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. During January, Dr. Lewis worked 20 shifts. During February, she worked three times as many shifts as she did during January. During March, she worked half the number of shifts she worked during February. Which equation below describes the number of shifts Dr. Lewis worked in March?

• A. shifts = 20 + 3 + 1/2
• B. shifts = (20)(3)(1/2)
• C. shifts = (20)(3) + 1/2
• D. shifts = 20 + (3)(1/2)

Correct answer: B

Rationale: During January, Dr. Lewis worked 20 shifts. Shifts for January = 20. During February, she worked three times as many shifts as she did during January. Shifts for February = (20)(3) = 60. During March, she worked half the number of shifts she worked in February. Shifts for March = (60)(1/2) = 30. Therefore, the correct equation to describe the number of shifts Dr. Lewis worked in March is 'shifts = (20)(3)(1/2)', representing the calculation based on the given scenario. Choices A, C, and D do not accurately represent the correct mathematical relationship between the shifts worked in the different months, making them incorrect.

3. Jacob has $100. She spends 87% of the money. She then invests the remaining amount and earns a profit of 75%. How much money does she now have?

• A. $13.00
• B. $87.00
• C. $22.75
• D. $9.75

Correct answer: C

Rationale: Jacob spends 87% of $100, which is $87, leaving her with $13. When she invests the remaining $13 and earns a 75% profit, she gains an additional $9.75. Thus, the total amount she now has is $13 (remaining amount) + $9.75 (profit) = $22.75. Choice A is incorrect as it reflects the remaining amount before investing and earning a profit. Choice B is incorrect as it does not account for the profit earned from the investment. Choice D is incorrect as it only considers the profit amount, not the total sum.

4. A gift box has a length of 14 inches, a height of 8 inches, and a width of 6 inches. How many square inches of wrapping paper are needed to wrap the box?

• A. 56
• B. 244
• C. 488
• D. 672

Correct answer: C

Rationale: To find the surface area of a rectangular prism, you use the formula SA = 2lw + 2wh + 2hl, where l is the length, w is the width, and h is the height. Substituting the given dimensions, the calculation would be SA = 2(14)(6) + 2(6)(8) + 2(8)(14) = 168 + 96 + 224 = 488 square inches. Therefore, 488 square inches of wrapping paper are needed to wrap the box. Choice A (56), Choice B (244), and Choice D (672) are incorrect because they do not represent the correct surface area calculation for the given box dimensions.

5. Andy has already saved $15. He plans to save $28 per month. Which of the following equations represents the amount of money he will have saved?

• A. y = 15 + 28x
• B. y = 43x + 15
• C. y = 43x
• D. y = 28 + 15x

Correct answer: A

Rationale: The correct equation to represent the amount of money Andy will have saved is y = 15 + 28x. This is because Andy has already saved $15 and plans to save an additional $28 per month. Therefore, the total amount he will have saved can be calculated by adding the initial $15 to the monthly savings of $28 (28x), resulting in y = 15 + 28x. Choices B, C, and D do not correctly account for the initial $15 that Andy has saved and therefore do not represent the total amount correctly.

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