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The symbol "^" is "to the power of", so that 4 x 4 x 4 can be written as 4^3. 5 x 5 x 5 x 5 x 5 x 5 x 5 x R x R x R xV xV can be written as 5^7 x R^3 x V^2. ---------------------- To show the square root of 9, we would write "sqrt (9)" = plus/minus 3
Questions and Answers
1.
The Associative Property says that you can change the way that numbers are grouped together without changing the final answer. .Which example below illustrates the Associative Property of Addition?
A.
(3 x 4) x 5 = 5 x (3 x 4)
B.
(3 x 4) x 5 = 3 x (4 x 5)
C.
3 + (4 + 5) = (4 + 5) + 3
D.
(3 + 4) + 5 = 3 + (4 + 5)
E.
3(4 + 5) = 3(4) + 3(5)
Correct Answer D. (3 + 4) + 5 = 3 + (4 + 5)
Explanation The example (3 + 4) + 5 = 3 + (4 + 5) illustrates the Associative Property of Addition. This property states that the grouping of numbers being added does not affect the final sum. In this example, the numbers 3, 4, and 5 are being added together. Regardless of whether we add 3 and 4 first and then add 5, or add 4 and 5 first and then add 3, the final sum will be the same. Therefore, this example demonstrates the Associative Property of Addition.
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2.
The symbol '^' means 'to the power of'Write in Scientific Notation: 74,900,000,000
A.
749 x 10^8
B.
.749 x 10^11
C.
7.5 x 10^10
D.
7.49 x 10^10
E.
None of the answers are correct.
Correct Answer D. 7.49 x 10^10
Explanation The given number 74,900,000,000 can be written in scientific notation as 7.49 x 10^10. In scientific notation, the number is expressed as a decimal number between 1 and 10 multiplied by a power of 10. In this case, the decimal number is 7.49 and the power of 10 is 10. This notation helps to represent very large numbers in a more compact and convenient form.
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3.
How much time elapses between 9:35 am and 2:15 pm?NO CALCULATOR ALLOWED! PAPER AND PENCIL ONLY.
A.
4 hr, 45 min
B.
4 hr, 40 min
C.
4 hr, 35 min
D.
5 hr, 40 min
E.
5 hr, 35 min
Correct Answer B. 4 hr, 40 min
Explanation To find the elapsed time between 9:35 am and 2:15 pm, we need to subtract the starting time from the ending time.
First, let's subtract the minutes. 15 - 35 = -20. Since we have negative minutes, we need to borrow 1 hour from the hours.
Next, let's subtract the hours. 2 - 9 = -7.
Now, we add the borrowed hour to the remaining hours. -7 + 12 = 5.
Therefore, the elapsed time is 5 hours.
Lastly, we add the remaining minutes. -20 + 60 = 40.
Thus, the correct answer is 4 hr, 40 min.
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4.
The symbol '^' means 'to the power of'Simplify: (3 ^ 7) ^ 2
A.
21 ^ 2
B.
3 ^ 9
C.
3 ^ 42
D.
3 ^ 14
E.
21 ^ 14
Correct Answer D. 3 ^ 14
Explanation The expression (3^7)^2 can be simplified by applying the exponent rule which states that when raising a power to another power, you multiply the exponents. In this case, the exponent 2 is applied to both 3 and 7. Thus, (3^7)^2 becomes 3^(7*2) which is equal to 3^14.
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5.
Which answer describes the relationship between any two models:Model A : y = -5x + 0.333Model B : y = 0.2x - 3Model C : y = 0.5x + 4Model D : y = -0.5x - 7SKETCH A PICTURE TO HELP IF YOU NEED.
A.
A and B are perpendicular because -3 and 0.333 are opposite reciprocals.
B.
C and D are parallel because they have the same slope.
C.
A and B are perpendicular because they have opposite reciprocal slopes.
D.
A and C are perpendicular because -5 and 0.5 are opposite reciprocals.
Correct Answer C. A and B are perpendicular because they have opposite reciprocal slopes.
