FTCE General Knowledge Mathematics Practice Test 1 With Complete Solutions Latest Update, Exams of Mathematics

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FTCE General Knowledge Mathematics Practice Test 1 With Complete Solutions Latest Update

The length of a deck is 5 less than twice the width with a perimeter of 62 feet. To thenearest tenth, what is the width of the deck?

A. 12. B. 12.3C. 12. D. 13.1 - ANSWER A. 12. This problem is asking you to find the perimeter. Perimeter is the result of ADDING allthe sides of the shape. 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 = To solve this equation, add 10 to both sides of the equation: 6w -10 = 6w = 72

Now, divide both sides by 6: w = 12

Left and right side of the rectangle- w Top and bottom of the rectangle- 2w- A car salesman receives 30% commission on all of his sales for the month. His base payis $240 per month, which includes his commission on sales. Which one 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 - ANSWER D. .3x + 240 ≥ 640 In this equation, you are being asked to write an equation, not solve an equation. Payclose 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, thecorrect choice should be greater than or equal to >_, and that makes D the correct choice.

D. 30%, 1/3, 3/4, .8 - ANSWER D. 30%, 1/3, 3/4,.

To put these numbers in order, convert them to decimals: 30% becomes .30, 3/4becomes .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 on your cell phone plan were each responsible for half of the bill. Themonthly 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 billcomes to $120. If the husband is responsible for 60% of the data charges, how much does he owe for the month? A. $41. B. $38. C. $63. D. $79.80 - ANSWER C. $63. Each pays half of the base charge of $82. So he pays $41 of base charge. He also pays60% of the data charges. To find the data charges subtract beach charge from whole bill: $120 -$82 = $38.00 Doesn't pay 60% of $38 which is $22.80. Add $22.80 his data tothe $41 for base. Total is $63.

Mrs. Kramer, a first-grade teacher, has a treasure box full of treats for students whoanswer the daily trivia question correctly. Today, Mindy was correct, so she gets to choose from the box, which was filled with 3 mints and 4 cookies. What is the probabilityshe picks mint?

A. 1/

B. 4/

C. 3/

D. 3/7 - ANSWER D. 3/

Use fractions for probability. Put the chosen over the total. Since there are 3 mints outof 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 55mph. 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 - ANSWER C. 12.5 gallons There is irrelevant information in this question that you don't need. The question asks forhow many gallons will be burned in 5 hours-not for the whole trip. Hence the information of 500 miles is irrelevant. Use the formula S = D/T ( speed equals distance over time).Speed is 55, time is 5 hours. Solve for D.

55 = D/

C. 12 3/4 lbs D. 13 3/4 Ibs - ANSWER D. 13 3/4 Ibs First, we have to change weight into ounces, knowing there are 16 oz in a lb. So, 2 1/2lbs is 40 oz. Then multiply 5 × 40 and 5 × 4. You get 200 and 20, respectively. All together, the books and notebooks weigh 220 total oz. Now divide 220 by 16 to convertthe oz into lbs, which = 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 - ANSWER C. 196 in squared First of all, turn the 4 ft 8 in into inches, which is 56 in. Remember, a square has fourequal sides, so divide the 56 by 4, which will give 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. On both sides there is 14.

Area = base x height ( 14 x 14) = 196 in squared Mr. and Mrs. Jones have five children. Two of the children are five years old. The medianage is nine in the range of the ages is seven. Which is A possible age of the second oldest Morton child? A. 2B. 4 C. 9 D. 14 - ANSWER C. 9 We know that the median is nine, so that goes in the middle. The only place for the 25 Vis before the nine. We do not know the age of the second oldest child nor the age of the oldest child, but we do know that the range is seven. The range is the biggest numberminus 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 going from his house to the airport. He goes at 60 miles per hour, he will getthere an hour early. But if he drives at 30 miles per hour, he will get there an hour late. How many miles is it from his house to the airport? A. 60 miles B. 120 miles C. 180 milesD. 240 miles - ANSWER B. 120 miles

Volume is height x length x width. So you find the volume for the first two boxes and thenadd 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= 96Box 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 21pens?

