Math Knowledge ASVAB
A: 8 Exponent rule: a^b ×a^c = a ^ b+c The 16 and 16 combine and now were left with just adding the exponents. 1) 1/4+2/4= 3/4 2) 16^3/4 3) Factor 16 to 2^4 4) (2^4)^3/4 5) 4 x 3/4 = 3 6) 2^3 = 8
What is the solution?
A: Division can be used to solve this problem. The division necessary is: (5.972 x 10²⁴)/(7.348x10²²) To compute this division, divide the constants first then use algebraic laws of exponents to divide the exponential expression. This results in about 0.8127x10², which written in scientific notation is 8.127x10¹.
What is the solution?
A. 12x²+2xy-30y² Remember FOIL (First, outer, inner, last)
Simplify the following expression (3x+5y)(4x-6y) A. 12x²+2xy-30y² B. 12x²+38xy+30y² C. 6x²-14xy+8y² D. 6x²-30y²
B. -4 We need to combine the system of equations. Since were looking for x lets get the Y's to cancel out. 10 x 3 is 30 6 x -5 is -30 1) 3 x ( 4x+10y=24) = 12x+30y=72 2) -5 x ( 10x+6y=-16) = -50x-30y=80 3) 12x+30y=72 -50x-30y=80 the Y's cancel out. 4) Combine like terms. -38x = 152 divide both sides x = -4
Solve the following system of equations for x: 4x+10y=24 10x+6y=-16 A. -6 B. -4 C. 2 D. 1
C. 2x+4z 1) 5x+2y - (2y+3x-4z) 2) Distribute the negative 3) 5x +2y - 2y -3x +4z 4) combine like terms 5) 2x+4z which is C
Subtract 2y +3x -4z from 5x +2y A. 2x+4y+4 B. 7x+4 C. 2x+4z D. 2x+4y
Answer B Remember to make something into a percent. Move the decimal 2 times to the right.
0.925 is equal to what percent? A. 925% B. 92.5% C. 9.25% D. 0.0925%
C: The mode for a set of data is the value that occurs the most. The grade that appears the most is 95. It's the only value that repeats in the set. The mean is around 84.3.
10. What is the mode for the grades shown in the chart below?
B. x⁶y⁹ 1) (x²y³)³ 2) We are simply multiplying the exponents. 3) x² = x⁶ 4) y³ = y⁹
(x²y³)³ = ? A. x⁵y⁶ B. x⁶y⁹ C. x⁷y⁸ D. x⁶y^10
B: The relationship between age and time for attention span is a positive correlation because the general trend for the data is up and to the right. As the age increases, so does attention span.
11. What type of relationship is there between age and attention span as represented in the graph below?
B: 1) move 7 to the right side. -4/5x < -32/5 2) Multiply both sides by -1, this will make them positive and switch the sign from < to > 4/5x > 32/5 3) Multiply both sides by 5 4x > 32 4) Divide both sides by 4 x > 8 Open circle so the line is going right to infinity. (8, infinity) which is B.
19. What is the solution to the following linear inequality?
B. 16.443 Remember when you're adding decimals to decimals or even whole numbers. Just align the decimals and do the arithmetic.
2.36 + 14 + 0.083 A. 14.059 B. 16.443 C. 16.69 D. 17.19
C. 23,900 Remember when you multiply by a multiple of 10 you move the decimal by however many zeros there are. In this case 10,000 has 4 zeros which means we move the decimal 4 times to the right which will give us 23,900 which is answer C.
2.39 x 10,000 A. 239 B. 2,390 C. 23,900 D. 239,000
C: First, the slope of the line must be found. This is equal to the change in y over the change in x, given the two points. The slope formula is m=(y2-y1)/(x2-x1) (-5-7)/(-1-(-3)) = -6 Therefore, the slope is -6. The slope and one of the points are then plugged into the slope-intercept form of a line: y-y₁ =m(x-x₁). This results in y-7=-6(x-(-3)). The -6 is simplified and the equation is solved for y to obtain y=-6x-11.
24. What is the equation of the line that passes through the two points (-3, 7) and (-1, -5)?
A. 10% First we need to know how many ounces of water and juice there are before the water is added. 1) 80% x 20 ounces = 16 ounces of water. 2) Which leaves 4 ounces of juice. 3) 20 ounces of water is added to the mixture 4) 20+16 = 36 ounces of water. With 4 ounces of fruit juice. 5) We need to find the percent of juice so get that number and put it over the total to get the percent. 6) Total = 20+16+4 = 40 7) 4/40 = .10 or 10% which is A.