Explanation A and B are perpendicular because they have opposite reciprocal slopes. The slope of A is -5, and the slope of B is 0.2. The reciprocal of -5 is -1/5, and the reciprocal of 0.2 is 5. Since the slopes of A and B are opposite reciprocals, they are perpendicular to each other.
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6.
A population of prairie dogs starts off at 88 and grows at a rate of 13% per year. Which two equations below do NOT represent the growth of the prairie dogs?
A.
88(1 + .13) ^ T
B.
88(1.13) ^ T
C.
88(1 + 13) ^ T
D.
88(113%) ^ T
E.
88(1.13%) ^ T
Correct Answer(s) C. 88(1 + 13) ^ T E. 88(1.13%) ^ T
Explanation The correct answer is 88(1 + 13) ^ T and 88(1.13%) ^ T do not represent the growth of the prairie dogs. The first equation, 88(1 + 13) ^ T, is incorrect because it adds 13 to 1, which would result in a growth rate of 14 instead of 13%. The second equation, 88(1.13%) ^ T, is incorrect because it multiplies 1.13% by 88, which would result in a growth rate of 0.0113 instead of 13%.
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7.
Which statement is false?
A.
Most absolute value problems have more than one answer.
B.
The square root of a negative number is negative.
C.
The negative of a square root of a number is always negative.
D.
The general form of a linear equation is y=mx+b.
E.
The general form of a quadratic equation is not y=ax^2+bx
Correct Answer B. The square root of a negative number is negative.
Explanation The statement "The square root of a negative number is negative" is false. The square root of a negative number is not a real number, as there is no real number that, when squared, would result in a negative number. Instead, we use the concept of imaginary numbers, where the square root of a negative number is represented by the imaginary unit, denoted as "i".
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8.
Which quadrant of a 10 x 10 coordinate plane would be the most shaded by the following two inequalities?y < -2x + 3 and y > 5x -9 For example, IF you graphed these on a graphing calculator, which quadrant would be the most shaded?SKETCH A PICTURE IF NECESSARY.
A.
Quadrant I
B.
Quadrant II
C.
Quadrant III
D.
Quadrant IV
E.
Not enough information is available to answer the question.
Correct Answer C. Quadrant III
Explanation The two inequalities y < -2x + 3 and y > 5x - 9 represent lines on the coordinate plane. Quadrant III is the region where both inequalities are true. In this quadrant, the shaded region would be the most because it satisfies both inequalities. The lines y < -2x + 3 and y > 5x - 9 intersect in Quadrant III, creating a shaded area that is not present in any other quadrant. Therefore, Quadrant III would be the most shaded quadrant.
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9.
Company ALpHA has sales of $60,000 and follows the Growth Model of 60,000(1.17)^10 for the first ten years. Company ZETA has sales of $35,000 and follows the Growth Model of 35,000(1.21)^10 for the first ten years. You have the opportunity to go back in time and invest in one of them. Which one is the better investment?
A.
ALPHA
B.
ZETA
C.
Not enough information to make a good choice.
Correct Answer B. ZETA
Explanation ZETA is the better investment because it has a higher growth rate compared to ALPHA. While both companies have the same time frame of 10 years, ZETA's growth model with a growth rate of 1.21 is higher than ALPHA's growth model with a growth rate of 1.17. Therefore, ZETA is expected to have a higher increase in sales over time, making it a more profitable investment option.
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10.
The use of the letter E on the calculator signifies "x 10 ^", so that 2x10^6 can be written as 2 E 6. Simplify (2 E 6) x (4 E 9)
A.
8 E 45
B.
6.0 E 45
C.
8.0 E 14
D.
8 E 15
E.
6 E 15
Correct Answer D. 8 E 15
Explanation The given expression (2 E 6) x (4 E 9) represents multiplying 2 times 10 raised to the power of 6, by 4 times 10 raised to the power of 9. To simplify this expression, we can multiply the coefficients (2 x 4 = 8) and add the exponents (6 + 9 = 15). Therefore, the simplified form is 8 times 10 raised to the power of 15, which can be written as 8 E 15.
