# MCAT Math Practice Test 1: Mathematics

### Test Information 15 questions minutes

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1. How would the number 17,060 be written in scientific notation?

• A. 1706 × 101
• B. 1.706 × 104
• C. 1.7060 × 104
• D. 0.17060 × 105

2. How does the number of significant digits differ between 14,320,010 and 3.618000?

• A. 14,320,010 has more significant digits than 3.618000
• B. 14,320,010 has fewer significant digits than 3.618000
• C. 14,320,010 has the same number of significant digits as 3.618000
• D. A comparison cannot be made because the numbers are not both in scientific notation.

3. Using the appropriate number of significant digits, what is the answer to the following math problem? (Note: Assume all numbers are the results of measurements.)

3.060 × 4.10 + 200. =

• A. 210
• B. 213
• C. 212.5
• D. 212.55

4. Which of the following would be the most appropriate setup for estimating the value 3.6 × 4.85 for questions in which answer choices differ by a small margin?

• A. 3.5 × 5
• B. 3.5 × 4.5
• C. 4 × 4
• D. 4 × 5

5. The value of 2000.25 is closest to:

• A. 4
• B. 14
• C. 50
• D. 800

6. Which of the following equations is INCORRECT?

• A. A3 × B3 = (AB)3
• B. A5 ÷ A7 = A-2
• C. (A0.5)4 + A2 = 2A2
• D. (A3)2 = A9

7. How can the value of a natural logarithm be converted to the value of a common logarithm?

• A. The natural logarithm is divided by a constant.
• B. A constant is added to or subtracted from the natural logarithm.
• C. The natural logarithm is raised to an exponent.
• D. The inverse of the natural logarithm is taken.

8. What is the minimum value of 2 cosθ - 1?

• A. -3
• B. -2
• C. -1
• D. 0

9. Which of the following relationships is INCORRECT?

• A. |sin θ × cos θ| < |sin θ| + |cos θ|
• B. sin θ ÷ cos θ = tan θ
• C. tan 90° is undefined
• D. sin θ = sin (90° - θ)

10. What is the approximate pH of a solution with a pKa of 3.6, [HA] = 100 mM, and [A-] = 0.1 M? (Note: )

• A. 1.6
• B. 3.6
• C. 5.6
• D. 7.6

11. At what temperature do the Fahrenheit and Celsius scales give equal values?

• A. 0 K
• B. 233 K
• C. 273 K
• D. 313 K

12. In a certain rigid container, pressure and temperature are directly proportional in a 1:3 ratio. If the pressure is changed from 540 torr to 180 torr via a temperature change, by what factor has the temperature changed?

• A. 360
• B. 3
• C. 1
• D. 13. A 150 pound man must be given a drug that is dosed at Approximately how many milligrams of the drug should be administered per dose? (Note: 1 lb = 4.45 N)

• A. 33 mg
• B. 67 mg
• C. 100 mg
• D. 225 mg

14. The rate of a reaction is calculated as a change in concentration per time. What are the units of the rate constant, k, in a reaction that is second order overall with respect to one species? (Note: A second-order reaction of this type has a rate law with the form rate = k[A]2, where [A] is the concentration of the species.)

• A. • B. • C. • D. 15. Middle-aged men require a base level of 900 Calories per day plus an additional 12 Calories per kilogram of body mass per day. Young adult women require a base level of 500 Calories per day, plus 15 Calories per kilogram of body mass per day. At what mass do middle-aged men and young adult women have the same caloric needs?

• A. 26 kg
• B. 67 kg
• C. 133 kg
• D. 266 kg

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