20 ounces of a drink mixture contain 20% fruit juice and 80% water. It is further diluted by adding 20 ounces of additional water. What is the percent of fruit juice in the diluted mixture? A. 10% B. 12% C. 40% D. 8%
C: The mean for the number of visitors during the first 4 hours is 14. The mean is found by calculating the average for the four hours. Adding up the total number of visitors during those hours gives 12 + 10 + 18 + 16 = 56. Then, 56 divide 4 = 14
9. Using the graph below, what is the mean number of visitors for the first 4 hours?
B: The outlier is 35. When a small outlier is removed from a data set, the mean and the median increase. The first step in this process is to identify the outlier, which is the number that lies away from the given set. Once the outlier is identified, the mean and median can be recalculated. The mean will be affected because it averages all of the numbers. The median will be affected because it finds the middle number, which is subject to change because a number is lost. The mode will most likely not change because it is the number that occurs the most, which will not be the outlier if there is only one outlier.
22. The following set represents the test scores from a university class: {35,79, 80, 87, 87, 90, 92, 95, 95, 98, 99}. If the outlier is removed from this set, which of the following is TRUE? a. The mean and the median will decrease. b. The mean and the median will increase. c. The mean and the mode will increase. d. The mean and the mode will decrease. e. The mean, median, and mode will increase.
C. y^2p 1) remember the rules with dividing quantities with exponents. 2) x^m/x^n = x ^m-n 3) y^p+q-(q-p) - remember that youa are subtracting from the quantity so we must distribute the negative first. 4) - (q-p) = -q+p 5) p+q-q+p = 2p 6) y^2p which is C.
(y^(p+q))/(y^(q-p)) = ? A. y^2q B. y^p+q C. y^2p D. y^p-q
Answer A. Simply reduce. 5/8 x 4/16 - reduce 1/2 x 1/3 = 1/6 which is A.
5/8 x 4/15 A. 1/6 B. 2/5 C. 9/15 D. 7/45
Answer B. The wall, the ladder, and the ground in the tennis court forma right triangle. The ladder is on a slant, and is opposite the right angle formed by the wall and the ground. In this position, the ladder is the "hypotenuse" of the right triangle. In geometry, the Pythagorean Theorem states that the square of the hypotenuse (c^2) equals the sum of the squares of the other two sides (a^2 +b^2). 1) a^2+b^2 = c^2 2) 8^2 + x^2 = 10^2 Solve for x 3) 64 + x^2 = 100 4) x^2 = 100-64 5) x^2 = 36 -square root each side 6) x = 6 which is Answer B.
A 10-foot-high ladder is resting against an 8-foot-high wall surrounding a tennis court. If the top of the ladder is exactly even with the top of the wall, how far is the base of the ladder from the wall? A. 18 feet B. 6 feet C. 12 feet D. 9 feet
Answer D. First find the area of the entire wildlife preserve. Since its a circle. Use the formula for the area of a circle. Area(A) = pi x r^2 1) 3.18 x 14^2 2) 3.18 x 196 3) 318 x 196 = 62,328 go back 2 = 628.28 square miles The lions territory is a wedge formed by a 90 degree angle at the center of the circle. Since a circle has 360 degrees, we can find the part of the preserve inhabited by lions. 4) 90/360 = 1/4 Next find what this equals in square miles 5) 1/4 x 628/1 = 628/4 = 157 (close to 154) answer D.
A wildlife preserve is laid out in the shape of a perfect circle whose radius is 14 miles. The lions' territory in this preserve is shaped like a wedge and has a fence around it. Two inner sides of a fence meet at a 90 degree angle in the center of the preserve. How much territory do the lions have? A. 140 square miles B. 3 (1/2) miles C. 210 square miles D. 154 square miles
C. 15.68 Remember PEMDAS. You go left to right when its just addition and subtraction. First do 12.00 - 0.92 = 11.08 Then we add 11.08 to 4.60 which will give is 15.68 which is C.
12 - 0.92 + 4.6 A. 17.52 B. 16.68 C. 15.68 D. 8.4
A: The area of the shaded region is calculated in a few steps. First, the area of the rectangle is found using the formula A =length x width = 6 x 2 = 12. Second, the area of the triangle is found using the formula: A = 1/2 x base x height = 1/2 x 3 x 2 = 3. The last step is to take the rectangle area and subtract the triangle area. The area of the shaded region is A = 12 -3 = 9m².
12. What is the area of the shaded region?
D: The volume for a cylinder is found by using the formula: V = (π x r²h = pi(2²) x 3.5 = 43.9in².
13. What is the volume of the cylinder below?
C: There are 0.006 kiloliters in 6 liters because 1 liter=0.001kiloliters. The conversion comes from the chart where the prefix kilo- is found three places to the left of the base unit.
14. How many kiloliters are in 6 liters?
Answer A. Simply make 2 (2/5) into improper fraction 2 (2/5) = 14/5 14/5 ÷ 7 - remember 7 is really 7/1 we can flip it and multiply. 14/5 x 1/7 = 3/5 answer A.
2 (4/5) ÷ 7 = A. 2/5 B. 9 (8/5) C. 5/2 D. 24/35
D: Let x be the missing quantity. The problem can be expressed as the following equation: 3(5-x) = x-5. Distributing the 3 results in: 15 -3x = x+5. Subtract 5 from both sides, add 3x to both sides, and then divide both sides by 4. This results in: 10/4 = 5/2 =2.5
20. Triple the difference of five and a number is equal to the sum of that number and 5. What is the number?
A: The formula for the rate of change is the same as slope: change in y over change in x. The y-value in this case is percentage of smokers and the x-value is year. The change in percentage of smokers from 2000 to 2015 was 8.1 percent. The change in x was 2000-2015 = -15. Therefore, 8.1%/-15 = -0.54%. The percentage of smokers decreased 0.54 percent each year.