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11.
Which series shows numbers in decreasing order?
A.
3.54, 3.5, 3.45, 3.44, 3.40, 3.04
B.
4.3, 4.32, 4.38, 4.83, 4.88, 4.33
C.
8.090, 8.009, 8.08, 8.80, 8.88, 9.8
D.
1.0, 2.0, 2.1, 2.2, 1.2, 1.1
Correct Answer A. 3.54, 3.5, 3.45, 3.44, 3.40, 3.04
Explanation The series 3.54, 3.5, 3.45, 3.44, 3.40, 3.04 shows numbers in decreasing order because each subsequent number in the series is smaller than the previous one.
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12.
A store can sell 5o boxes of cereal a day if the price is $2.80 per box and 65 boxes a day if the price is $2.65. Assuming that the relationship is linear, how many boxes would you expect them to sell each day if the selling price was $2.20? NO CALCULATOR ALLOWED! PAPER AND PENCIL ONLY.
A.
220
B.
110
C.
20
D.
130
Correct Answer B. 110
Explanation The relationship between the number of boxes sold and the price per box is linear. This means that as the price decreases, the number of boxes sold also decreases in a consistent manner. Since the price is decreasing from $2.80 to $2.20, we can expect the number of boxes sold to also decrease. By comparing the price decrease of $0.60 ($2.80 - $2.20) to the corresponding decrease in the number of boxes sold, we can determine that the number of boxes sold will decrease by the same ratio. Therefore, we can estimate that the store would sell 110 boxes if the selling price was $2.20.
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13.
If you have a parabola that is graphed and you wanted to slide the parabola up 5 units, which step below would you take?NO CALCULATOR ALLOWED! PAPER AND PENCIL ONLY.
A.
Add 5 to the 'c' value.
B.
Subtract 5 from the 'c' value.
C.
Add 5 to the 'b' value.
D.
Subtract 5 from the 'b' value.
E.
Add 5 to the 'a' value
Correct Answer A. Add 5 to the 'c' value.
Explanation To slide the parabola up 5 units, you would add 5 to the 'c' value. The 'c' value represents the y-intercept of the parabola, which determines its vertical position. By adding 5 to the 'c' value, the entire parabola will shift upward by 5 units.
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14.
IF 40% of Bogarts are Gables, and 50% of Gables are Davis's, then a population of 60 Bogarts would have how many Davis's'?NO CALCULATOR ALLOWED! PAPER AND PENCIL ONLY.
A.
54
B.
45
C.
14
D.
12
E.
10
Correct Answer D. 12
Explanation If 40% of Bogarts are Gables, then out of 60 Bogarts, there would be 60 * 0.40 = 24 Gables.
If 50% of Gables are Davis's, then out of the 24 Gables, there would be 24 * 0.50 = 12 Davis's.
Therefore, a population of 60 Bogarts would have 12 Davis's.
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15.
Consider the following and determine what will be the seventh term. Assume that the first term is the "7".7, 11, 13, 17, 19, ____, _____
A.
25
B.
23
C.
21
D.
29
E.
31
Correct Answer D. 29
Explanation The series is formed by adding 4 to the previous term. Starting with 7, we add 4 to get 11, then add 4 again to get 15, and so on. Therefore, the seventh term will be 19 + 4 = 23.
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16.
Balthazar rolls a 6-sided green die. Jedediah rolls a 4-sided purple die. Obi-wan also rolls a 4-sided black die. Which answer below is NOT a possible result of the product of all three rolls?NO CALCULATOR ALLOWED! PAPER AND PENCIL ONLY.
A.
48
B.
75
C.
80
D.
8
E.
60
Correct Answer B. 75
Explanation The product of the three rolls is obtained by multiplying the numbers on each die. The green die has 6 sides, so the maximum number that can be rolled is 6. The purple and black dice have 4 sides, so the maximum number that can be rolled on each is 4. The maximum possible product is therefore 6*4*4 = 96. Since 75 is less than 96, it is not a possible result of the product of all three rolls.
