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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 ๐‘ฅ^2 - ๐‘ฆ^2 is a difference of squares, which follows the identity: ๐‘ฅ^2 - ๐‘ฆ^2 = (๐‘ฅ + ๐‘ฆ)(๐‘ฅ - ๐‘ฆ). Therefore, the given expression becomes: (๐‘ฅ^2 - ๐‘ฆ^2) / (๐‘ฅ - ๐‘ฆ) = (๐‘ฅ + ๐‘ฆ)(๐‘ฅ - ๐‘ฆ) / (๐‘ฅ - ๐‘ฆ). Since (๐‘ฅ - ๐‘ฆ) appears in both the numerator and the denominator, they cancel each other out, leaving ๐‘ฅ + ๐‘ฆ. Thus, the simplified form of (๐‘ฅ^2 - ๐‘ฆ^2) / (๐‘ฅ - ๐‘ฆ) is ๐‘ฅ + ๐‘ฆ. 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. Simplify the following expression: (1/4) ร— (3/5) รท 1 (1/8)

Correct answer: C

Rationale: First, convert the mixed number 1 (1/8) into an improper fraction: 1 (1/8) = 9/8. Now, simplify the expression: (1/4) ร— (3/5) รท (9/8). To divide by a fraction, multiply by its reciprocal: (1/4) ร— (3/5) ร— (8/9) = 24/180 = 2/15. Thus, the simplified expression is 2/15. Choice A (8/15) is incorrect because the correct answer is 2/15. Choice B (27/160) is incorrect as it is not the result of the given expression. Choice D (27/40) is incorrect as it does not match the simplified expression obtained.

3. Futuristic Furniture gave the man two choices: pay the entire amount in one payment with cash, or pay $1000 as a down payment and $120 per month for two full years in the financing plan. If the man chooses the financing plan, how much more would he pay?

Correct answer: B

Rationale: If the man chooses the financing plan, he pays $1000 as a down payment initially. Over the two-year period, he will be paying $120 per month for a total of 24 months, which amounts to $120 x 24 = $2880. Therefore, the total amount he pays for the furniture through the financing plan is $1000 (down payment) + $2880 (monthly payments) = $3880. Comparing this total with the entire amount paid in one payment with cash would be $3880 - $3000 = $880 more. So, the man would pay $880 more if he chooses the financing plan. Therefore, the correct answer is $1280 more, not $1480, $1600, or $2480. These amounts do not accurately represent the additional cost incurred by choosing the financing plan.

4. A book has a width of 5 decimeters. What is the width of the book in centimeters?

Correct answer: B

Rationale: To convert decimeters to centimeters, you need to multiply by 10 since 1 decimeter is equal to 10 centimeters. Therefore, to find the width of the book in centimeters, multiply 5 decimeters by 10: 5 decimeters * 10 = 50 centimeters. This means the width of the book is 50 centimeters, making choice B, "25 centimeters," the correct answer. Choices A, C, and D are incorrect because they do not correctly convert decimeters to centimeters.

5. How many centimeters are in 7 meters?

Correct answer: C

Rationale: The prefix 'centi-' means one-hundredth. In the metric system, 1 meter is equal to 100 centimeters. Therefore, to convert meters to centimeters, you multiply the number of meters by 100. In this case, 7 meters is equal to 7 * 100 = 700 centimeters. Choice A is incorrect as it does not consider the conversion factor properly. Choice B is incorrect as it only accounts for a factor of 10 instead of 100. Choice D is incorrect as it overestimates the conversion by a factor of 10.

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