25. The percentage of smokers above the age of 18 in 2000 was 23.2 percent. The percentage of smokers above the age of 18 in 2015 was 15.1 percent. Find the average rate of change in the percent of smokers above the age of 18 from 2000 to 2015. a. -.54 percent b. -54 percent c. -5.4 percent d. -15 percent e. -1.5 percent What is the solution?
A: The probability of .9 is closer to 1 than any of the other answers. The closer a probability is to 1, the greater the likelihood that the event will occur. The probability of 0.05 shows that it is very unlikely that an adult driver will wear their seatbelt because it is close to zero. A zero probability means that it will not occur. The probability of 0.25 is closer to zero than to one, so it shows that it is unlikely an adult will wear their seatbelt. Choice E is wrong because probability must fall between 0 and 1.
26. A study of adult drivers finds that it is likely that an adult driver wears his seatbelt. Which of the following could be the probability that an adult driver wears his seat belt? a. 0.90 b. 0.05 c. 0.25 d. 0 e. 1.5 What is the solution?
A: A proportion should be used to solve this problem. The ratio of tagged to total deer in each instance is set equal, and the unknown quantity is a variable x. The proportion is 300/x = 5/ 400. Cross-multiplying gives 120,000 =5x, and dividing through by 5 results in 24,000.
27. In order to estimate deer population in a forest, biologists obtained a sample of deer in that forest and tagged each one of them. The sample had 300 deer in total. They returned a week later and harmlessly captured 400 deer, and 5 were tagged. Use this information to estimate how many total deer were in the forest. a. 24,000 deer b. 30,000 deer c. 40,000 deer d. 100,000 deer e. 120,000 deer What is the solution?
A: A vertical line has the same x value for any point on the line. Other points on the line would be (1, 3), (1, 5), (1, 9,) etc. Mathematically, this is written as x=1. A vertical line is always of the form x = a for some constant a.
28. Which of the following is the equation of a vertical line that runs through the point (1, 4)?
C: The Pythagorean Theorem can be used to find the missing length x because it is a right triangle. The theorem states that 6²+8²=x², which simplifies into 100=x². Taking the positive square root of both sides results in the missing value x =10.
29. What is the missing length x?
E: First, the common factor 2 can be factored out of both terms, resulting in: 2(y³ - 64) The resulting binomial is a difference of cubes that can be factored using the rule: a³-b³=(a-b)(a²+ab+b²) a =y and b =4, therefore, the results is: 2(y-4)(y²+4y+16)
30. What is the correct factorization of the following binomial? 2y^3 - 128
B: Look on the horizontal axis to find 3:00 p.m. Move up from 3:00p.m. to reach the dot on the graph. Move horizontally to the left to the horizontal axis to between 20 and 25; the best answer choice is 22. The answer of 25 is too high above the projected time on the graph, and the answers of 20 and 16 degrees are too low.
32. Use the graph below entitled "Projected Temperatures for Tomorrow's Winter Storm" to answer the question.
B: N=k x P, where N is number of representatives, k is the variation constant, and P is total population in millions. Plugging in the information for New York allows k to be solved for. This process gives 27=k x 19.8, Divide both sides by 19.8 so k=1.36. Therefore, the formula for number of representatives given total population in millions is N=1.36 x 11.8 = 16.04 or just 16.
33. The number of members of the House of Representatives varies directly with the total population in a state. If the state of New York has 19,800,000 residents and has 27 total representatives, how many should Ohio have with a population of 11,800,000? A. 12 B. 16 C. 15.8 D. 15 E. 13
B: This is a statistical question because in order to determine this answer one would need to collect data from each person in the class and it is expected the answers would vary. The other answers do not require data to be collected from multiple sources; therefore, the answers will not vary.
34. Which of these answer choices is a statistical question? a. What was your grade on the last test? b. What were the grades of the students in your class on the last test? c. What kind of car do you drive? d. What was Sam's time in the marathon? e. What textbooks does Marty use this semester?
E: The mean is found by adding all the times together and dividing by the number of times recorded. 25 18 23 28 30 22.5 23 33 20 222.5, divided by 9 24.7. Rounding to the nearest minute, the mean is 25 minutes.
35. What is the mean of Eva Jane's time? a. 26 minutes b. 19 minutes c. 24.5 minutes d. 23 minutes e. 25 minutes
C: The mode is the time from the data set that occurs most often. The number 23 occurs twice in the data set, while all others occur only once, so the mode is 23.
