FTCE General Knowledge Mathematics practice test 1 with complete solution 2023

FTCE General Knowledge Mathematics practice test 1 with complete solution 2023The length of a deck is 5 less than twice the width with a perimeter of 62 feet. What is the width of the deck rounded to the nearest tenth? A. 12.0 B. 12.3 C. 12.8 D. 13.1 A. 12.0 This question is asking you to find the perimeter. Perimeter is the result of ADDING all the sides of the shape. In this case, we have a rectangular deck. The length is 5 less than twice the width, which is written 2w-5. And the width is just w. When you add up all the sides, you get; 2w-5 + 2w-5 + w +w=62 6w - 10 =62 Solve the equation by adding 10 to each side: 6w -10 =62 6w = 72 Divide each side by 6: w = 12 Left and right side of the rectangle- w Top and bottom of the rectangle- 2w-5 A car salesperson makes 30% commission from all sales during the month. His base pay is $240 per month plus what he makes on sales commission. Which of the following inequalities represents his pay at the end of the month so that he makes no less than $640? A. .3x + 240 < 640 B. .3x + 240 > 640 C. .3x + 240 <_ 640 D. .3x + 240 >_ 640 D. .3x + 240 >_ 640 In this equation, you are being asked to write an equation, not solve an equation. Pay attention to the very last line in the question, "..... he make NO LESS THAN $640?" Immediately eliminate any answer choice with a less than sign (<), so A and C are out. Then look at the greater than (>) signs in your answer choices. If he makes NO LESS than $640, that means he can make exactly $640 and he can make more than $640. So, the correct choice should be greater than or equal to (>_), and that makes D the correct choice. Of the following, which number is greatest? -12, - 10, -21/2, -Square root 145 A. -12 B. -10 C. -21/2 D. - square root 145 D. - square root 145 Pay attention to the negative numbers here. -10 is greater than any of the other numbers: -12, -21/10 = -10.5, - square root 145 = -12.04 Put the following in order from least to greatest. 30%, 3/4, 1/3, .8 A. 1/3, 3/4, .8, 30% B. 1/3, .8, 3/4, 30% C. 30%, 1/3, .8, 3/4 D. 30%, 1/3, 3/4, .8 D. 30%, 1/3, 3/4, .8 To put these numbers in order, convert them to decimals: 30% becomes .30, 3/4 becomes .75, 1/3 becomes .33 repeating, and .8 becomes .80 (same .8). The order should be .30 (30%), .33 (1/3), .75 (3/4), .80 (.8). My husband was your cell phone plan were each responsible for half the bill. The monthly base charge for service is $82. On top of the base charge, their dirty chargers, which each person is responsible for individually. At the end of the month, the total bill comes to $120. If the husband is responsible for 60% of the data charges, how much does he owe for the month? A. $41.00 B. $38.00 C. $63.80 D. $79.80 C. $63.80 Each person responsible for half the base charge of $82. Therefore, the husband pays $41 of the base charge. He also pays 60% of the data charges. To find the data charges, subtract the beach charge from the whole bill $120 -$82 = $38.00. Doesn't pay 60% of $38, which is $22.80. Add $22.80 (his data) to the $41 for the base. The total is $63.80 Mrs. Kramer, a first grade teacher, keeps a treasure box full of treats for students who answers the daily trivia question correctly. Today, Mindy answered correctly, so she gets to choose from the box, which was filled 3 mints and 4 cookies. What is the probability she picks mint? A. 1/7 B. 4/7 C. 3/4 D. 3/7 D. 3/7 Use fractions for probability. Put the selected over the total. Because there are 3 mints out of 7 items in the treasure chest, the fraction is 3/7 On a trip from Naples to Tallahassee, a car travels a total of 500 miles at a rate of 55 mph. If the car gets 22 miles per gallon, how many gallons of gas will be consumed in 5 hours? A. 7.0 gallons B. 10.0 gallons C. 12.5 gallons D. 14.0 gallons C. 12.5 gallons There is extra information in this question that you do not need. The question is asking how many gallons will be burned in 5 hours, not the entire trip. Therefore, the 500 miles is irrelevant information. Use the formula S = D/T ( speed equals distance over time). The speed is 55, the time is 5 hours. Solve for D. 55 = D/5 D= 275 Divide 275 by 22 mpg, which gives you 12.5 gallons