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 ๐ฅ^2 - ๐ฆ^2 is a difference of squares, which follows the identity: ๐ฅ^2 - ๐ฆ^2 = (๐ฅ + ๐ฆ)(๐ฅ - ๐ฆ). Therefore, the given expression becomes: (๐ฅ^2 - ๐ฆ^2) / (๐ฅ - ๐ฆ) = (๐ฅ + ๐ฆ)(๐ฅ - ๐ฆ) / (๐ฅ - ๐ฆ). Since (๐ฅ - ๐ฆ) appears in both the numerator and the denominator, they cancel each other out, leaving ๐ฅ + ๐ฆ. Thus, the simplified form of (๐ฅ^2 - ๐ฆ^2) / (๐ฅ - ๐ฆ) is ๐ฅ + ๐ฆ. 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 length of the unknown leg of a right triangle that has one leg measuring 9 feet and a hypotenuse of 19 feet? (Round to the nearest tenth.)
- A. 16.7 feet
- B. 16.0 feet
- C. 17.4 feet
- D. 8.4 feet
Correct answer: A
Rationale: To find the length of the unknown leg (a) of a right triangle, use the Pythagorean theorem: aยฒ + 9ยฒ = 19ยฒ. Substitute the known values, solve for a: aยฒ + 81 = 361. Subtract 81 from both sides to get aยฒ = 280. Taking the square root of 280 gives a โ 16.7 feet. Therefore, the correct answer is 16.7 feet. Choice B (16.0 feet) is incorrect as it does not accurately round to the nearest tenth. Choice C (17.4 feet) and choice D (8.4 feet) are incorrect as they do not match the calculated value using the Pythagorean theorem.
3. What is the domain for the function f(x)=2x+5?
- A. All real numbers
- B. x โฅ 0
- C. x > 0
- D. x โค 0
Correct answer: A
Rationale: The domain of a function represents all possible input values that the function can accept. In this case, the function f(x)=2x+5 is a linear function, and linear functions have a domain of all real numbers. This means that any real number can be substituted for x in the function f(x)=2x+5, making choice A, 'All real numbers,' the correct domain for this function. Choices B, C, and D, restrict the domain unnecessarily by limiting the values of x to specific subsets of real numbers, which does not accurately reflect the nature of the given function.
4. Solve for x: 3(x - 5) = 2(x + 3)
- A. x = 3
- B. x = 6
- C. x = 9
- D. x = 12
Correct answer: A
Rationale: To solve the equation 3(x - 5) = 2(x + 3) for x, start by distributing the terms inside the parentheses. This gives you 3x - 15 = 2x + 6. Next, combine like terms by moving all terms with x to one side and the constants to the other side. Subtracting 2x from both sides gives x - 15 = 6. Finally, adding 15 to both sides results in x = 21. Therefore, the correct answer is A: x = 3. Choices B, C, and D are incorrect as they do not result from the correct calculations of the equation.
5. If a box of 55 syringes costs $660.00, what is the cost of four syringes?
- A. $51.00
- B. $26.00
- C. $32.00
- D. $48.00
Correct answer: D
Rationale: To find the cost of one syringe, divide the total cost by the number of syringes: $660.00 รท 55 = $12. Therefore, the cost of four syringes is 4 x $12 = $48. Choices A, B, and C are incorrect because they do not correctly calculate the cost per syringe or the total cost of four syringes.
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