36. What is the mode of Eva Jane's time? a. 16 minutes b. 20 minutes c. 23 minutes d. 33 minutes e. 25 minutes
D. 1.312 Remember you align the decimals. In this case we need to add extra zeros to the 1.5 to fill the problem so it will look like this. 1.500 0.188 - ------------ Solve Answer should be 1.312 which is D
1.5 - 0.188 A. 0.62 B. 1.262 C. 1.27 D. 1.312
Answer C. Do the fractions first. Eventually you will reduce the 16s and be left with 3.
1/2 x 16 x 3/8 = A. 1/4 B. 2 (5/16) C. 3 D. 4 (1/4)
A: To find the median of a data set, you must first list the numbers from smallest to largest, and then find the number in the middle. If there are two numbers in the middle, as in this data set, add the two numbers in the middle together and divide by 2. Putting this list in order from smallest to greatest yields 18, 20, 22.5, 23, 23, 25, 28, 30, and 33, where 23 is the middle number, so 23 minutes is the median.
37. What is Eva Jane's median score? a. 23 minutes b. 17 minutes c. 28 minutes d. 19 minutes e. 25 minutes
D: The area for a rectangle is found by multiplying the length by the width. The area is also measured in square units, so the correct answer is Choice D. The answer of 26 is the perimeter. The answer of 13 is found by adding the two dimensions instead of multiplying.
38. What is the area of the following figure?
B: The volume of a rectangular prism is found by multiplying the length by the width by the height. This formula yields an answer of 144 cubic units. The answer must be in cubic units because volume involves all three dimensions. Each of the other answers have only two dimensions that are multiplied, and one dimension is forgotten, as in D, where 12 and 3 are multiplied, or have incorrect units, as in E.
39. What is the volume of the given figure? a. 36 cm2 b. 144 cm3 c. 72 cm3 d. 36 cm3 e. 144 cm2
Answer A. Simply make 1 (4/5) into improper 1 (4/5) = 9/5 4/1-9/5 - make the denominator the same 20/5 - 9/5 = 11/5 -improper only choice is A.
4 - 1(4/5)= A. 2 (1/5) B. 2 (4/5) C. 3 (3/10) D. 3 (1/5)
D: This is a one-step real-world application problem. The unknown quantity is the number of cases of cola to be purchased. Let be equal to this amount. Because each case costs $3.50, the total number of cases times $3.50 must equal $40. This translates to the mathematical equation 3.5x = 40 Divide both sides by 3.5 to obtain x = 11.4286, which has been rounded to four decimal places. Because cases are sold whole (the store does not sell portions of cases), and there is not enough money to purchase 12 cases, there is only enough money to purchase 11.
4. How many cases of cola can Lexi purchase if each case is $3.50 and she has $40? a. 10 b. 12 c. 11.4 d. 11 e. 12.5
A: Surface area is a type of area, which means it is measured in square units. Cubic units are used to describe volume, which has three dimensions multiplied by one another. Quartic units describe measurements multiplied in four dimensions.
40. What type of units are used to describe surface area? a. Square b. Cubic c. Single d. Quartic e. Volumetric
B: The perimeter is found by adding the length of all the exterior sides. When the given dimensions are added, the perimeter is 22 meters. The equation to find the perimeter can be P=5+1.5+1.2+4.5+3.8+6=22. The last two dimensions can be found by subtracting 1.2 from 5, and adding 1.5 and 4.5, respectively.
41. What is the perimeter of the following figure? a. 13.4 m b. 22 m c. 12.2 m d. 22.5 m e. 24.4 m
A: The surface area for a cylinder is the sum of the areas of the two circle bases and the rectangle formed on the side. This is easily seen in the net of a cylinder. The area of a circle is found by multiplying pi times the radius squared. The rectangle's area is found by multiplying the circumference of the circle by the height. The equation SA=2π x 5 x 10+2(π5²) shows the area of the rectangle as 2πx5x10, which yields 314. The area of the bases is found by π5², which yields 78.5, then multiplied by 2 for the two bases.
42. Which equation correctly shows how to find the surface area of a cylinder?
C: A hexagon can be formed by any combination of the given shapes except for two rectangles. There are no two rectangles that can make up a hexagon.
43. Which shapes could NOT be used to compose a hexagon? a. Six triangles b. One rectangle and two triangles c. Two rectangles d. Two trapezoids e. One rectangle and four
Answer D. Simply put 45% over 100 and reduce 45/100 -reduce with 5 9/20 and it can't be reduced any further so the answer is D.
45% is equal to what fraction? A. 4/5 B. 5/8 C. 25/50 D. 9/20
A. 0.0315 Make the decimal whole by moving to the right 4 times which give us 63. (Remember to move back 4 times). Now it will be 63 x 5 = 315 Move back 4 times 0.0315
5 x 0.0063 A. 0.0315 B. 0.315 C. 3.15 D. 31.5
A: First, the variables have to be defined. Let be the first integer; therefore, x = 1 is the second integer. This is a two-step problem. The sum of three times the first and two less than the second is translated into the following expression: 3x + (x + 1 -2). This expression is set equal to 411 to obtain 3x + (x + 1 -2) = 412. The left-hand side is simplified to obtain 4x -1 = 411. The addition and multiplication properties are used to solve for x. First, add 1 to both sides and then divide both sides by 4 to obtain x = 103. The next consecutive integer is 104.
