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 4 + 5 + 12 + 9?
- A. 20
- B. 30
- C. 40
- D. 50
Correct answer: B
Rationale: The correct answer is B: 30. To find the sum, you need to add 4 + 5 + 12 + 9, which equals 30. Choice A (20) is incorrect because it does not account for the correct addition of the numbers provided. Choice C (40) is incorrect as it represents the sum of the numbers incorrectly. Choice D (50) is also incorrect as it is not the sum of the given numbers.
3. Solve the equation for the unknown. 3x + 2 = 20
- A. x = 2
- B. x = 4
- C. x = 6
- D. x = 8
Correct answer: C
Rationale: Simplify the equation step by step: Subtract 2 from both sides: 3x + 2 - 2 = 20 - 2 3x = 18 Divide both sides by 3: x = 18 รท 3 x = 6 Therefore, the correct answer is C (x = 6).
4. How many kiloliters are in 147 liters?
- A. 0.147 kiloliters
- B. 1.47 kiloliters
- C. 1,470 kiloliters
- D. 147,000 kiloliters
Correct answer: A
Rationale: To convert liters to kiloliters, divide by 1000 since there are 1000 liters in a kiloliter. Therefore, 147 liters = 0.147 kiloliters. Choice B is incorrect as it incorrectly moves the decimal point. Choices C and D are significantly larger than the correct answer, indicating an incorrect conversion factor used.
5. What is the result of multiplying 3/5 by 5/7?
- A. 3/7
- B. 1
- C. 2
- D. 4
Correct answer: A
Rationale: To multiply fractions, multiply the numerators together and the denominators together. Multiplying 3/5 by 5/7 gives (3*5)/(5*7) = 15/35. This fraction simplifies to 3/7 by dividing the numerator and denominator by their greatest common factor, which is 5. Therefore, the correct answer is 3/7. Choices B, C, and D are incorrect as they do not result from multiplying 3/5 by 5/7.
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