FTCE Practice Test General Knowledge (Mathematics) — Questions and Answers

Question 1: How many diagonals a dodecagon has?

109
54 (Correct answer)
14
26

Correct answer: 54

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?

Set of real numbers
Set of whole numbers (Correct answer)
Set of rational numbers
Set of integers

Correct answer: Set of whole numbers

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?

Path of a bullet (Correct answer)
The distance traveled by an object over time when the rate is constant
Radioactive decay
Path of a sound wave

Correct answer: Path of a bullet

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?

200
96
252 (Correct answer)
216

Correct answer: 252

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?

35,280
544,320 (Correct answer)
3,265,920
5,040

Correct answer: 544,320

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.

Question 6: Rose tutored students in math, chemistry, and the ACT last year. She tutored ten students in math, eight in chemistry, and seven in preparation for the ACT. She tutored five students in both math and chemistry, four students in chemistry and for the ACT, and five students in math and for the ACT. She was a tutor in all three subjects for three students. Rose tutored how many students last year?

14 (Correct answer)
28
36
24

Correct answer: 14

This problem requires the Principle of Inclusion-Exclusion for three sets. The formula is: Total = |M| + |C| + |A| - (|M∩C| + |C∩A| + |M∩A|) + |M∩C∩A|. Plugging in the given values: 10 + 8 + 7 - (5 + 4 + 5) + 3 = 25 - 14 + 3 = 14 students.

Question 7: Darwin's current rent is $800 per month. He is relocating to a new apartment complex with a monthly rent of $1,100. What was the percentage increase in his monthly rent?

37.5% (Correct answer)
36%
25.5%
26%

Correct answer: 37.5%

To find the percentage increase, first calculate the amount of increase: $1,100 - $800 = $300. Then, divide the increase by the original amount and multiply by 100 to get the percentage. So, ($300 / $800) * 100% = 0.375 * 100% = 37.5%.

Question 8: Which of the following statements is correct?

The set of integers is a subset of the set of natural numbers
The set of whole numbers is a subset of the set of natural numbers
The set of rational numbers is a subset of the set of integers
The set of integers is a subset of the set of rational numbers (Correct answer)

Correct answer: The set of integers is a subset of the set of rational numbers

Integers include all positive and negative whole numbers, plus zero. Rational numbers are any number that can be expressed as a fraction p/q, where p and q are integers and q is not zero. Since any integer 'n' can be written as n/1, all integers are rational numbers, making the set of integers a subset of the set of rational numbers.

Question 9: Jonathan pays $45 for a jacket that has been reduced by 25%. What was the jacket's original price?

$60 (Correct answer)
$70
$65
$75

Correct answer: $60

If the jacket was reduced by 25%, then $45 represents 100% - 25% = 75% of the original price. To find the original price, divide the current price by the percentage it represents. So, $45 / 0.75 = $60.

Question 10: Ryan spends $24,210 on a car. The car's price has been reduced by ten percent. What was the car's original cost?

$26,500
$27,000
$25,900
$26,900 (Correct answer)

Correct answer: $26,900

If the car's price was reduced by 10%, then $24,210 represents 100% - 10% = 90% of the original cost. To find the original cost, divide the current price by the percentage it represents. Therefore, $24,210 / 0.90 = $26,900.

Question 11: Sam spends 1/8 of his monthly salary on utilities. What is his monthly salary if his utility bills total $320?

$2,520
$2,560 (Correct answer)
$2,480
$2,650

Correct answer: $2,560

If $320 represents 1/8 of Sam's monthly salary, then to find the full salary, you need to multiply $320 by 8. This is because 1/8 of the salary is $320, so 8/8 (the full salary) would be 8 times that amount. Therefore, $320 * 8 = $2,560.

Question 12: Which is closed under the operation of division?

integers
nonzero rational numbers (Correct answer)
irrational numbers
whole numbers

Correct answer: nonzero rational numbers

A set is closed under an operation if performing that operation on any two elements of the set always results in an element that is also in the set. While integers, irrational numbers, and whole numbers are not closed under division, dividing any nonzero rational number by another nonzero rational number always yields a rational number. This is because a rational number is a fraction, and dividing fractions results in another fraction.

Question 13: ABG Appliances pays $800 to their suppliers for a computer and sells the same computer for $960 in their retail store. Calculate their markup as a percentage of their cost price.

20% (Correct answer)
80.5%
18.7%
130%

Correct answer: 20%

To calculate the markup as a percentage of the cost price, first find the markup amount by subtracting the cost ($800) from the selling price ($960), which is $160. Then, divide the markup amount by the cost price: $160 / $800 = 0.20. Finally, multiply by 100 to express it as a percentage: 0.20 * 100% = 20%.

Question 14: You go to Wal-Mart knowing the TV you want costs $1050, but you notice it is on sale for $700. What is the percentage drop?

1/3%
36%
33%
33 1/3% (Correct answer)

Correct answer: 33 1/3%

First, calculate the dollar amount of the drop by subtracting the sale price ($700) from the original price ($1050), which gives $350. To find the percentage drop, divide this amount by the original price: $350 / $1050 = 1/3. Converting this fraction to a percentage yields 33 1/3%.

Question 15: In a test, ten students received the following scores: 2, 6, 6, 7, 8, 8, 9, 11, 15, and x are all prime numbers. There is only one mode, and the mean, median, and mode all have the same value. What is the numerical value of x?