5. Two consecutive integers exist such that the sum of three times the first and two less than the second is equal to 411. What are those integers? a. 103 and 104 b. 104 and 105 c. 102 and 103 d. 100 and 101 e. 101 and 102
A: Let be the unknown, the number of hours Erin can work. We know Katie works , and the sum of all hours is less than 21. Therefore, x + 2x < 21, which simplifies into 3x < 21. Solving this results in the inequality x < 7 after dividing both sides by 3. Therefore, Erin can work less than 7 hours.
6. Erin and Katie work at the same ice cream shop. Together, they always work less than 21 hours a week. In a week, if Katie worked two times as many hours as Erin, how many hours could Erin work? a. Less than 7 hours b. Less than or equal to 7 hours c. More than 7 hours d. Less than 8 hours e. More than 8 hours
A: The chart is a bar chart showing how many men and women prefer each genre of movies. The dark gray bars represent the number of women, while the light gray bars represent the number of men. The light gray bars are higher and represent more men than women for the genres of Comedy and Action.
7. From the chart below, which two types of movies are preferred by more men than women? a. Comedy and Action b. Drama and Comedy c. Action and Horror d. Action and Romance e. Romance and Comedy
D. (v²-u²)2s What its asking is get (a) by itself from v² = u²+2as 1) Solve for a 2) subtract u² to both sides 3) v² - u²=2as 3) Since 2as is multiplication lets divide both sides by 2s to get a by itself 4) a = (v²-u²)/2s which is D.
Express a in term of u, v , and s: v² = u²+2as A. (v²+u²)/2s B. (u²-v²)/2s C. (v²-u²)/s D. (v²-u²)2s
E: A line graph represents continuous change over time. The line on the graph is continuous and not broken, as on a scatter plot. Stacked bar graphs are used when comparing multiple variables at one time. They combine some elements of both pie charts and bar graphs, using the organization of bar graphs and the proportionality aspect of pie charts. A bar graph may show change but isn't necessarily continuous over time. A pie graph is better for representing percentages of a whole. Histograms are best used in grouping sets of data in bins to show the frequency of a certain variable.
8. Which type of graph best represents a continuous change over a period of time? a. Stacked bar graph b. Bar graph c. Pie graph d. Histogram e. Line graph
Answer D. Simply make 13 (3/4) into an improper fraction. 13 (3/4) = 55/4 55/4 ÷ 5 = 55/4 x 1/5 = 11/4 11/4 is 2 (3/4) which is answer D.
A cement truck must distribute 13 (3/4) tons of cement evenly to five work sites. How many tons should it give to each work site? A. 2(1/4) B. 2 (1/2) C. 2(3/8) D. 2 (3/4)
Answer D. To find the volume (V) of a cylinder, multiply pi times the square of the radius (r) times the height (h). V = pi x r^2 x h 1) V = 3.18 x 7^2 x 15 2) V = 3.18 x 49 x 15 3) V = 155.82 x 15 4) V = 2337 Now we divide this by 231 to get the gallons 2337/231 = 10 gallons which is D.
A cylindrical can has a radius of 7 inches and a height of 15 inches. How many gallons of milk can it hold? (There are 231 cubic inches in a gallon.) A. 15 gallons B. 14 gallons C. 140 gallons D. 10 gallons
B. $20.40 1) Make 25.50 whole - 2 steps. 2) Make .20 whole - 2 steps. 3) 4 steps total to move back. 4) 2550 x 20 or 255x2 = 51000 5) Move back 4 times. 6) 5.10 7) Subtract 5.10 from 25.50 = 20.40 which is B.
