welcome to the GED math 2024 test preparation video from Ultimate ged.com in this video we'll be looking at how to easily solve 50 of the most important GED math questions from experience of helping thousands of test takers to pass the GED with ease we've noticed that the best way by a far margin to prepare for the GED is to use standard gedd test questions so let's Dive Right In question one which of the following algebraic expressions is represented by the product of seven and a number increased by 5 is 30 to pass the GED math you have to know how to translate from word to mathematical Expressions this will help you solve a lot of word problems we will just solve this and add a link in the description to a complete free lesson and a downloadable sheet on translations of expression please check it out let's translate it the product of seven and a number here product implies multiplication if we let a number be represented by a variable say x this part of the phrase translates to 7 * x 7 * X is the same as 7 x increased by five increased by implies addition so we add five to it is 30 is in mathematical Expressions implies equality so is 30 means equals 30 therefore the correct answer is a 7 x + 5 = 30 question 2 on a coordinate plane plot the following Four Points a -4 -3 b42 C 52 and D 5 -3 after plotting these points connect them in the order a to B B to C C to D and D to a to form a figure what is the figure formed to answer this question you have to know how to plot points on the coordinate plane and also identify shapes let's start by plotting our points we know that on a point notation the first value is your x value and the second value is your y value so for a -4 -3 the x value is -4 and the Y value is -3 so this is our point for B -42 the x value is -4 and the Y value is two so this is our point for C 52 the x value is five and the Y value is two so this is our point and for D 5 -3 the x value is 5 and the Y value is -3 so this is our point we are told to connect the points in the order a to B B to C C to D and D to a after connecting the points we will notice that opposite sides are parallel and equal and the angles are at 90° so this is a rectangle before we look at our next question we want you to know that we have a lot of resources at ultimate ged.com to help you pass the GED we have more free videos a complete GED math course this is a step-by-step course from the absolute beginning to advanced level we have a social group you can talk to people that have taken the GED or are working on taking the GED get more at ultimate ged.com and pass the GED with ease question three find the volume of a cylinder that has a diameter of 12 ft and a height of 15 ft a lot of the GED geometry questions are just formula work all the formulas will be given to you on the G GED formula sheet so no need to memorize it it is good to be familiar with them however because they can increase your speed the formula for finding the volume of a cylinder is pi r^ 2 H where R is the radius and H is the height to solve this question we need to know the value of pi which is given to us on the GED formula sheet as 3.14 we need to know the value of height H which has been given to us as 15 then finally we need to know the value of the radius R which has not been given to us we were given the diameter but we know that the radius is diameter divided by 2 so we divide 12 by 2 to get six as our radius so we have the volume to be Pi which is 3.14 * 6^ 2 * 15 we input this into our calculator and get the volume of the cylinder to be 1 , 695.2rpm a cylinder so you can replace the word barrel with cylinder second you have to know that volume of the cylinder will be the same as the volume of the oil that will be put into it without spilling once you know these two things you'll go through the exact same process to get the volume of the oil as 1, 16956 ft cubed find the slope and Y intercept of the line line Y = -3x + 5 slope questions are now very common on the GED math almost everyone gets something on slopes for this question you'll use the formula for the slope intercept form of the equation of a line which is y = mx + b this will be given on the GED formula sheet so you don't have to memorize it but being familiar with it can help with your speed in this form the slope is the m this is the coefficient of the x or simply put what is with the X so here the -3 which is the coefficient of the x is our slope the Y intercept is the B this is the constant or simply put what is without the X so here the five will be our Y intercept slope is -3 Y intercept is five pretty straightforward once you know the formula we will look at some twist to this this question later on in this video please encourage us to post more videos by liking sharing and subscribing we really appreciate it question five a singer borrows $5,000 for 2 years at 4% per anom simple interest what is the interest the singer will pay at the end of the term simple interest questions are basically formula work and the formula will be given to you on the GED formula sheet simple interest equals the principal time the rate time the time we just substitute our values into the formula and solve here the principal is $5,000 the rate is 4% we convert it to the decimal form 4% is 4 ided 100 this is the same as 0.04 so we