apply the polynomial identity to rewrite a b 6251518
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ATI TEAS 7

TEAS Test Math Questions

1. Apply the polynomial identity to rewrite (a + b)².

Correct answer: C

Rationale: When you see something like (a + b)², it means you're multiplying (a + b) by itself: (a + b)² = (a + b) × (a + b) To expand this, we use the distributive property (which says you multiply each term in the first bracket by each term in the second bracket): Multiply the first term in the first bracket (a) by both terms in the second bracket: a × a = a² a × b = ab Multiply the second term in the first bracket (b) by both terms in the second bracket: b × a = ab b × b = b² Now, add up all the results from the multiplication: a² + ab + ab + b² Since ab + ab is the same as 2ab, we can simplify it to: a² + 2ab + b² So, (a + b)² = a² + 2ab + b². This is known as a basic polynomial identity, and it shows that when you square a binomial (a two-term expression like a + b), you get three terms: the square of the first term (a²), twice the product of the two terms (2ab), and the square of the second term (b²). Therefore, the correct answer is C (a² + 2ab + b²)

2. Which of the following answer choices is spelled correctly?

Correct answer: A

Rationale: The correct spelling is 'intrude,' which means to enter a place or situation where one is unwelcome or not invited. The other answer choices, 'aclimate,' 'wisen,' and 'alude,' are misspelled. 'Aclimate' should be spelled as 'acclimate,' meaning to become accustomed to a new climate or environment. 'Wisen' is likely intended to be 'wisen' but is not a recognized word. 'Alude' should be spelled as 'allude,' meaning to suggest or call attention to indirectly.

3. What would be the most helpful advice for the student starting a research assignment on Japanese-American internment camps during World War II?

Correct answer: D

Rationale: The best advice for the student would be to locate texts in the library related to World War II in America and look for references to internment camps. This choice is the most appropriate as it focuses on accessing specific and credible sources directly related to the research topic. Choices A and C are too broad and may not provide in-depth information on the internment camps. Choice B, while related to American history, may not offer the specific details needed for the research assignment on Japanese-American internment camps during World War II.

4. What is the rigid structure that provides shape and support to plant cells?

Correct answer: A

Rationale: The correct answer is the cell wall, as it is the rigid structure that provides shape and support to plant cells. The cell wall is located outside the plasma membrane and is primarily composed of cellulose, giving it its rigid nature. The plasma membrane (option B) is a semi-permeable membrane surrounding the cell that regulates the movement of substances in and out of the cell. The nucleus (option C) houses the cell's genetic material and controls cellular activities. Cytoplasm (option D) is the gel-like substance within the cell that surrounds organelles and where various cellular processes take place, but it does not provide the rigid structure and support that the cell wall does.

5. According to the passage, what effect does encountering an automobile with eighteen wheels have on the hypothesis 'All automobiles have only four wheels'?

Correct answer: C

Rationale: Encountering an automobile with eighteen wheels contradicts the hypothesis that all automobiles have only four wheels. This contradicts the initial hypothesis, proving it to be false. The passage explains that when evidence disproves a hypothesis, it directly contradicts the hypothesis, leading to its disproof. In the context of the monkey example provided, encountering a hairless monkey out of many hairy monkeys disproved the hypothesis 'All monkeys are hairy.' Therefore, the presence of an automobile with eighteen wheels disproves the hypothesis that all automobiles have only four wheels. Other choices are incorrect because encountering such an automobile directly contradicts the initial hypothesis, leading to its disproof, rather than proving it, raising its probability, or decreasing its probability.

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