A shirt normally costs $25.50. How much do you need to pay if it is purchased at a 20% discount? A. $12.50 B. $20.40 C. $21.40 D. $24.00
D. 9x²-30x+25 1) (3x-5)² = (3x-5)x(3x-5) 2) FOIL = First, outer, inner, last 3) 9x² -15x-15x+25 4) 9x² -30x+25 answer D
Expand (3x-5)² A. 9x²+30x-25 B. 9x²-15x+25 C. x²-30x+25 D. 9x²-30x+25
B. (z-5)(x+y) 1) Factor out common terms 2) xz-5x = x( z-5) 3) yz-5y = y (z-5) 4) x( z-5) + y (z-5) = (z-5) 5) (z-5)(x+y) which is B
Factorize completely: xz-5x+yz-5y A. (z+5)(x+y) B. (z-5)(x+y) C. (x-5)(x+z) D. (x+5)(x-y)
Answer B. One way to solve this is to square each of the suggested answers to see which is close to 85. 9.1 x 9.1 = 82.81 9.2 x 9.2 = 84.64 - close 9.3 x 9.3 = 86.49 - too big. Answer has to be 9.2
Find the square root of 85 to the nearest tenth A. 9.1 B. 9.2 C. 9.3 D. 9.4
Answer A. Solve by doing each arithmetic operation and combining answers. Remember that the product of two negatives or two positives numbers is a positive number. The product of a negative and a positive is negative. 1) (-3)^4 = (-3) x (-3) x (-3) x (-3) = 81 2) (-2)^4 = (-2) x (-2) x (-2) x (-2) = 16 3) (-1)^4 = (-1) x (-1) x (-1) x (-1) = 1 81+16+1 = 98 which is A
Find the value of (-3)^4 + (-2)^4 + (-1)^4 A. 98 B. -98 C. -21 D. 21
Answer C 1 ounce = 1/16 of a pound Four ounces = 4/16 reduce by 4 = 1/4
Four ounces is what fraction of a pound? A. 1/3 B. 3/8 C. 1/4 D. 1/6
Answer A. First change all measurement to yards. We know 3 feet = 1 yard since were dealing with cubic yards we cube the transfer 9 feet = 3 yards. 6 inches = 1/6 yards Since its 12 ft by 6 feet lets get the area. 1) 12 x 9 = 108 ft^2 Convert to yards 2) 108/9 = 12 yards Now with the inches we divide 6 inches = 1/6 yards 12 x 1/6 = 12/6 which is 2 cubic yards answer A.
How many cubic yards of concrete are needed to make a cement floor that is 9 feet by 12 feet by 6 inches thick? A. 2 cubic yards B. 18 cubic yards C. 54 cubic yards D. 648 cubic yards
D. 2.5 L Remember we are looking for 2% of some amount of water that will give us the solution we need. Hence why the 5% does not have the x. 1) Use the equation (5%) (1) = (2%) x or (0.05)(1) = (0.02) x 2) Solve for X 3) x = 2.5L which is D.
How much water must be added to 1 liter of a 5% saline solution to get a 2% saline solution? A. 1 L B. 1.5 L C. 2 L D. 2.5 L
Answer D. 40% = x/30 .4 = x/30 -isolate the x x = .4 x 30 4 x 30 = 120 go back 1 X = 12 which is answer D.
If 40 percent is equal to the fraction x/30, what is the value of X? A. 0.4 B. 15 C. 1,200 D. 12
A. 0 f(x²) = 144 1) x² = 144 - square root both sides 2) x = 12 3) plug in 12 back to the equation. 4) 1/4 x 12 - 3 5)12/4 - 3 6) 3-3= 0 which is A.
If f(x²) = (1/4)x-3, what is the value of f(144)? A. 0 B. 1 C. 4 D. 8
Every right triangle contains an angle of 90 degrees. This particular right triangle also has an angle of 30 degrees. To find the third angle, subtract the sum of these two angles by 180 degrees. 1) 90+30 = 120 2) 180 -120 = 60 degrees. The other 2 angles are 60 and 90 which is C.
If one of the angles of a right triangle is 30 degrees, what are the other 2 angles. A. 30 degrees, 120 degrees B. 60 degrees, 45 degrees C. 60 degrees, 90 degrees D. 45 degrees, 90 degrees
D. 27 (a/b)/c = a/(b×c) a/(b/c) = (a×c)/b 1) 2/(1/3) = (2×3)/1 = 6 2) (8/9)/4 = 8/ (9×4) = 8/36 3) 6 ÷ 8/36 4) 6/1 x 36/8 = 27
If p = 1/3 and q =8/9, then which is equal to 2/p ÷ q/4? A. 21 B. 23 C. 25 D. 27
Answer B. Well we need to know what times 28% will give us 42 pages. We can right the problem like this. 1) 28%x = 42, solve for x 2) x = 42/28% 3) x = 42/.28 - make whole 4) x = 4200/28 = 150
Katherine has a written 42 pages of her doctorate thesis. If she has written 28% of her doctorate thesis, how many pages will her finished thesis be? A. 70 pages B. 150 pages C. 162 pages D. 1,175 pages
Answer B When it says to 36th means the denominator will be 36. For 9 to get to 36 we need to multiply by 4. What we do to the bottom we do to the top. So 5x4 = 20 20/36 will be your answer. Which is B.
Raise 5/9 to 36ths. A. 18/36 B. 20/36 C. 24/36 D. 30/36
Answer A. First find how mnay ounces of the original mixture were fruit juice. 1) 10 x 20% = 10 x .2 = 2 ounces Next find the total number of ounces in the new mixture 2) 10+40 = 50 ounces Then find what part of the new mixture is fruit juice, and convert it to a percentage. 3) 2/50 = 0.04 convert to percentage 4% which is A.
Ten ounces of liquid contain 20 percent fruit juice and 80 percent water. The mixture is diluted by adding 40 additional ounces of water. What is the percentage of fruit juice in the new solution? A. 4% B. 10% C. 20% D. 40%
Answer B. The product of all integers from 1 to x is called the x factorial. The product of all numbers from 1 to 5 is 5 factorial. Thus, 5 x 4 x 3 x 2 x 1 = 120 which is answer B.
