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FTCE General Knowledge Mathematics Practice Test 1 | 50
Questions With Correct Answers
The 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. B. 12. C. 12. D. 13.1 Ans ➡ A. 12. 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= 6w - 10 = Solve the equation by adding 10 to each side: 6w -10 = 6w = 72 Divide each side by 6: w = 12
Left and right side of the rectangle- w Top and bottom of the rectangle- 2w- 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 Ans ➡ 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. - B. - C. -21/ D. - square root 145 Ans ➡ D. - square root 145
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. 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/ B. 4/ C. 3/ D. 3/7 Ans ➡ D. 3/ 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/ 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 Ans ➡ 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/
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 Ans ➡ 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 Ans ➡ 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.
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 Ans ➡ 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. - B. 0 C. 1 D. 3 Ans ➡ 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^ B. 872 in^ C. 1,156 in^ D. 1,728 in^3 Ans ➡ C. 1,152 in^ 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= Add them= Big box: 12 x 12 x 12 =1, Subtract the first two from the big box to get the space. 1,728-576=1, 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/ D. 24/16=21/x Ans ➡ 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
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 Ans ➡ 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^ B. 4.037 x 10^ C. -4.037x10^- D. 4.037x10^-3 Ans ➡ D. 4.037x10^- 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^- 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 Ans ➡ B. Perpendicular Use the formula Y = MX + B That makes the lines: Y=-3/2x + 3 Slope=-3/ Y=2/3x + Slope=2/ The slopes are the exact opposite of each other so they are perpendicular Solve: 5x - 7 <_ 2x - 10 A. X <_ 1 B. X <_ - C. X >_ 1 D. X >_ -1 Ans ➡ B. X <_ -
| 6-8 | + 3÷3 x 4^2 - 2 P. Parenthesis. So do | 6-8 | first. Which is 2 2+ 3÷3 x 4^2 - E. Exponent. So do 4 to the second power, which is 16. 2+ 3÷3 x 16 - M/D. Multiplication and division IN ORDER from left to right. So do 3/3 then x 16 2+16- Answer= In the coordinate plane, which of the following is a function? A. Ellipse B. Horizontal line C. Circle D. Vertical line Ans ➡ B. Horizontal line In a function, X does not repeat. In an ellipse the X repeats. In a circle the X repeats. In a vertical line the X repeats. However, in a horizontal line the X does not repeat only the Y does. The chart shows the results from an experiment where baking soda and ammonia were used S remedies did ant and tick bites. The time shown refers to when the pain subsided. According to the chart, which of the following statements is true? Baking soda: 5 min ticks Ants 10 min Ammonia: 5 min ticks. Ants 7 min I. Baking soda works better on ticks than ammonia.
II. Ammonia works better on ants than baking soda. III. Ammonia works better than baking soda both ants and ticks IV. If given the choice for the most effective remedy between the two, ammonia would be the best option. A. I only B. I and III C. II and IV D. IV only Ans ➡ C. II and IV The only true statements are II and IV. The two charts above show two different companies' earnings over a period of time. Which of the following statements is true? Company A Company B 1 year: 3 million 1 year: 2 million 3 years: 7 million 2 years: 4 million 5 years: 11 million 3 years: 6 million 7 years: 15 million 4 years: 8 million A. Company A increased earnings $4 million per year B. Company A's yearly earnings were greater than Company B's yearly earnings C. Both companies had the same yearly earnings
During a homework check, you received the following problem. In which step, if any, did the student make a mistake? (x-1) squared - (x-1) (x + 1) Step 1: (x squared - 2x + 1) - (x squared - 1) Step 2: x squared - 2x + 1 - x squared - 1 Step 3: -2x A. Step 1 B. Step 2 C. Step 3 D. No mistake was made. Ans ➡ B. Step 2 In the second step, student did not distribute the need to sign all the way through the equation. The student calculated this: x squared - 2x + 1 - x squared - 1 The student should have gotten: x squared - 2x + 1 - x squared + 1 Use the information to write an equation. r g
A. r = 3/4g B. r = 1/3g C. g = 3/4r D. g = 4/3r Ans ➡ C. g = 3/4r In the table, g is smaller than r by 3/ Which of the following statements is true? A. 4 (to the 3rd power) = 3 ( to the 4 power) B. 5 ( to the 0 power) X 8 squared > 2 ( to the 5th power) C. 7 ( to the 4th power) + 7 ( to the 3rd power) = 7 (to the 7th power) D. 5 squared + 5 (to the 8th power) = 5 ( to the 10th power) Ans ➡ B. 5 ( to the 0 power) X 8 squared > 2 ( to the 5th power)
Find the area of the lawn, which is 50 X 10 = 500. Sod cost three dollars per 10 ft. sq. So divide the 500 by 10, which gives you 50. Multiply the 50 by $3.00, which gives you $150. What is the name of a shape where:
- The bases (top and bottom) are parallel.
- One pair of interior angles are acute.
- One pair of interior angles are obtuse.
- The diagonals are congruent. A. Triangle B. Trapezoid C. Square D. Rectangle Ans ➡ B. Trapezoid If you draw the shape out, you will discover it is a trapezoid. The biggest giveaway is the top and the bottom are parallel, but one part of interior angles are acute. If the total amount of money per month is $2,500, how much of the budget does the family spend on food and clothes? Family Budget: Pie Chart Food: 38% Misc: 9% Eating Out: 11% Clothes: 12% Bills: 30% A. $1,
B. $1,
C. $1,
D. $1,250 Ans ➡ D. $1, In this budget, 50% spent on clothes and food. So multiply $2,500 by 50 % or divide it by 2. That gives you $1, Out of 30 students, 1 scores 70%, 5 others score 90%, and the rest score 80%. Which of the following measures of central tendency has the highest value? A. Mean B. Median C. Mode D. Range Ans ➡ A. Mean This is another case where you do not have to write all these numbers down. The mode in the median are the same - 80%. So B and C are out. The range will be significantly smaller than the mean, so capital D is out. That leaves A. Nancy is putting an 8 X 10 picture in a frame. To make it fit, she needs to trim the sides. She takes 2.5 inches from the top and bottom. She takes .5 inches in from both sides. What is the area of the picture after she makes these changes? A. 56 in.² B. 54 in.² C. 42 in.² D. 35 in.² Ans ➡ D. 35 in.²