burned. A triangle has interior angle measurements of 20 degrees, 50 degrees, and 110 degrees. Classify the triangle. A. acute scalene B. isosceles C. obtuse scalene D. equilateral C. obtuse scalene Pay attention to the obtuse angle mentioned - 110 degrees. Choose the answer with the word obtuse in it. If a textbook weighs 2 1/2 lbs. and the notebooks weigh 4 oz., what is the total weight of 5 notebooks and 5 textbooks? A. 13 1/2 lbs B. 12 1/2 lbs C. 12 3/4 lbs D. 13 3/4 Ibs D. 13 3/4 Ibs Convert the weight of the textbooks to ounces. There are 16 oz in 1 lb. Therefore, 2 1/2 lbs is 40 oz. Multiply 5 times 40 ( the textbook) and 5 times 4 ( the notebooks). That gives you 200 and 20, respectively. Together, the books and notebooks weigh 220 total oz. Divide 220 by 16 to convert the oz to lbs, which equals 13.75 or 13 3/4. An Artist used a piece of wire that was 4 feet and 8 inches long and bent it into a square. What is the area of the square? A. 57 in squared B. 112 in squared C. 196 in squared D. 212 in squared C. 196 in squared Convert the 4 ft 8 in into inches, which is 56 in. A square has four equal sides, so divide 56 by 4, which gives you 14. Area is base times height, 14 x 14 = 196 in squared 4 ft 8 in = 57 in —————————— 56 divide 4 = 14 All four sides of the square are 14 on the top and bottom. 14 on both sides. Area = base times height ( 14 x 14) = 196 in squared Mr. and Mrs. Jones have five children. Two of the children are five years old. The median age is nine in the range of the ages is seven. Which is A possible age of the second oldest Morton child? A. 2 B. 4 C. 9 D. 14 C. 9 We know the median is nine, so that number goes in the middle. The only place for the 25 V is before the nine. We do not yet know the age of the second oldest child or the age of the oldest child, but we do know the range is seven. The range is the biggest number minus the smallest. Therefore, if the range is seven and the smallest number is five, the last child is 12. The only number in the answer choice that will fit is nine. Cosmo is taking a trip from his house to the airport. If he drives 60 mph, he will arrive one hour early. If he drives 30 mph, he will arrive one hour late. What is the distance from his house to the airport? A. 60 miles B. 120 miles C. 180 miles D. 240 miles B. 120 miles If he goes 60 mph, he arrives an hour early. If he goes 30 mph, he arrives an hour late. That is a two hour difference in time. Use your answer choices to solve. 120 miles is the only answer that has a two hour difference. 120 miles/60 mph=2 hours 120 miles/30 mph=4 hours You and some friends decide to play a game of frisbee. Person a start by throwing the frisbee 3 meters forward. Person be throws the frisbee and a gust of wind takes it 5 meters backward. Person C throws the frisbee 2 meters forward. Finally, person D throws the frisbee up in the air and it travels 1 meter forward. Where is the frisbee in relation to the start? A. -1 B. 0 C. 1 D. 3 C. 1 Use a number line to answer the question. Start at zero and add or subtract based on the question. Tony is shipping two boxes. The first box has dimensions of 2 inches x 8 inches x 6 inches. The second box has dimensions 6 inches x 8 inches x 10 inches. He puts both boxes into a third box with dimensions of 12 inches x 12 inches x 12 inches. How much empty space is left in the third box? A. 576 in^3 B. 872 in^3 C. 1,156 in^3 D. 1,728 in^3 C. 1,152 in^3 Volume is height x length x width. So you find the volume for the first two boxes and then add those numbers together. Then you find the volume for the box they are being put inside of. Subtract the number of the first two boxes from the box they are going inside. Box 1: 2 x 8 x 6= 96 Box 2: 6 x 8 x 10=480 Add them=576 Big box: 12 x 12 x 12 =1,728 Subtract the first two from the big box to get the space. 