PREDIKSI TES MANDIRI UNRAM 2025 PART 3

Summary

This video provides a detailed explanation of various mathematical problems, including concepts like combined averages, arranging books with constraints, arithmetic sequences, and maximizing volume. It covers the method of solving for unknowns using algebraic equations, such as determining the number of students in a class based on average scores, or calculating the maximum volume of a box formed from cardboard. The script includes step-by-step breakdowns of each problem, illustrating how to approach and solve them efficiently, making it both educational and practical for students tackling similar math questions.

Takeaways

• 😀 The first problem discusses the combined average score of male and female students, where the combined average is 76. The ratio of male to female students is calculated to be 3:2 using the combined average formula.
• 😀 The second problem involves arranging books on a shelf with the condition that similar books must be placed side by side. The number of ways to arrange the books is 1728, calculated using factorials.
• 😀 In the third problem, an arithmetic sequence with 21 terms is given. The middle term is 52, and the sum of certain terms (U3 + U5 + U15) equals 106. The seventh term of the sequence is found to be 30 using algebraic equations.
• 😀 The fourth problem involves finding the 20th term of an arithmetic series where the sum of the first n terms is given by Sn = n² + 5n. The 20th term is calculated to be 44 after determining the first term (a) and the common difference (b).
• 😀 The fifth problem involves a rectangular box created from cardboard by cutting identical squares at the corners and folding the sides. The maximum volume of the resulting box is calculated to be 200 cm³.
• 😀 The ratio of male to female students is solved using the combined average formula, and the final result is 3:2.
• 😀 The book arrangement problem requires the use of factorials to account for the number of ways to arrange books in groups. The answer is 1728 arrangements.
• 😀 In the arithmetic sequence, the solution involves setting up equations for various terms in the sequence and solving for the seventh term using basic algebra.
• 😀 The approach to solving the maximum volume problem involves using the formula for volume, taking derivatives to find critical points, and determining the maximum volume based on the dimensions of the box.
• 😀 The overall theme of the script is mathematical reasoning and problem-solving, covering topics such as averages, sequences, permutations, and volume maximization.

Q & A

What is the combined average score formula for male and female students?

The combined average score formula is: (N1 * average1 + N2 * average2) / (N1 + N2), where N1 is the number of male students, average1 is the average score of male students, N2 is the number of female students, and average2 is the average score of female students.

How is the ratio of male and female students determined in the script?

The ratio of male and female students is found by setting up an equation based on the combined average score. Using the given values, N1/N2 = 6/4, which simplifies to 3/2, thus the ratio of male to female students is 3:2.

What is the number of ways to arrange Budi's books with similar books side by side?

The total number of ways to arrange the books is 1728. This is calculated by considering the arrangements of each group of similar books (math, engineering, and programming), then multiplying the factorials of each group: 3! for math books, 2! for engineering books, and 4! for programming books, resulting in 1728 ways.

What is the formula for finding a term in an arithmetic sequence?

The formula for finding the nth term in an arithmetic sequence is: Un = a + (n - 1) * d, where 'a' is the first term, 'n' is the term number, and 'd' is the common difference.

How do you find the 7th term of an arithmetic sequence?

To find the 7th term, we use the formula for the nth term: Un = a + (n - 1) * d. After solving for the constants 'a' and 'd' from the given conditions, substitute n = 7 to find U7.

What are the first steps to solve for the 7th term in an arithmetic sequence where U3 + U5 + U15 = 106?

Start by writing the terms in terms of 'a' (the first term) and 'd' (the common difference). For U3, U5, and U15, use the formula Un = a + (n - 1) * d, then set up equations and solve for 'a' and 'd'.

How do you solve for the difference in an arithmetic sequence if you know the middle term and other terms?

You can solve for the common difference 'd' by eliminating terms from the system of equations. For example, subtract one equation from another to isolate 'd' and then solve for its value.

What is the correct approach to solve the volume of a box formed by cutting squares from a rectangular cardboard?

The volume is calculated by multiplying the length, width, and height of the resulting box. After cutting identical squares, the length becomes 24 - 2x, the width becomes 9 - 2x, and the height is x. The volume formula is: V = (24 - 2x)(9 - 2x)(x).

How do you find the value of x that maximizes the volume of the box?

To find the value of x that maximizes the volume, take the derivative of the volume equation and set it equal to zero. Solve the resulting equation for x to find the critical points, and use these to determine the maximum volume.

Why is x = 9 not a valid solution for the volume maximization problem?

x = 9 is not valid because it would make the width of the box negative (24 - 2*9 = 6, and 9 - 2*9 = -9), which is physically impossible. Therefore, only the valid solution, x = 2, is considered.