multiply this by 0.04 the time is 2 years so we have times two we compute this on the calculator 5,000 * 0.04 * 2 to get 400 so the interest the singer will pay is $400 hope you've noticed that we keep mentioning the GED formula sheet it's something you have to be familiar with before taking the test you can check ultimate g.com for more on that question six find the number of years needed to pay $6,000 with an interest of $360 if the interest rate is 3% perom for every formula you are given you can be asked to find any of the values in that formula you can be asked to find the rate principal interest or time here we are supposed to find time we know our principal is $6,000 our interest is $360 and our rate is 0.03 we divided the 3 by 100 to get the decimal form of 3% simple interest equals the principal times the rate times the time as we saw in the previous question we have 360 equal 6,000 * 0.03 * T we solve for T since the 6,000 * 0.03 are multiplying we can divide both sides by it this will cancel out we can now compute this side with our calculator 360 / 6,000 * 0.03 this will give us T equals 2 meaning the time is 2 years question 7 find the slope of the line the slope of a line is the change in y over the change in X the change in y simply means how many points you are going up or down if you are going up then you have a positive change if you are going down then you have a negative change the change in X simply means how many points you are going to the right or left if you are going to the right then you have a positive change if you are going to the left then you have a negative change take a moment and let this sink in it is the basis of most of the things we will be doing with slopes and graphs let's look at our question our first step will be to choose any two point points on the line I am choosing these two points let me call them A and B you can choose any two points on the line however it is important to choose points that will make your work easier choose points whose X and Y values can be easily determined normally points at the corners are best any of these points would have worked well also now to find the slope all we are doing is moving from one point of the line to the other on the slope triangle let's move from B to a we moved down two points notice moving down is negative so we have -2 here then we will move to the left one to get to a notice that moving to the left is negative we have 1 here -2 over- 1 is simply 2 so our slope is 2 we could have also moved from A to B let's look at it we have our slope triangle here we move two points up moving up is positive so we have two then we will move to the right one moving to the right is positive so we have one 2 over 1 is the same as two we notice that we got the same answer there are other things you can do but I don't want to get you confused with that notice that our first movement is always change in y that is moving up or down then our second movement is change in X that is moving left or right question 8 in order to ship 2,500 gallons of a product to another country Stan shipping company had to package the gallons into boxes if they had 20 packaged boxes and 100 gallons left that are not in boxes how many gallons were in a box this kind of two-step equation word problem is very common on the G Ed we are first going to solve it in details for teaching purpose then I'll show you how you can solve it in less than 10 seconds on an actual GED test you have three values in these type of questions let's write them down we have 2,500 gallons we have 20 boxes and finally we have 100 gallons the 2,500 gallons represents the total so we have equals 2,500 the 20 boxes is what I call the group The gallons have been grouped into boxes for most questions the group can also be identified as the number that represents something different from the other two numbers so here 2,500 represents gallons the 100 also represent gallons but the 20 represent boxes so the 20 will be the group the group is the one with the X so we will have 20x we can now add the 100 Gall left to the equation and solve for the X in this two-step equation subtract 100 from both sides these will cancel out 2,500 minus 100 will be 2,400 we now have 20x = 2,400 divide both sides by 20 the 20 will cancel out 2,400 / 20 will be 120 this means there were 120 gallons in each box the hard part of this question is to be able to pull out the values from the word problem let's look at how you can speed up solving this question first there's absolutely no reason to write this part if you know what you're doing you can go straight to writing your two-step equations we have our group 20x our other + 100 and our total 2,500 then you can solve the two-step equation an even faster method to solve this question in less than 10 seconds is to do 2500 minus 100 divided by 20 on your calculator to get 120 we did the total minus other divided by the group a big caution when using fast methods is to note that they are very specific to specific questions and little twist to the question can let you get it wrong so when in doubt use the longer methods question 9 simplify the algebraic expression 4x^2 - 5x + 3 - the quantity 2x^2 - 4x + 1 simplifying and expanding are very common on the Note calculator section of the GED so it's important you are