FTCE Practice Test General Knowledge (Mathematics)

Question 1

How many diagonals a dodecagon has?

Accepted Answer

54

Answer

The number of diagonals in a polygon with 'n' sides is given by the formula n(n-3)/2. A dodecagon has 12 sides, so n=12. Plugging this into the formula, we get 12(12-3)/2 = 12(9)/2 = 108/2 = 54.

Question 2

Which of the following number sets does -4 NOT belong to?

Accepted Answer

Set of whole numbers

Answer

Whole numbers are the set of non-negative integers: {0, 1, 2, 3, ...}. Since -4 is a negative number, it does not belong to the set of whole numbers. It does belong to real numbers, rational numbers, and integers.

Question 3

Which of the following can be represented by a quadratic function?

Accepted Answer

Path of a bullet

Answer

The path of a projectile, such as a bullet, under the influence of gravity follows a parabolic trajectory. A quadratic function, when graphed, produces a parabola. Therefore, a quadratic function can accurately model the path of a bullet.

Question 4

The intelligence quotients (IQs) of a randomly selected group of 300 people are normally distributed, with a mean IQ of 100 and a standard deviation of 15. In a normal distribution, approximately 68% of values are within one standard deviation of the mean. How many people in the chosen group have IQs of at least 85?

Accepted Answer

252

Answer

In a normal distribution, approximately 68% of values fall within one standard deviation of the mean. This means 68% of people have IQs between 85 (100-15) and 115 (100+15). The remaining 32% are outside this range, with 16% below 85 and 16% above 115. To find the number of people with IQs of at least 85, we add the 68% (between 85 and 115) and the 16% (above 115), totaling 84%. Therefore, 84% of 300 people is 0.84 * 300 = 252.

Question 5

How many different seven-digit phone numbers can be generated where no digit repeats and zero cannot be the first digit?

Accepted Answer

544,320

Answer

This is a permutation problem with restrictions. For a seven-digit phone number, the first digit cannot be zero (9 choices), and no digits repeat. So, for the subsequent digits, there are 9, 8, 7, 6, 5, and 4 choices respectively. The total number of different phone numbers is calculated by multiplying these choices: 9 * 9 * 8 * 7 * 6 * 5 * 4 = 544,320.

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Uncategorized Practice Test

FTCE Practice Test General Knowledge (Mathematics)