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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. What is the area of a square that measures 3.1m on each side?

Correct answer: B

Rationale: To find the area of a square, you square the length of one side. In this case, the side length is 3.1m. So, Area = sideΒ² = 3.1m Γ— 3.1m = 9.61mΒ². Therefore, the correct answer is 9.61mΒ². Choice A (12.4mΒ²) is incorrect as it is the result of multiplying 3.1m by 4 instead of squaring it. Choice C (6.2mΒ²) is incorrect as it is half of the correct answer. Choice D (9.1mΒ²) is incorrect as it is the result of squaring the wrong value (3.1Β²).

3. You measure the width of your door to be 36 inches. The true width of the door is 75 inches. What is the relative error in your measurement?

Correct answer: A

Rationale: The relative error is calculated using the formula: (|Measured Value - True Value| / True Value) * 100%. Substituting the values given, we have (|36 - 75| / 75) * 100% = (39 / 75) * 100% β‰ˆ 0.52 * 100% = 0.52%. Therefore, the relative error in measurement is approximately 0.52%. Choice A is correct because it reflects this calculation. Choice B is incorrect as it represents a lower relative error than the actual value obtained. Choice C is incorrect as it overestimates the relative error. Choice D is incorrect as it underestimates the relative error.

4. What defines a composite number?

Correct answer: C

Rationale: A composite number is a positive integer greater than one that has more than two factors. Choice A is incorrect because a number with only two factors is a prime number. Choice B is incorrect as being a fraction does not define a composite number. Choice D is incorrect because a number with exactly two factors is a prime number, not a composite number.

5. Simplify the expression below. Which of the following is correct? 3.45 * 0.53

Correct answer: A

Rationale: To solve 3.45 * 0.53, multiply the numbers to get 1.8285. Therefore, the correct answer is A. Choice B is incorrect because it incorrectly moves the decimal point. Choice C is incorrect as it is a fraction of the correct answer. Choice D is incorrect as it results from an error in moving the decimal point.

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