Nursing Elites

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

• A. a² + b²
• B. 2ab
• C. a² + 2ab + b²
• D. a² - 2ab + b²

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 is the independent variable in the equation below? f(t)=4t+9

• A. f
• B. 9
• C. t
• D. 4

Correct answer: C

Rationale: The independent variable in a function is the variable that is being manipulated or changed to obtain different values. In the equation f(t) = 4t + 9, the variable 't' is the independent variable. It is the variable that the function f(t) depends on, and changing its value will result in different outputs for the function. The other choices, 'f', '9', and '4', are not the independent variable as they do not represent the variable that is being manipulated to determine the function's output.

3. Which number is larger, 0.5 or 1/3?

• A. 0.5
• B. 1/3
• C. They are equal
• D. Cannot be determined

Correct answer: A

Rationale: To compare 0.5 and 1/3, we can convert 0.5 to a fraction, which is 1/2. When comparing 1/2 and 1/3, we find that 1/2 is greater than 1/3. Therefore, 0.5 is larger than 1/3. Choice B is incorrect as 1/3 is smaller. Choice C is incorrect as the numbers are not equal. Choice D is incorrect as a clear comparison can be made.

4. Jessica buys 10 cans of paint. Red paint costs $1 per can, and blue paint costs $2 per can. In total, she spends $16. How many red cans did she buy?

• A. 2
• B. 3
• C. 4
• D. 5

Correct answer: C

Rationale: Let r be the number of red cans and b be the number of blue cans. The total cans equation is r + b = 10. The total cost equation is r + 2b = 16. By solving these equations simultaneously, we find r = 4. Therefore, Jessica bought 4 red cans. Choice A, 2 red cans, is incorrect because it does not satisfy the total cans or total cost condition. Choices B and D are also incorrect as they do not fulfill both conditions simultaneously.

5. What is the area of a triangle with a base of 10 cm and a height of 7 cm?

• A. 70 cm²
• B. 35 cm²
• C. 140 cm²
• D. 100 cm²

Correct answer: B

Rationale: To find the area of a triangle, you use the formula A = 1/2 × base × height. Substituting the given values: A = 1/2 × 10 cm × 7 cm = 35 cm². Therefore, the correct answer is B. Choice A (70 cm²) is incorrect as it seems to be the product of the base and height rather than the area formula. Choice C (140 cm²) is incorrect as it appears to be twice the correct answer, possibly a result of a miscalculation. Choice D (100 cm²) is incorrect as it does not reflect the correct calculation based on the given base and height values.

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