familiar with them to solve this we will first distribute the negative sign in front of the parentheses a negative sign in front of parenthesis affects all the terms in the parenthesis when we distribute the negative sign it changes each sign inside the parentheses the term 2x^2 becomes -2 x^2 -4x becomes POS 4X because a negative * a negative is a positive and + 1 becomes minus one after distribution the expression becomes 4x^2 - 5x + 3 - 2x^2 + 4x - 1 next we combine like terms combine the x^2 terms 4x^2 - 2x^2 = 2x2 combine the X terms - 5x + 4x = --1x or simply - x combine the constant terms 3 - 1 = 2 so after simplifying the expression is 2x^2 - x + 2 question 10 find the length of the side marked X when you see this mark on a triangle it means it's a right triangle right triangles have this angle being 90° when you have a right triangle you can use the Pythagoras Theorem to find the sides this formula will be given to you on the GED hypotenuse which is the long side squar equal a 2 + b^ 2 where A and B are the two other sides here the long side or hypotenuse is what we are finding so we have x^2 = 4^2 + 3 2 4 2 is 16 and 3^ 2 is 9 we add them 16 + 9 is 25 to find X we will find the square root of both sides this will cancel out square T of 25 is 5 therefore x equal 5 please note that most questions can be converted to word problems let's look at a word problem similar to this question 11 a pole which is 4T tall casts a shadow 3 ft on the ground what is the distance from the top of the pole to the end of The Shadow it casts when it come to solving geometry word problems your diagram is one of the most important things let's get a diagram so so this is our pole which is 4 ft this is the shadow at Cass which is 3 ft we are supposed to find the distance from the top of the pole to the end of The Shadow let's call this x we see that we have formed a right triangle now this question is just like the previous you can try it out yourself we can use the Pythagoras Theorem to solve it this formula will be given to you on the GED the hypotenuse which is the long side 2 = a^2 + b^2 here the long side or hypotenuse is what we are finding so we have x^2 = 4 2 + 3^ 2 4 2 is 16 and 32 is 9 we add them 16 + 9 is 25 to find X we will find the square root of both sides this will cancel out square < TK of 25 is 5 therefore x equal 5 so the distance from the top of the pole to the end of The Shadow is 5 ft question 12 find the mean mode and median of Four 3 4 5 7 4 and 8 finding the mean is the same as finding the average we will add all the values and divide it by the number of values there are seven values here so we will have 4 + 3 + 4 + 5 + 7 + 4 + 8 divided by the number of values which we know is 7 adding this we will have 35 over 7 35 / 7 is 5 therefore the mean is five the mode is the item with the highest frequency here there are more fours than any other number so four is the mode the median is the middle number to find the med median we first have to arrange the numbers so we have 3 4 4 4 5 7 and 8 here the median will be four it's the number in the middle please note that if you have an even number of values you'll add the two middle numbers and divide it by two please let us know if you have questions on this part question 13 in order to graduate Michael has to make an average score of at least 90 if he made 95 and 94 on his first two tests what should his minimum score be in his final test in order to graduate this is an average or mean question to find the average we need to add all the scores divided by the number of tests taken we've been given the average he must get which is 90 so we can put it here now we also know the number of tests he is taking he's taken two and there's one more left so VI's taken a total of three tests so we can put it here we know what goes at the top is the sum of the tests two of them have been given we have 95 as the first score plus 94 as the second score we don't know the third score so we will represent it by X and solve for x please learn this set up it's quite common on the GED okay let's solve it since the three is dividing we can multiply both sides by three this three will cancel out 90 * 3 is 270 now let's add this 94 + 95 is 189 we have a onstep equation since the 189 is adding we can subtract 189 from both sides this will cancel out 270 - 189 is 81 so Michael must get a minimum score of 81 to graduate there are other ways we could have solved this but we chose this method because it helps you solve any average or mean question no matter the twist find the slope of a line that passes through the points 2 4 and the point 65 to find the slope of a line given two points we will use the slope formula M = Y2 - y1 1 over X2 - X1 formulas are given on the GED so don't worry too much about it please note that you can call any of the point one or two I'm choosing this as one and this as two we know that when you have a point the first value is your X and the second value is your y since we are calling this point one we will have X1 y1 here same thing for this since we are calling this our Point 2 we can call this X x 2 Y 2 we just put the values into the formula we have 5 which is Y2 - 4 which is y1 divided by 6 which is X2 - 2 which is X1 we simplify 5 - 4 is 1 over 6 - 2 which is 4 so the slope is 1 over 4 question 