simplifying and differentiating the volume function, we find that the height that maximizes the volume is 5/3 dm.

How do you solve the inequality involving square roots, √(x² + 2x - 8) > √(x² + x - 2)?

First, we find the conditions for the square roots to be valid by ensuring the expressions inside the square roots are positive. We then square both sides and simplify the resulting inequality. The solution gives us that x > 6.

What is the result of the composition of the functions F(x) = x² + 2x + 1 and G(x) = 2x - 1?

To find F(G(x)), we substitute G(x) = 2x - 1 into the function F. This results in F(G(x)) = (2x - 1)² + 2(2x - 1) + 1, which simplifies to 4x². Therefore, the answer is 4x².

If the average score of a math class is 60, what is the new average after adding 5 to each student's score and multiplying by 125%?

Let the original average be 60. After adding 5 to each score, the total becomes 60n + 5n, where n is the number of students. Then, multiplying by 125% (or 1.25), we find the new average is 81.25.

How many different ways can a football team finish a season of 10 matches with at least 7 wins?

To find the number of ways to have at least 7 wins, we calculate the combinations for 7, 8, 9, and 10 wins out of 10 matches. The total number of ways is 120 (for 7 wins) + 45 (for 8 wins) + 10 (for 9 wins) + 1 (for 10 wins) = 176 ways.

What is the probability of drawing two cards of the same color from an envelope containing four cards: red, green, blue, and green?

There are 6 possible ways to choose 2 cards from the 4, and only 1 way to pick two green cards. Therefore, the probability is 1/6.

If all fish breathe with gills, and whales are not fish, what conclusion can be drawn?

Using the premise that all fish breathe with gills and that whales are not fish, we conclude that whales do not breathe with gills.

How do you rationalize the expression involving the series with square roots: 1/√(a + √b) + 1/√(b + √c) + ...?

To rationalize the expression, we multiply each term by its conjugate. This results in terms like √a - √b / (a - b), and the terms in the series will cancel out. After simplification, the final result is √2023 - √2.

What is the value of x such that the vector a = i - j + 3k and b = 4i + 10j - 8k are orthogonal?

To find x, we use the condition that the dot product of the vectors a + bx and a must be zero. After solving the equation, we find that x = 11/30.