Free CMAS Mathematics Questions and Answers — Questions and Answers
Question 1: 150 students were surveyed and asked whether they played a sport and whether they played a musical instrument. The results are shown in the table above.
- 1/5 (Correct answer)
- 1/7
- 1/6
- 3/5
Correct answer: 1/5
Without the specific table, it is assumed that the question asked for a fraction representing a particular group of students out of the total 150 surveyed. The answer 1/5 indicates that 30 students (150 / 5 = 30) fell into the category being questioned, such as those who play only a musical instrument or neither a sport nor an instrument.
Question 2: What fraction of the total surveyed students play a sport?
- 2/7
- 7/15 (Correct answer)
- 1/3
- 3/5
Correct answer: 7/15
To determine the fraction of students who play a sport, one would need to sum the number of students who play a sport (including those who also play an instrument) from the provided table. If 70 out of the total 150 students play a sport, this simplifies to 70/150, which reduces to the fraction 7/15. This calculation directly leads to option B.
Question 3: Which of the following is an integer?
- 1/4
- -12.5
- -3 (Correct answer)
- 0.454545…
Correct answer: -3
An integer is a whole number (not a fraction or decimal) that can be positive, negative, or zero. Options A (1/4) is a fraction, B (-12.5) is a decimal, and D (0.454545…) is a repeating decimal. Only -3 fits the definition of an integer, as it is a whole number without any fractional or decimal part.
Question 4: The point (4, 3) is rotated 90 degrees clockwise about the origin. What are the coordinates of the resulting point?
- (-3, 4)
- (-4, 3)
- (4, -3)
- (3, -4) (Correct answer)
Correct answer: (3, -4)
When a point (x, y) is rotated 90 degrees clockwise about the origin, the transformation rule is (x, y) → (y, -x). Applying this rule to the given point (4, 3), the new x-coordinate becomes the original y-coordinate (3), and the new y-coordinate becomes the negative of the original x-coordinate (-4). Therefore, the resulting coordinates are (3, -4).
Question 5: The population of California is approximately 3.7 x 10^7 people. The land area of California is approximately 1.6 x 10^5 square miles. Divide the population by the area to find the best estimate of the number of people per square mile in California.
- 24 people
- 240 people (Correct answer)
- 2,400 people
- 24,000 people
Correct answer: 240 people
To find the people per square mile, divide the population by the area: (3.7 x 10^7) / (1.6 x 10^5). Dividing the numerical parts gives approximately 3.7 / 1.6 ≈ 2.3125. Dividing the powers of ten gives 10^(7-5) = 10^2 = 100. Multiplying these results (2.3125 * 100) yields approximately 231.25, which is best estimated as 240 people per square mile.
Free CMAS Mathematics Questions and Answers
150 students were surveyed and asked whether they played a sport and whether they played a musical instrument.
The results are shown in the table above.