simplify x y x y

ATI TEAS 7

TEAS Test Math Questions

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

A. x + y
B. x - y
C. 1
D. (x + y)/(x - y)

Correct answer: A

Rationale: The expression 𝑥^2 - 𝑦^2 is a difference of squares, which follows the identity: 𝑥^2 - 𝑦^2 = (𝑥 + 𝑦)(𝑥 - 𝑦). Therefore, the given expression becomes: (𝑥^2 - 𝑦^2) / (𝑥 - 𝑦) = (𝑥 + 𝑦)(𝑥 - 𝑦) / (𝑥 - 𝑦). Since (𝑥 - 𝑦) appears in both the numerator and the denominator, they cancel each other out, leaving 𝑥 + 𝑦. Thus, the simplified form of (𝑥^2 - 𝑦^2) / (𝑥 - 𝑦) is 𝑥 + 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 range in the number of flights made per month by the flight attendant?

A. 20
B. 25
C. 29
D. 32

Correct answer: C

Rationale: The range is calculated by finding the difference between the highest and lowest values. In this case, the highest number of flights made per month is 32, and the lowest is 3. Therefore, the range is 32 - 3 = 29. Choice C, '29', is the correct answer. Choice A, '20', Choice B, '25', and Choice D, '32', are incorrect as they are individual data points and do not represent the range, which is a measure of spread between the highest and lowest values.

3. Curtis measured the temperature of water in a flask in his science class. The temperature of the water was 35 °C. He carefully heated the flask so that the temperature of the water increased by about 2 °C every 3 minutes. Approximately how much had the temperature of the water increased after 20 minutes?

A. 10 °C
B. 13 °C
C. 15 °C
D. 35 °C

Correct answer: B

Rationale: To find the increase in temperature after 20 minutes, calculate how many 3-minute intervals are in 20 minutes (20 ÷ 3 = 6.66, rounding to 7 intervals). Then, multiply the temperature increase per interval (2 °C) by the number of intervals (7 intervals), giving a total increase of 14 °C. Therefore, after 20 minutes, the temperature of the water would have increased by approximately 14 °C. Choice A, 10 °C, is incorrect as it underestimates the total increase. Choice C, 15 °C, is incorrect as it overestimates the total increase. Choice D, 35 °C, is incorrect as it represents the initial temperature of the water, not the increase in temperature.

4. Gordon purchased a television when his local electronics store had a sale. The television was offered at 30% off its original price of $472. What was the sale price Gordon paid?

A. $141.60
B. $225.70
C. $305.30
D. $330.40

Correct answer: D

Rationale: To find the sale price after a 30% discount, you need to subtract 30% of the original price from the original price. 30% of $472 is $141.60. Subtracting this discount from the original price gives $472 - $141.60 = $330.40, which is the sale price Gordon paid. Choice A, $141.60, is incorrect as it represents only the discount amount, not the final sale price. Choices B and C are also incorrect as they do not account for the correct calculations of the discount and final sale price.

5. Out of 9 trips, a person chooses the longest route for 3 of them. What percentage of their trips is the longest route?

A. 0.25
B. 0.33
C. 0.5
D. 0.75

Correct answer: B

Rationale: To find the percentage of trips where the person chose the longest route, divide the number of longest route trips (3) by the total number of trips (9) and multiply by 100. This gives (3/9) * 100 = 33.33%, which can be rounded to 33%. Therefore, the correct answer is B. Choice A (0.25), C (0.5), and D (0.75) are incorrect because they do not accurately represent the percentage of trips where the longest route was chosen based on the given information.