# FTCE Practice Test General Knowledge (Mathematics)

#### How many diagonals a dodecagon has?

Correct answer: 54

Because drawing a dodecagon and counting its diagonals is a time-consuming task, a different problem-solving strategy is recommended. One such strategy is to draw polygons with fewer sides and look for a pattern in the number of diagonals between the polygons. A quadrilateral has two more diagonals than a triangle, a pentagon has three more than a pentagon, and a hexagon has four more diagonals than a pentagon. By following this pattern, you can determine that a dodecagon has 54 diagonals.

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

Correct answer: Set of whole numbers

The number -4 does not appear in the set of whole numbers (0,1,2,3,...). Because -4 is an integer, it is also a rational and real number.

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

Correct answer: Path of a bullet

A bullet's path is a parabola, which is the graph of a quadratic function. A sine or cosine function can be used to model the path of a sound wave. The distance traveled by an object over time at a constant rate is modeled by a linear relationship, whereas radioactive decay is modeled by an exponential function.

#### 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?

Correct answer: 252

A score of 85 deviates from the mean by one standard deviation. Because approximately 68 percent of the data is within one standard deviation of the mean, approximately 32 percent of the data (1000/0-680/0) is outside of one standard deviation within the mean. Normally distributed data is symmetric about the mean, which means that approximately 16% of the data is less than one standard deviation below the mean and approximately 16% of the data is greater than one standard deviation above the mean. As a result, approximately 16% of people have IQs lower than 85, while 84 percent of the population has an IQ of at least 85. Because 84 percent of 300 equals 252, approximately 252 people in the chosen group have Iqs of at least 85.

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

Correct answer: 544,320

Because the first digit can be any of the numbers 1-9, there are nine different ways to assign it. There are nine different ways to assign the second digit because it can be any digit from 0 to 9 EXCEPT the digit assigned in place 1. Because there are ten digits, there are eight ways to assign the third number, two of which have already been assigned. There are seven different ways to assign the fourth number, six different ways to assign the fifth, five different ways to assign the sixth, and four different ways to assign the seventh. As a result, the number of possible combinations is 9-9-8-7-6-5-4= 544,320.

#### 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?

Correct answer: 14

To help organize the information, draw a Venn diagram. Begin by filling in the space between the three circles: Rose tutored three students in each of the three disciplines. Fill in the gaps where two circles intersect: for example, she tutored four students in chemistry and for the ACT, and three of those were students she tutored in all three areas, so one student was tutored in chemistry and for the ACT but not in math. After you've completed the diagram, add the number of students who were tutored in all areas to the number of students who were tutored in only two of the three areas to the number of students who were tutored in only one area. The total number of tutored students was 3+2+2+1+3+2+1=14.

#### 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?

Correct answer: 37.5%

The percentage increase is represented as (1100 − 800)/800, which equals 0.375 or 37.5%.

#### Which of the following statements is correct?

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

The set of integers is contained within the set of rational numbers and thus is a subset of that set. A rational number can be written as the ratio a/b, where a and b are integers and b ≠ 0.

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

Correct answer: $60

The original cost can be represented by the equation 45 = x − 0.25x or 45 = 0.75x. By dividing both sides of the equation by 0.75, we get x = 60.

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

Correct answer: $26,900

The original price can be expressed as 24,210 = x 0.10x or 24,210 = 0.9x. When both sides of the equation are divided by 0.9, the result is x = 26,900.

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

Correct answer: $2,560

His monthly wage can be calculated as 1/8 x = 320. When both sides of the equation are multiplied by 8, the result is x = 2,560.

#### Which is closed under the operation of division?

Correct answer: nonzero rational numbers

A nonzero rational number divided by another nonzero rational number always yields a nonzero rational number.

#### 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.

Correct answer: 20%

Cost price = $800

Selling price = $960

Mark-up = $960 - $800 = $160

Mark-up as a percent of the cost price = (Mark-up)/(Cost price) * 100%

M= 160/800 * 100%

M= 20%

#### 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?

Correct answer: 33 1/3%

1050- 700 = 350

350 / 1050 = 33 1/3%

#### 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?

Correct answer: 8

Because there are two 6s and two 8s, the mode can only be a 6 or an 8.

If the mode is 6, then x is 6, and the marks are: 2, 6, 6, 6, 7, 8, 8, 9, 11, and 15,

the median = (7 + 8)/2 = 7.5 and the mean = 78/10 = 7.8.

The mean, median, and mode are not all the same.

If the mode is 8, then x = 8 and the marks are as follows: 2, 6, 6, 7, 8, 8, 8, 9, 11, and
15 median = (8 + 8)/2 = 8 and mean = 80/10 = 8

The mean, median, and mode are all the same.

x = 8

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

Correct answer: 11

Divide 192 books by 18 books per box to determine how many boxes Joshua will require. The correct answer is 10.67. He will need 11 boxes to pack all of his books.

#### 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?

Correct answer: Bisons 14, Cubs 7

Let c represent the number of points the Cubs scored in the first half. In the first half, the Bisons score twice as many points as the Cubs, for a total of 2c. The Cubs scored 7 points in the second half while the Bisons scored none. So the Bisons' score remained 2c, while the Cubs' score was c + 7. As a result, 2c = c + 7. Subtraction of c from both sides of the equation yields c = 7. At halftime, the score was Bisons 14, Cubs 7.

#### Solve 5+8×(−2)–[4+22×5]÷6

Correct answer: −30

Use PEMDAS (operational order):

5+8×(−2)–[4+22×5]÷6=5+8×(−2)–[4+110]÷6=5+8×(−2)–[114]÷6=5+(−16)–195+(−16)–19= −11–19=−30

#### 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?

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

To calculate the discount, multiply the number by (100% – rate of discount). As a result, for the first discount: (200)(100 percent – 15% )=(200)(0.85)=170 For the next 15% off, please follow these steps: (200)(0.85)(0.85)

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

Correct answer: 44

Assume x is an integer. Then, 2x–5=83

5 on both sides: 2𝑥=88

Divide both sides by 2 to get x=44

#### How many inches are there in 11 yards, 6 feet, and 4 inches?

Correct answer: 472

11×36+6×12+4=472

#### What is the difference between the smallest and largest 4–digit numbers?

Correct answer: 8999

The smallest 4-digit number is 1000, and the largest 4–digit number is 9999. The difference is 8999.

#### 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?

Correct answer: 60

Multiply the number of options for each factor to determine the number of possible outfit combinations: 3×5×4=60

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

Correct answer: 30

The total of the supplement angles is 180. Let x represent that angle. As a result, x+5x=180.

6x=180; divide both sides by 6 to get x=30.

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

Correct answer: 10%

The percentage of female tennis players is:

40%×25%=0.40×0.25=0.10=10%