High School

**Feature: Chess and ACT Math Preparation**

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**ACT Math Section Overview:**

You've prepared for the ACT math section, but are you ready to tackle its most challenging questions? This guide is designed to help you understand why these questions are difficult and how best to solve them. If you're aiming for a perfect score or are simply curious about the most challenging questions, this guide is for you.

**Content:**

- We've compiled what we believe to be the 21 most difficult ACT math questions from the past 10 years, complete with strategies and answer explanations. These are real ACT questions, so studying them is one of the best ways to improve your score.

**Brief Overview of the ACT Math Section:**

- The ACT math section is one complete section with 60 questions to be completed in 60 minutes.
- Questions are arranged in order of ascending difficulty:
- Questions 1-20: Easy
- Questions 21-40: Medium
- Questions 41-60: Difficult

- The ACT categorizes difficulty based on the time it takes the average student to solve a problem and the percentage of correct answers.

**Should You Focus on the Hardest Math Questions Now?**

- If you're just starting your study prep, take a full practice test to gauge your current score level and percentile.
- For scores in the 0-16 or 17-24 range, focus first on key math strategies before tackling the most difficult problems.
- If you're scoring 25 or above, proceed to the guide for tackling the most difficult ACT math questions.

This guide will help you identify the most challenging ACT math problems and provide strategies to solve them.

Answer :

Answer:

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Step-by-step explanation:

Final answer:

The z-score for an SAT score of 720 is 1.74, indicating it is relatively high. A math SAT score 1.5 standard deviations above the mean is 697.5. The person who took the ACT math test performed better based on z-scores.

Explanation:

The question is asking about the distribution of scores in the math section of the SAT exam. The mean (µ) is 520 and the standard deviation (σ) is 115. To calculate the z-score for an SAT score of 720, we use the formula: z = (x - µ) / σ. Plugging in the given values, we have z = (720 - 520) / 115 = 1.74. This means the SAT score of 720 is 1.74 standard deviations above the mean. In the context of this situation, a score of 720 is relatively high compared to the average.


To find the math SAT score that is 1.5 standard deviations above the mean, we multiply the standard deviation by 1.5 and add it to the mean. So, x = µ + (1.5 * σ) = 520 + (1.5 *115) = 697.5. Therefore, a math SAT score of 697.5 is 1.5 standard deviations above the mean.


To determine who did better on their respective tests, we need to compare the scores to the mean and standard deviation of each test. For the SAT math test, the person scored 700, which is (700 - 514) / 117 = 1.59 standard deviations above the mean. For the ACT math test, the person scored 30, which is (30 - 21) / 5.3 = 1.7 standard deviations above the mean. Since a higher z-score means a higher relative score compared to the mean, the person who took the ACT math test did better in terms of their test score.

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