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17.
In the Richter Scale for measuring earthquakes, each whole number is 10X greater than the previous whole number. So that a 4.0 is ten times greater than a 3.0 and a 9.0 is ten times greater than an 8.0. Using that information, which answer below is true?
A.
A 2.0 is half as powerful as a 4.0
B.
A 4.0 is 100 times more powerful than a 6.0
C.
A 8.0 is 1000 times more powerful than a 5.0.
D.
A 5.0 is 100 times more powerful than a 7.0.
E.
A 2.5 is half as powerful as a 5.0.
Correct Answer C. A 8.0 is 1000 times more powerful than a 5.0.
Explanation According to the Richter Scale, each whole number increase represents a tenfold increase in the magnitude of an earthquake. Therefore, an 8.0 earthquake is ten times greater than a 7.0 earthquake, and this pattern continues for each whole number increase. Since the difference between an 8.0 and a 5.0 earthquake is three whole numbers, the magnitude of the 8.0 earthquake is ten times greater than the magnitude of the 5.0 earthquake, repeated three times, which equals 1000 times more powerful.
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18.
Which statement is true?
A.
On every x-intercept the x-coordinate is always zero.
B.
Every y-intercept has an x-coordinate of zero.
C.
Every point on the y-axis is the y-intercept of a line.
D.
Every parabola has at least one x-intercept.
Correct Answer B. Every y-intercept has an x-coordinate of zero.
Explanation Every y-intercept has an x-coordinate of zero. This statement is true because the y-intercept is the point where a line or curve intersects the y-axis. The y-axis represents the x-coordinate of zero, so any point on the y-axis will have an x-coordinate of zero. Therefore, every y-intercept will have an x-coordinate of zero.
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19.
8 + 9 - 12 + 4(5) + 2 - 8NO CALCULATOR ALLOWED! PAPER AND PENCIL ONLY.
A.
19
B.
20
C.
18
D.
17
E.
21
Correct Answer A. 19
Explanation To solve this problem, we need to follow the order of operations (PEMDAS/BODMAS). First, we perform the multiplication: 4(5) = 20. Then, we perform the addition and subtraction from left to right: 8 + 9 - 12 + 20 + 2 - 8 = 19. Therefore, the correct answer is 19.
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20.
Which one is greater than 3/4? NO CALCULATOR ALLOWED! PAPER AND PENCIL ONLY.
A.
2/3
B.
9/18
C.
12/20
D.
4/5
E.
3/5
Correct Answer D. 4/5
Explanation To determine which fraction is greater than 3/4, we can compare the numerators of each fraction. The numerator of 4/5 is 4, which is greater than the numerator of 3/4, which is 3. Therefore, 4/5 is greater than 3/4.
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21.
Which answer is closest to the product of 36 and 7?
NO CALCULATOR ALLOWED! PAPER AND PENCIL ONLY.
A.
250
B.
258
C.
198
D.
210
E.
244
Correct Answer A. 250
Explanation To find the product of 36 and 7, we can break down the multiplication into smaller, more manageable steps. We can start by multiplying 6 (the ones digit of 36) by 7, which equals 42. Then, we can multiply 30 (the tens digit of 36) by 7, which equals 210. Adding these two results together, we get 42 + 210 = 252. Since 250 is the closest answer to 252, it is the correct answer.
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22.
Four people weigh an average of 16 stone each. They lose an average of 3.5 stone each. What is their new total weight? NO CALCULATOR ALLOWED! PAPER AND PENCIL ONLY.
A.
46 stone
B.
47 stone
C.
48 stone
D.
49 stone
E.
50 stone
Correct Answer E. 50 stone
23.
What is the probability of randomly selecting the letter E from the word Tennessee?T E N N E S S E E
A.
4/5
B.
4/9
C.
5/9
D.
4/1
E.
9/4
Correct Answer B. 4/9
Explanation The word "Tennessee" has a total of 9 letters. Among these 9 letters, there are 4 letter E's. Therefore, the probability of randomly selecting the letter E from the word Tennessee is 4/9.