15 the slope of a line is 2 2 which of the lines will be parallel to it a y = 3x + 2 b y = 2x + 3 c y = x + 2 d y = -1 4x + 3 lines with the same slope are parallel since the slope of the line is two we are basically looking for the answer which also has slope of two all the answers are in the slope intercept form of the equation equation of a line that is y = mx + b we know that in this form the coefficient of the x or simply put what is with the x is the slope Choice B has the coefficient of the X to be two that means it has the same slope of two as the question therefore it's parallel let's look at our question 16 here we are supposed to solve for x given this rectangle we know that perimeter simply means adding all the sides we know this is a rectangle so opposite sides have the same size this place will also be 2x + 3 this will be 3x + 7 now we can add all these parts and it must be equal to the perimeter 50 we have 3x + 7 + 2 x + 3 + 3 x + 7 + 2 x + 3 this is equal to 5050 we can add all the X terms 3x + 2 x + 3 x + 2x this will give us 10 x we can add the numbers 7 + 3 + 7 + 3 this will give us 20 we have a two-step equation here which you should be very familiar with how to solve you can check out our video on equations if you need help subtract 20 from both sides the 20 will cancel out 15 - 20 is 30 now we have 10 x = 30 we can divide both sides by 10 the 10 will cancel out 30 / 10 is 3 so we have x = three question 17 we want to multiply the polinomial 2x + 3 and 2x - 4 we multiply each term in the second parenthesis by the terms in the first so 2x will multiply 2x to get 4x^2 then 2x will multiply -4 to give us -8x next we will multiply by the 3 3 * 2x is 6X 3 * -4 is -12 please note that the method we used is what is commonly known as the foil method I'm personally not a fun of most acronyms in Mass they bring little benefits and can actually cause you to get questions wrong next we check if there are like terms we can add or subtract we can add -8x and 6X to get -2X so our final answer is 4x^2 - 2x -2 question 18 find 20% of 300 there are three good methods for solving questions like this please watch our other videos to see other ways of solving it and pick the one that's best for you we will use the proportion method for this method we will put our is value here we will put our of value here we will put our percent value here then 100 here for this question we have 20% so we put 20 for our percent value we have of 300 so the 300 is our of value we will put it here we have 100 here which is constant now we have our a value left so we can represent by X and solve for x this is a one-step equation since the 300 is dividing we will perform the opposite operation on both sides of the equation we will multiply both sides by 300 the 300 will cancel out we simplify this part 300 / 100 is 3 we have 20 * 3 which is 60 therefore x = 60 so 60 is 20% of 300 we can see that once you can set it up it takes a little algebra and basic math to get the answer the only problem I see is when the question is phrased like what is 20% of 300 students get confused if the 20 is an es value or a percent value numbers with percentage symbols are always the percent value irrespective of where they placed so this question is exactly like what we just solved let's look at another example question 18b 30% of what number is 15 we are using the same method as the question 18 please watch our other videos for other methods for this method we have our as value year we have our off value here we have our percent value here and then 100 here now let's look at our question we just replace the values let's write our 100 here first we know it's constant we can write the 30 here because it's our percent value we have is 15 so we write 15 as our is value finally we have off but there's no number with it we represent it by X and solve for x since the X is in the denominator your first step will be to cross multiply so we have x * 30 this will give us 30X then we have 15 * 100 this is 1,500 now we have a one-step equation the 30 is multiplying so we will divide both sides by 30 the 30 will cancel out 1,500 / 30 is 50 therefore x = 50 meaning 30% of of 50 is 15 please I cannot overstress the importance of knowing how to solve these kind of percentage problems you have to master it graph the inequality X greater than4 let's bring our number line when graphing inequalities the first thing is to locate your point which will be the number here it is -4 then you'll draw a shaded or unshaded Circle at the point if you have less than or greater than then the circle will not be shaded if you have less than or equal to or greater than or equal to you will use the Shaded Circle so basically if it has an equal to you will shade in this case since it's just greater than we will not shade the circle then finally we draw an arrow the easiest way to get this always right without thinking is to make sure your inequality is in the form variable inequality sign and then the number in that form the direction of your arrow will be the same as the direction of the inequality sign here since this is in that form we will draw our Arrow facing here and we are done graph the inequality 2 greater or equal to X let's bring our number line we follow our steps we first locate our point in this case too