The expression "5 factorial" equals A. 125 B. 120 C. 25 D. 10
Answer B. The perimeter of a rectangle is the sum of its four sides. If x equals its width, then x +3 equals the length. (The length is 3 inches more than the width.) From this, you can write an equation to find the perimeter. Use the formula for perimeter. 2L+2W = P 1) x+x+(x+3)+(x+3) = 38 2) x+x+x+x+3+3 = 38 3) 4x+3+3 = 38 4) 4x+6 = 38 - solve for x 5) 4x = 38-6 6) 4x=32 7)x = 8 (inches) which is B.
The perimeter of a rectangle is 38 inches. If the length is 3 inches more than the width, find the width. A. 17 (1/2) inches B. 8 inches C. 11 inches D. 14 (1/2) inches
Answer C. The formula for the area of a circle is pie x r^2. Find the area of the larger circle first. 1) pi x 10^2 = 100 pi Find the rea of the smaller circle 2) pi x 7^2 = 49 pi To find the part of the larger circle that the smaller oen doesn't touch, subtract the two areas. 100-49 =51 pi square inches which is C.
Two circles have the same center. If their radii are 7 inches and 10 inches, find the area that is part of the larger circle but not the smaller one. A. 3 square inches B. 17 square inches C. 51 pi inches D. 70 pi square inches
B. 0.78
What is 0.7849 rounded to the nearest hundredth? A. 0.8 B. 0.78 C. 0.785 D. 0.79
Answer B. Well 10% of 60 is just 6 is 12% would be a bit more than that and the only option that leaves is B. Long way would be to do 60/1 x 12/100 -reduce by 10 6/1 x 12/10 - reduce by 2 3/1 x 12/5 = 36/5 = 7.2 but do note this takes more time and we can't afford that in the test.
What is 12% of 60? A. 5 B. 7.2 C. 50 D. 72
C. 16.9 First make the mixed into an improper fraction. 5 1/5% = 26/5% Now in order to get form fraction to decimal we multiply by 1/100 26/5 x 1/100 = 26/500 26/500 = 0.052 - make whole = 52 three steps. Now compute. 325 x 52 = 16900 - go back 3 times. 16.9
What is 5 1/5% of 325? A. 1.69 B. 169 C. 16.9 D. 32.5
A. 6√3 1) We can simplify √12 to √ 2² x 3 2) Since 2² is by 3 we can rewrite this whole problem. 3(2√3) 3) Distribute the 3 and just multiply 3 to the 2. 4) We are left with 6√3 which is A.
What is another way to write 3√12 A. 6√3 B. 3√4 C. 12√3 D. 12
B. 1/2 0.125 = 1/8 Remember cube root means what times itself 3 times will get you the number inside. Cube root of 1/8 is cube root of 1/ cube root of 8 Cube root of 1 = 1 Cube root of 8 = 2 x 2 x2 = 2 Answer 1/2
What is the cube root of 0.125? A. 5/2 B. 1/2 C. 1/4 D. 3/2
Answer B We know 4/8 reduced will be 1/2 or .5 1/4 is .25 Half of that 1/8 will be .125 Lets add both .5 and .125 giving us 0.625 which is B.
What is the decimal value of 5/8? A. 0.56 B. 0.625 C. 0.8 D. 0.835
B. (5,6) Midpoint formula: (x1+x2/2, y1+y2/2) 1) (2+8/2), (3+9/2) 2) 10/2 = x = 5, 12/2 = y= 6 3) (5,6) which is B.
What is the mid point of the joining line segment between P(2,3) and Q (8,9)? A. (3,7) B. (5,6) C. (2,8) D. (4,6)
Answer C. Remember FOIL First, outer, inner, Last (a+b) x (c+d) = ac+ad+bc+bd It should all come out to get C.
What is the product of (a-5) and (a+3) A. a^2-15 B. a^2 +2a -15 C. a^2 -2a-15 D. a^2 -2
C. 5x^2+7x-8 Remember it says subtracting from the whole. Thus, 1) 8x^2 +2x -9 - (3x^2 - 5x -1) 2) Distribute the negative 3) 8x^2 +2x -9 - 3x^2 + 5x + 1 -- combine like terms 4) C. 5x^2+7x-8
What is the result of subtracting 3x^2 - 5x -1 from 8x^2 +2x -9 A. 5x^2-3x-10 B. -5x-3x-10 C. 5x^2+7x-8 D. -5x^2-7x+8
C. -3 Slope intercept form: y=mx+b m = -3
What is the slope of the line y = -3x+1? A. 8 B. 3 C. -3 D. 8
A: First, the distributive property must be used on the left side. This results in 3x + 6 = 14x -5. The addition property is then used to add 5 to both sides, and then to subtract 3x from both sides, resulting in 11 = 11x. Finally, the multiplication property is used to divide each side by 11. Therefore, x = 1 is the solution.
What is the solution?