1,728-576=1,152 In an office supply store it cost $24 for 16 pens. What proportion will find the cost for 21 pens? A. 24/21=16/x B. 16/24=21/x C. 16/x=21/24 D. 24/16=21/x B. 16/24=21/x When you set up proportions, just make sure everything matches. In answer choice B you have the number of pens over the price. So the equal proportion should be the number of pens over X (the number you are trying to figure out) Person one in person to each have annual salaries of $24,000. At the end of the year, they net a gross income of $56,000. Any monies collected after their salary is the result of a return on investments. What fraction of the years total income is from investments? A. 1/7 B. 1/8 C. 6/7 D. 3/8 A. 1/7 To simplify it, just take out the zeros. So together the couple makes 48 in income. Their gross income is 56. So subtract 48 from 56 and you get 8. So that means that 8 comes from investments. Put 8 over the total and you get 8÷56. That is the same as 1÷7. Company AAA is hiring for many positions shown below in the salary chart. Given the information, what would be the best measure of central tendency the company a would advertise to make the salary options look the best? Salary/Year $15k. $20k. $35k. $100k $150k Positions open 1. 4. 7. 1. 1. A. Mean B. Median C. Mode A. Mean For mean median and mode problems where there are many numbers, try process of elimination. Also do not factor in the zeros to make the problem simpler. You have 14 salaries, one 15, four 20s, seven 35s, one 100, and one 150. The number 35 is going to be the mode because it comes up the most. 35 is also the median. You can eliminate B and C, therefore your answer is A. The range of teacher salaries is $40,000-$60,000. During negotiations, the teachers union worked out a deal for a flat rate of $1000 for every teacher. Which of the following is true? A. Mean and median salary stay the same; standard deviation changes B. Mean and median salaries change; standard deviation stays the same C. Mean and median salaries change; standard deviation changes D. Mean and median salaries stay the same; standard deviation stays the same B. Mean and median salary change; standard deviation stays the same Let's factor this without zeros. Let's say there are three teachers with salaries at 40, 50, and 60. The median of this set is 50 and the mean is 50. The standard deviation is 10 because there is a difference of 10 between each teacher. If I give everyone a raise of one, the set changes to 41, 51, and 61. Notice the mean and median changed to 51, but the standard deviation is still 10 because 41 to 51 is 10 just like 40 to 50 was 10 In a bag, there is one red marble, one yellow marble, one blue marble, and one green marble. After making a selection, the marble must stay out of the bag. How many possibilities are there when making two choices with the first being a red marble? A. 2 B. 3 C. 4 D. 5 B. 3 If the first choice has to be read every time, there are only three possibilities. Red followed by a blue, yellow, or green. I just realized that there are four total marbles. If you take one out (the red one) then there are three left. Therefore, there are only three possibilities Which of the following choices falls between 0 and 2? A. -4.037 x 10^3 B. 4.037 x 10^2 C. -4.037x10^-2 D. 4.037x10^-3 D. 4.037x10^-3 If you are multiplying a number times 10 to a certain power, you just move the decimal spot however many numbers the exponent is. So for this answer choice, you move the decimal three places to the left since it is a -3. 4.037 x 10^-3 move the decimal to the left 3 spots and you get . This number is between 0 and 2. Classify the following: 3x + 2y = 6 -2x + 3y = 12 A. Parallel B. Perpendicular C. Parallel and intersecting D. Concurrent B. Perpendicular Use the formula Y = MX + B That makes the lines: Y=-3/2x + 3 Slope=-3/2 Y=2/3x +6 Slope=2/3 The slopes are the exact opposite of each other so they are perpendicular Solve: 5x - 7 <_ 2x - 10 A. X <_ 1 B. X <_ -1 C. X >_ 1 D. X >_ -1 B. X <_ -1 Get X on one side of the equation by subtracting 2X from both sides and adding seven to both sides. 5x - 7 <_ 2x -10 -2x from both sides 3x -7 <_ -10 Add 7 to both sides 3x <_ -3 Divide both sides by 3 X <_ -1 Over the course of the school year in the JROTC class, Jennifer logged the following total of pull-ups: 2, 3, 22, 23, 23, 6, 8, 7, 9, 11, and 13. If she wanted to show the best looking result, which measure of central tendency will she use? A. Mean B. Median C. Mode D. Range C. Mode The highest number would be the mode since 23 comes up twice and it is the most frequent number. So the results look the best if she says her mode was 23.