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ATI TEAS 7

TEAS Test Math Questions

1. Simplify (x^2 - y^2) / (x - y)

Correct answer: A

Rationale: The expression π‘₯^2 - 𝑦^2 is a difference of squares, which follows the identity: π‘₯^2 - 𝑦^2 = (π‘₯ + 𝑦)(π‘₯ - 𝑦). Therefore, the given expression becomes: (π‘₯^2 - 𝑦^2) / (π‘₯ - 𝑦) = (π‘₯ + 𝑦)(π‘₯ - 𝑦) / (π‘₯ - 𝑦). Since (π‘₯ - 𝑦) appears in both the numerator and the denominator, they cancel each other out, leaving π‘₯ + 𝑦. Thus, the simplified form of (π‘₯^2 - 𝑦^2) / (π‘₯ - 𝑦) is π‘₯ + 𝑦. Therefore, the correct answer is A (x + y). Option B (x - y) is incorrect as it does not result from simplifying the given expression. Option C (1) is incorrect as it does not account for the variables x and y present in the expression. Option D ((x + y)/(x - y)) is incorrect as it presents the simplified form in a different format than the correct answer.

2. Divide 52 by 27 and 51 by 27 and simplify.

Correct answer: A

Rationale: To divide 52 by 27 and 51 by 27, you get 52/27 and 51/27, respectively. When simplified, 52/27 is the correct answer. The other choices, 51/27, 52/29, and 51/29, are incorrect because they do not reflect the correct result of dividing the given numbers.

3. Simplify the following expression: 6 + 7 Γ— 3 - 4 Γ— 2

Correct answer: B

Rationale: ollow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)): Multiply: 7 Γ— 3 = 21, and 4 Γ— 2 = 8 Perform addition and subtraction: 6 + 21 - 8 = 19 Thus, the simplified expression equals 19.

4. In the winter of 2006, 6 inches of snow fell in Chicago, IL. The following winter, 3 inches of snowfall fell in Chicago. What was the percent decrease in snowfall in Chicago between those two winters?

Correct answer: C

Rationale: To calculate the percent decrease in snowfall between the two winters, use the formula: Percent Decrease = ((Initial Value - Final Value) / Initial Value) * 100. In this case, the initial value is 6 inches and the final value is 3 inches. Plug these values into the formula: ((6 - 3) / 6) * 100 = (3 / 6) * 100 = 0.5 * 100 = 50%. Therefore, the correct answer is 50%, which is not listed among the choices provided. Among the given choices, the closest percentage is 41.00%, which corresponds to choice C.

5. A rectangular solid box has a square base with a side length of 5 feet and a height of h feet. If the volume of the box is 200 cubic feet, which of the following equations can be used to find h?

Correct answer: C

Rationale: The volume formula for a rectangular solid is V = l Γ— w Γ— h. In this case, the length and width are both 5 feet. Substituting the values into the formula gives V = 5 Γ— 5 Γ— h = 25h = 200. Therefore, h = 200 Γ· 25 = 8. Option A is incorrect because the product of length, width, and height is not directly equal to the volume. Option B is incorrect as squaring the height is not part of the volume formula. Option D is incorrect as it oversimplifies the relationship between height and volume, not considering the base dimensions.

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