we decide if it should be shaded Circle or not in this case it will be shaded because it's greater than or equal to we set it's shaded if there is equal to then finally we find out the direction of our Arrow we said if the inequality is in the form variable inequality sign and the number the direction of your arrow will be the same as the direction of the inequality sign this is not in the form so your arrow will face the opposite direction as the inequality here normally your arrow will face this way but now it will rather face this way so we will draw our Arrow here another way to look at inequalities in this form is to always convert it to the form variable inequality sign and the number if your brother is older than you it means that you are younger than your brother so if 2 is greater or equal to X then we can say that X is less or equal to 2 you can look at it as just a mirror image in this form we can easily notice the direction of the arrow we get exactly the same answer question 21 which line is perpendicular to y = 2x + 5 a y = 2x - 1 B Y = -2x + 5 c y = 3 4x + 5 d y = -1 / 2x + 1 the slope of a perpendicular line is the negative reciprocal of the slope of the original line the reciprocal of a number is basically flipping the numerator and denominator so 3 over 4 will be 4 over 3 here we know the slope of the question is two since this is in the slope intercept form of the equation of a line please revise question 14 and 15 if you have gotten the slope intercept form 2 is the same as 2 over 1 the reciprocal is 1/ 2 the negative reciprocal of 2 is therefore -1 /2 we are looking for the answer which has a slope of -1 /2 Choice D has the coefficient of the X to be -1 over2 that means Choice D has a slope of -1 / 2 this is the negative reciprocal of the slope 2 in the question therefore or it's perpendicular the product of two consecutive integers is 30 find the two numbers this is a question that you can easily solve without using any mathematical methods consecutive integers are simply numbers that follow each other so 3 4 5 6 are consecutive integers 25 and 26 are also consecutive integers I'm sure you get the point so we are looking for two numbers that multiply to get 30 the two numbers must also follow each other the two numbers are five and six 5 * 6 is 30 pretty straightforward if you know your multiplication table question 23 the product of two consecutive integers is 30 if the smaller number is X write an equation to find the value this is the same as question 22 just harder the GED is now having more questions questions in which the answers are not actual values but an expression a function or an equation this is a typical example we know that consecutive integers are numbers that follow each other for consecutive integers if the smaller number is X then the next number will be x + 1 so if x is 2 then the next number will be 2 + 1 which is equal to three product means multiplication so we have the smaller number X * the next number x + 1 to be equal to 30 we can expand this we have x * X this will give x^2 then we have x * 1 which is 1 X or simply X so the equation is x^2 + x = 30 find the area of the figure below use Pi = 3.14 the work here is to be able to identify that you can break this into multiple shapes find the area of each shape and add the areas for this figure we can draw a line here so that we have a rectangle a and a semicircle B area of a rectangle is length time width this formula is given on the GED formula sheet we know the length as 12 in and the width as 5 in we multiply it to get 60 in squared next we have to to find the area of the semicircle the area of a circle is < R 2 this formula is also provided on the G so the area of a semicircle or half a circle will be p piun r^ 2 / 2 we don't know R we know that since this is a rectangle if this side is 5 in it means this side will also be 5 in this means the diameter of the circle is five the radius of a circle is half the diam diameter so we divide the 5 by 2 to get 2.5 as the radius now we find the area of the semicircle Pi which has been given as 3.14 * 2.52 / 2 we compute it on the calculator to get 98125 in squared finally we add the area of the two shapes we have 60 + 9. 8125 this will give us 69. 8125 in squar as the area to two decimal places will be 69.81 in squared please questions here can be in any form break them into multiple shapes find the measurements you need to find the area of each shape then combine the shapes what function represents the information in the table a f ofx = 2x + 1 b f ofx = x - 3 c f ofx = x + 3 D FX = 3x - 3 here the best way is to solve it from the answers we input the X values into the various functions and see if we will get our f of x values for teaching purpose we are going through everything you don't have to on the test you can accurately eyeball and eliminate obvious wrong choices since it's easy to work with zero I'll try that first so I can narrow the possible answers replace x with 0 for Choice a 2 * 0 + 1 = 1 it was supposed to be -3 so Choice a is definitely wrong replace X in Choice B with 0 0 - 3 = -3 so Choice B is a possible answer now replace x with one in Choice B to confirm 1 - 3 = -2 it was supposed to be zero so Choice B is wrong replace X in Choice C with 0 0 + 3 = 3 it was supposed to be -3 so Choice C