FTCE General Knowledge Mathematics Practice Test 1: A Comprehensive Guide with Solutions, Exams of Advanced Education

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FTCE GENERAL KNOWLEDGE MATHEMATICS

PRACTICE TEST 1

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 - 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 - 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 - 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. Put the following in order from least to greatest. 30%, 3/4, 1/3,. A. 1/3, 3/4, .8, 30% B. 1/3, .8, 3/4, 30% C. 30%, 1/3, .8, 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 - 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 - 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/ 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

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 - 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/ B. 1/ C. 6/ D. 3/8 - A. 1/ 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. X <_ 1

B. X <_ -

C. X >_ 1

D. X >_ -1 - B. X <_ -

Get X on one side of the equation by subtracting 2X from both sides and adding seven to both sides. 5x - 7 <_ 2x - -2x from both sides 3x -7 <_ - Add 7 to both sides 3x <_ - Divide both sides by 3 X <_ - 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. Solve: | 6-8 | + 3÷3 x 4^2 - 2 A. 12 B. 16 C. 8 D. 1/8 - 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. Ellipse B. Horizontal line C. Circle D. Vertical line - 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.

C. 30

D. 20 - C. 30

This 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 30 more teachers. 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. - 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 16 12 12 9 8 6 4 3 A. r = 3/4g B. r = 1/3g C. g = 3/4r D. g = 4/3r - 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)

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 - 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 - 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 - 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 - D. 35 in.² If you subtract two, 2.5 in from the top and two, 2.5 in from the bottom, you took off 5 in total. Also, two, .5 in in from each side, is 1 in from the sides. That means the 8 X 10 picture becomes a 5 X 7. The right side has 5 on it The bottom has 7 on it 10-5 = 5 8 - 1 = 7 Cindy is selling different necklaces at the flea market. She has two 15-inch necklaces, one 18 inch necklace, and two 20 inch necklaces. If she adds an additional 18 inch necklace and a 20 inch necklace, how does the mean change with all the necklaces?

If the baseball team won 40% of 40 games, they won 16 games (40% x 40 = 16). Your goal is to win 70% of the total things. They have 70 more games to go, the total is 110 games because 40+70 = 110. Therefore, 70% of 110 is 77 games. They have already won 16, so they need to win 61 more games. The width of a garden is 4 less than 3 times length. If the perimeter of the garden is 32ft, what is the length of the garden? A. 2ft B. 3ft C. 5ft D. 9ft - C. 5ft Choose the greatest number; A. 6.4% B. Squared root 39 C. |-6.5| D. 29/5 - C. |-6.5| Which symbol should be in the box? -15/8 [ ] -34/ A. < B. > C. = D. ~ ~ - A. < Which symbol should be in the box? 1.34 x 10^-2 [ ] 134%

A. <

B. >

C. =

D. ~

~ - A. <

Put the following numbers in order from least to greatest: -.61, -2/3, -7/11, -.- 61 A. -.61, -2/3, -7/11, -.- 61 B. -2/3, -7/11, -.- ,. 61 C. -.61, -.-, -7/11, -2/ 61 D. -2/3, -7/11, -.61, -.- 61 - B. -2/3, -7/11, -.- ,. 61 In a bag of marbles, there are 2 blue marbles, 3 green marbles, and 7 yellow marbles. What is the probability of choosing a marble that is not yellow? A. 5/ B. 7/ C. 1/ D. 2/3 - A. 5/ Ryan has an average of 88.6% in his math class after the first four tests. What does Ryan need to score on the 5th test to receive at least 90% in the class? A. 92%