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24.
You take a job as a delivery person for a toilet paper company. Each case of TP sells for $29. You are paid $1.50 per case that you deliver. In the first 30 min., you deliver 16 cases and receive $7 in tips. IF THIS ENTIRE PATTERN CONTINUES for the rest of your 8 hour working shift, how much money would you expect to make that day?NO CALCULATOR ALLOWED! PAPER AND PENCIL ONLY.
A.
$1,344
B.
$496
C.
$488
D.
$283
Correct Answer B. $496
Explanation Based on the given information, the delivery person earns $1.50 per case delivered. In the first 30 minutes, they delivered 16 cases, so they earned 16 * $1.50 = $24 from deliveries. They also received $7 in tips. Assuming this pattern continues for the entire 8-hour shift, they would earn $24 from deliveries every 30 minutes, which is $24 * 16 = $384 for the entire shift. Adding the $7 in tips, the total amount they would expect to make that day is $384 + $7 = $391. Therefore, the correct answer is $496, which is not among the options provided.
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25.
Which two expressions do NOT give you a result of 17?
"x" means multiplicationNO CALCULATOR ALLOWED! PAPER AND PENCIL ONLY.
A.
5 + 7 + -9 + 7 x 3
B.
7 * 2 - 9 + 12
C.
(15 x 3) - 18
D.
85 / 5
Correct Answer(s) A. 5 + 7 + -9 + 7 x 3 C. (15 x 3) - 18
26.
Prime numbers are numbers that have only two factors, one and itself. For example, the number 7 is prime because its only two factors are 1 x 7. The number 9 is not prime because it has three factors, 1 x 9 and 3 x 3 (although the number 3 appears twice, it is only counted once). Which set contains only prime numbers?NO CALCULATOR ALLOWED! PAPER AND PENCIL ONLY.
A.
{ 41, 59, 63, 71 }
B.
{ 31, 49, 53, 59 }
C.
{ 79, 83, 89, 90 }
D.
{ 1, 3, 5, 7 } (This is a trick. The number 1 is not prime, because it has only one factor)
E.
{ 101, 47, 61, 19 }
Correct Answer E. { 101, 47, 61, 19 }
27.
Which decimal is closest to "two and one-fourth"NO CALCULATOR ALLOWED! PAPER AND PENCIL ONLY.
A.
2.66
B.
2.5
C.
2.33
D.
2.10
E.
Both 2.66 and 2.33 are equally close.
Correct Answer C. 2.33
28.
Calculate mentally.NO CALCULATOR ALLOWED! NO PAPER AND PENCIL.
53 x 3
A.
91
B.
109
C.
159
D.
153
E.
141
Correct Answer C. 159
Explanation The correct answer is 159 because when multiplying 53 by 3 mentally, you can start by multiplying the ones place of 53 (which is 3) by 3, resulting in 9. Then, you multiply the tens place of 53 (which is 5) by 3, resulting in 15. Finally, you add the product of the tens place (15) to the product of the ones place (9), giving you a total of 24. Therefore, 53 multiplied by 3 is equal to 159.
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29.
Calculate Mentally: 39 x 4NO CALCULATOR ALLOWED! NO PAPER AND PENCIL.
A.
154
B.
156
C.
158
D.
160
Correct Answer B. 156
Explanation The answer is 156 because when you multiply 39 by 4, you can break it down into two parts. First, multiply 30 by 4, which equals 120. Then, multiply 9 by 4, which equals 36. Finally, add the two results together: 120 + 36 = 156.
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30.
Simplify: (2x + 3) ( 3x + 1)
A.
6x^2 + 11x + 3
B.
6x^2 + 9x + 3
C.
6x^2 - 9x + 3
Correct Answer A. 6x^2 + 11x + 3
Explanation The given expression is a product of two binomials. To simplify the expression, we need to multiply each term of the first binomial by each term of the second binomial using the distributive property. After multiplying, we combine like terms by adding the coefficients of the terms with the same degree of x. The resulting expression is 6x^2 + 11x + 3.
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