8 (Correct answer)
10
7
12

Correct answer: 8

The problem states there is only one mode, and the mean, median, and mode are all equal. The given numbers are 2, 6, 6, 7, 8, 8, 9, 11, 15. For there to be a single mode, 'x' must be either 6 or 8, making one of them appear three times. If x=8, the sorted list is 2, 6, 6, 7, 8, 8, 8, 9, 11, 15. The mode is 8, the median (average of the 5th and 6th terms) is (8+8)/2 = 8, and the mean (sum 80 / 10 terms) is 8, satisfying all conditions.

Question 16: Joshua purchases boxes that can hold an average of 18 books. How many boxes should he buy if he wants to pack 192 books?

11 (Correct answer)
12
14
13

Correct answer: 11

To find the number of boxes needed, divide the total number of books (192) by the number of books each box can hold (18). This calculation gives 192 / 18 = 10 with a remainder of 12. Since Joshua needs to pack all 192 books, he will need 10 full boxes plus one additional box for the remaining 12 books, totaling 11 boxes.

Question 17: At the end of a football game's first half, the Bisons have scored twice as many points as the Cubs. The Cubs tie the game in the second half by scoring 7 points while holding the Bisons scoreless. What was the score at the half?

Bisons 14, Cubs 14
Bisons 7, Cubs 7
Bisons 14, Cubs 7 (Correct answer)
Bisons 7, Cubs 14

Correct answer: Bisons 14, Cubs 7

Let B be the Bisons' score and C be the Cubs' score at halftime. The problem states B = 2C. In the second half, the Cubs score 7 points and the Bisons score 0, resulting in a tie. So, B = C + 7. Substituting the first equation into the second gives 2C = C + 7, which simplifies to C = 7. Therefore, B = 2 * 7 = 14, making the halftime score Bisons 14, Cubs 7.

Question 18: Solve 5+8×(−2)–[4+22×5]÷6

−10
−30 (Correct answer)
0
−20

Correct answer: −30

To solve the expression, follow the order of operations (PEMDAS/BODMAS). First, calculate inside the brackets: 22 × 5 = 110, then 4 + 110 = 114. The expression becomes 5 + 8 × (−2) – 114 ÷ 6. Next, perform multiplication and division: 8 × (−2) = −16 and 114 ÷ 6 = 19. Finally, perform addition and subtraction from left to right: 5 – 16 – 19 = −11 – 19 = −30.

Question 19: A $200 bag is discounted by 15%. After a month, the bag is discounted by another 15%. Which of the following expressions can be used to calculate the bag's selling price?

(200)–200(0.30)
(200)(0.85)(0.85) (Correct answer)
(200)(0.70)
(200)(0.15)–(200)(0.15)

Correct answer: (200)(0.85)(0.85)

A 15% discount means the bag is sold for 100% - 15% = 85% of its current price. So, after the first discount, the price is $200 * 0.85. When it's discounted by another 15%, it means 85% of the *new* discounted price. Therefore, the final selling price is calculated by multiplying the original price by 0.85 twice: (200)(0.85)(0.85).

Question 20: The answer is 83, which is 5 less than twice a positive integer. What is the integer?

42
39
44 (Correct answer)
41

Correct answer: 44

Let the positive integer be 'n'. The problem states that 83 is 5 less than twice this integer, which can be written as the equation 2n - 5 = 83. To solve for n, first add 5 to both sides: 2n = 88. Then, divide by 2: n = 44. Thus, the integer is 44.

Question 21: How many inches are there in 11 yards, 6 feet, and 4 inches?

472 (Correct answer)
478
385
470

Correct answer: 472

To convert all measurements to inches, use the conversion factors: 1 yard = 3 feet and 1 foot = 12 inches. First, convert 11 yards to feet: 11 yards * 3 feet/yard = 33 feet. Add the 6 feet to get a total of 39 feet. Next, convert 39 feet to inches: 39 feet * 12 inches/foot = 468 inches. Finally, add the remaining 4 inches: 468 + 4 = 472 inches.

Question 22: What is the difference between the smallest and largest 4–digit numbers?

6789
6666
8999 (Correct answer)
8888

Correct answer: 8999

The smallest 4-digit number is 1000, as it is the first number with four digits. The largest 4-digit number is 9999, as it is the last number before reaching five digits. The difference between these two numbers is found by subtracting the smallest from the largest: 9999 - 1000 = 8999.

Question 23: Mr. Jacob's family is deciding on a menu for their party. There are three appetizer options, five entree options, and four cake options. How many different menu combinations do they have to choose from?

60 (Correct answer)
125
32
14

Correct answer: 60

To find the total number of different menu combinations, multiply the number of options available for each category. Mr. Jacob's family has 3 appetizer options, 5 entree options, and 4 cake options. Therefore, the total number of combinations is 3 * 5 * 4 = 60.

Question 24: An angle is one-fifth the size of its supplement. What is the angle's measurement?

30 (Correct answer)
65
25
40

Correct answer: 30

Let the angle be 'A'. Its supplement is 180° - A. The problem states that the angle is one-fifth the size of its supplement, so A = (1/5)(180 - A). Multiply both sides by 5 to get 5A = 180 - A. Add A to both sides, resulting in 6A = 180. Finally, divide by 6 to find A = 30 degrees.

Question 25: If 40% of a class is made up of girls and 25% of the girls play tennis, what percentage of the class plays tennis?

20%
40%
15%
10% (Correct answer)

Correct answer: 10%

To find the percentage of the class that plays tennis, multiply the percentage of girls in the class by the percentage of girls who play tennis. This is 40% (0.40) of the class multiplied by 25% (0.25) of the girls. So, 0.40 * 0.25 = 0.10, which is 10% of the class.

FTCE Practice Test General Knowledge (Mathematics)

How many diagonals a dodecagon has?