B: The slopes of perpendicular lines are negative reciprocals, meaning their product is equal to -1. The slope of the line given needs to be found. Its equivalent form in slope-intercept form is y = -4/7x + 23, so its slope is -4/7, The negative reciprocal of this number is 7/4, only line in the options given with this same slope is y = 7/4x -12.
What is the solution?
C: By switching from a radical expression to rational exponents, ⁴√x⁶ = x^6/4 = x^3/2. Also, properties of exponents can be used to simplify x/x³ into x¹⁻² = x⁻² = 1/x².The other terms can be left alone, resulting in an equivalent expression x^3/2 - 1/x² + x - 2.
What is the solution?
D: First, like terms are collected to obtain 12 - 5x = -5x + 12. Then, the addition principle is used to move the terms with the variable, so 5x is added to both sides and the mathematical statement 12 = 12 is obtained. This is always true; therefore, all real numbers satisfy the original equation.
What is the solution?
D: The exponential rules (ab)^m =(a^m)(b^m) and (a^m)^n = a^(m)(n) can be used to rewrite the expression as
What is the solution?
E: The conversion between feet and centimeters requires a middle term. As there are 2.54 centimeters in 1 inch, the conversion between inches and feet must be found. As there are 12 inches in a foot, the fractions can be set up as follows: 3ft x 12in/1tft x 2.54cm/1in The feet and inches cancel out to leave only centimeters for the answer. The numbers are calculated across the top and bottom to yield: (3x12x2.5)/(1x1) =91.44 The number and units used together form the answer of 91.44 cm.
What is the solution?
E: The distributive property is used on both sides to obtain 4x + 20 + 6 = 4x + 6. Then, like terms are collected on the left, resulting in 4x + 26 = 4x + 6. Next, the addition principle is used to subtract 4x from both sides, and this results in the false statement 26 = 6. Therefore, there is no solution.
What is the solution?
E: Using Descartes' Rule of Signs, count the number of sign changes in coefficients in the polynomial. This results in the number of possible positive zeros. The coefficients are 1, -3, 2, 1, and -3, so the sign changes from 1 to -3, -3 to 2, and 1 to -3, a total of 3 times. Therefore, there are at most 3 positive zeros.
What is the solution?
A. 36 | | = Means that anything inside will be positive. Ex. | -7 | = 7 | x | = 7 , x = 7 and x = -7 Thus 1) z-18 = 5 and z-18 = -5 "we must add the sum of all possible values" as stated in the question. 2) Solve for z for both problems. 3) x-18 = 5 = x = 23 4) z-18 = -5 = x = 13 5) 23 + 13 = 36 which is A.
What is the sum of all possible values of z in the following equation? |z-18| = 5 A. 36 B. 38 C. 40 D. 48
C. 5√3 1) √12 = 4 x 3= √4 = 2 2 √3 2) √27 = 9 x 3 = √9 = 3 3√3 2√3 + 3√3 = 5√3 which is C.
What value is equal to √12 + √27 ? A. 3√3 B. 4√3 C. 5√3 D. 6√3
Use the formula Substitute 20 degrees 1) (9/5 x 20) + 32 2) 36+32 = 68 degrees
When the temperature is 20 degrees C, what is it on the Fahrenheit (F) scale? Use the following formula: F = (9/5 x C) + 32 A. 93 (3/5) degrees B. 78 degrees C. 62 (3/5) degrees D. 68 degrees
Answer D -1/2 is -0.5 not as small as -1 so this one is ruled out. -1 can be answer 0 are not choices at all. -7/6 is more than one. 7 is more than 6 is the number will be greater. Since its negative this one is the smallest.
Which has the smallest value A. -1/2 B. -1 C. 0 D. -7/6
Answer C. A prime number is a number larger than 1 that has only itself and 1 as factors. (It can be evenly divided only by itself and by 1) 201 is divisible by 3 205 is divisible by 5 214 is divisible by 2 211 is only divisible by itself and 1 so this is the answer.
Which of the following is the smallest prime number greater than 200? A. 201 B. 205 C. 211 D. 214
A. 1 1) If the bases are equal. The exponents must also be equal. 2) 5 x 5 = 25 x5 = 125 x 5 =625 3) So that's 5⁴ 4) 5ⁿ⁺³ = 5⁴ 5) x = 1 so that we can get 5⁴.
Which one is the solution of the equation below? 5ⁿ⁺³ = 625 A. 1 B. 2 C. 3 D. 4
D. -2 1) First thing is FOIL the left side of the problem. 2) (-x-3)(-x-2) = x²+5x+6 = -4-2x 3) Make the problem equal to 0 so lets get everything on the left side. 4) add 4 to the left and add 2x to the left. 5) x²+7x+10=0 6) Factor. Find what numbers multiplied together get you 10 but when added get you 7. It will be 2 and 5 7) (x+2)(x+5)=0 8) Have each set equal to 0 9) x+2 = 0. x = -2 10) x+5=0, x = -5 11) X is either -2 or -5. Only answer with that is D.
Which one is the solution to the equation below? (-x-3)(-x-2)=-4-2x A. -1 B. 2 C. 3 D. -2 E. 5