A. 24/21=16/x B. 16/24=21/xC. 16/x=21/ D. 24/16=21/x - ANSWER B. 16/24=21/x When you set up proportions, just make sure everything matches. In answer choice Byou 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/

B. 1/8C. 6/

D. 3/8 - ANSWER A. 1/

Simplify, just take out the zeros. So together the couple pulls in 48 of income. Theirgross income is 56. Subtract 48 from 56 and you pull 8. 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 has various openings listed in the chart below with correspondingsalaries. Based on the provided data, which measure of central tendency would the company want to advertise to make the salary options appear the best? Salary/Year $15k. $20k. $35k. $100k $150k Positions open 1. 4. 7. 1. 1. A. Mean B. MedianC. Mode - ANSWER A. Mean

For mean median and mode problems where there are many numbers, try process ofelimination. 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 tobe the mode because it comes up the most. 35 is also the median. You can eliminate B and C, therefore your answer is A. Teacher salaries range from $40,000-$60,000. Following negotiations with theadministration, the teachers' union was able to negotiate a flat rate increase of $ for all teachers. Which of the following is correct?

A. -4.037 x 10^ B. 4.037 x 10^ C. -4.037x10^-2D. 4.037x10^-3 - ANSWER D. 4.037x10^-

If you are multiplying a number times 10 to a certain power, you just move the decimalspot 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. PerpendicularC. Parallel and intersecting D. Concurrent - ANSWER B. Perpendicular

Use the formula Y = MX + B That makes the lines: Y=-3/2x + 3Slope=-3/

Y=2/3x +6Slope=2/

The slopes are the exact opposite of each other so they are perpendicular Solve: 5x - 7 <_ 2x - 10 A. X <_ 1B. X <_ - C. X >_ 1 D. X >_ -1 - ANSWER B. X <_ - Get X on one side of the equation by subtracting 2X from both sides and adding seven toboth sides.

5x - 7 <_ 2x - -2x from both sides

B. 16

C. 8

D. 1/8 - ANSWER B. 16

Use the " please excuse my dear aunt sally" for order of operations. | 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. EllipseB. Horizontal line C. Circle

D. Vertical line - ANSWER B. Horizontal line In a function, X does not repeat. In an ellipse the X repeats. In a circle the X repeats. In avertical line the X repeats. However, in a horizontal line the X does not repeat only the Y does. This chart shows results of an experiment in which baking soda and ammonia were usedas remedies for ant and tick bites. The time on the chart is how long it took for the pain to subside. Based on the chart which of the following is correct? Baking Soda: 5 min ticks Ants 10 min Ammonia: 5 min ticks. Ants 7 min I. Baking soda is more effective for ticks than ammonia. II. Ammonia works better in killing ants than baking soda. III. Ammonia is stronger in killing ants and ticks than baking soda. IV. If a person wants to use the better one of the two remedies, he or she should chooseammonia.

A. I only B. I and III C. II and IV

Now, observe closely. Both the firms show the same profits. The only difference is thatcompany A shows profit every two years, well Company B shows the profits every year. However, they both healed $ 2 million every year. Company B yields $4 million every twoyears or $ 2 million every year.

Bayside High School has a student population of 1400 with a teacher to student ratio of1:35. How many more teachers must the principal hire in order to make the ratio 1:20. A. 40B. 70 C. 30 D. 20 - ANSWER C. 30This is a proportion. Currently, we have 1,400 students with a ratio of 1 teacher : 35 students. Set it up like this: X/1,400 = 1/35. Then cross multiply and solve. 35x = 1, X = 40 The desired ration in the school is 1 teacher: 20 students. Solve the proportion this way.X/ 1,400 = 1/20. Cross multiply and solve.

20x = 1, x = 70 Because the principal already has 40 teachers and needs 70, he or she must her 30more teachers.

You were given the following problem during a homework check. In which step, if any,

did the student go wrong? (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 2C. Step 3

D. No error was made. - ANSWER B. Step 2 Explanation: In step 2, student forgot to distribute the need to sign all the way throughequation.

Student worked this:

x squared - 2x + 1 - x squared - 1