is wrong so since choice a to c are wrong it means Choice D will be the answer let's confirm let's replace x with 0 we have 3 * 0 - 3 = = -3 as expected we try 1 we have 3 * 1 - 3 = 0 as expected then we try two we have 3 * 2 - 3 = 3 as expected so D is definitely the answer a bus can take 12 students for a trip how many such buses are needed to take 235 students for a school field trip this is a straightforward division question all you have to do to find the number buses needed is to divide 235 by 12 you compute this on the calculator to get that's why we simply use division but the right way to solve questions like this especially if complexities are introduced is to use proportion setting up proportions is one of the most important word problem skills on the GED for this we will have buses is to student one bus took 12 students X buses will take 235 students we solve for x we first cross multiply 12 * X is 12 x 1 * 235 is 235 next we can find the X by dividing both sides by 12 the 12 will cancel out 235 / 12 is hikes at the same rate how many hours will she spend hiking 15 miles this is a typical proportion question please note that on the geds you can have questions with lots of unnecessary reading this same question could have been faith wants to be the most athletic student in her school to achieve that she spends 3 hours hiking six miles on Mondays if she decides to hike for 15 mil to maximize her strength how many hours will she need to achieve that that assuming she hikes at the same rate okay let's solve it we have our hours here and Miles here 3 is to six since we know the miles 15 we'll put it here since we don't know the hours or the hours is what the question is asking for we will represent with X and solve for x we cross multiply 6 * X is 6 x 3 * 15 is 45 we will now divide both sides by six the six will cancel out 45 / 6 is 7.5 this is 7.5 hours which is the same as 7 hours 30 minutes which of the following is a point on the line y = 2x - 7 a 25 B 3 1 C 4 -3 D -22 two we know that for a point the first value is your x value and the second value is your y value if a point lies on this line then when you input the x value into the equation of the line you should get the corresponding y value so we start with option A we replace the X with 2 we have 2 * 2 - 7 This Is ne-3 It was supposed to be five so Choice a is wrong let's try Choice B we replace the X with 3 we have 2 * 3 - 7 this will give us - 1 which is what we expected so Choice B is the answer the following graph represents the score range of students in a math class how many students are in the class being able to read and interpret graphs is a must on the GED here here the x- axis represents the score range and the Y AIS represents the number of students whose score are within that range from the graph you'll notice that there are three students whose score ranged from 61 to 70 from the graph there are five students whose score ranged from 71 to 80 from the graph there are four students whose score ranged from 81 to 90 from the graph there are two students whose score ranged from 9 1 to 100 we add these to get the number of students 3 + 5 + 4 + 2 = 14 therefore there are 14 students in the class question 30 the following graph represents the score range of students in a math class what percentage of students failed the test if the passing score is 71 please it's very important you master how to find percentages especially from graphs from the graph we can see that three students scored 61 to 70 all the other students scored 71 or above percentage of students that failed will be the number of students that failed which is three over the total number of students which is 14 like we saw in question 29 this will be multiplied by 100 to get the percentage compute this on the calculator to get 21.43% failed with what you just learned you should be able to answer questions like what percentage of students passed and what percentage of students scored 71 to 80 question 31 the following graph represents the score range of students in a math class how many students scored exactly 95 this a trick question most students assume that the answer is to students since the 95 is within this range 91 to 100 this is wrong a range doesn't tell you the exact values within the range so the two students who scored between 91 and 100 could have scored 92 and 92 or 95 and 98 or 100 and 100 so the answer is there's not enough data or information to answer the question please watch out for a little trick question like this pay extra attention to your graphs question 32 convert 96 in to feet we are given our conversion factor as 1T equals 12 in we can use proportions to solve it like what we did in question 26 and 27 check out ultimate ged.com if you're interested in that method here we'll solve it in another way the best setup looks like this you'll first write down what you are converting in in this case 96 in then you'll bring your conversion factor you want to write it in a fraction form such that the inches will cancel out you basically want the bottom factor to be the same as the value you're converting so you can cancel here we will write 1T over 12 in the inches can cancel out we now have 96 * 1T over 12 this will give us 8 ft so 96 in is 8 ft let's take another example question 32b convert 6 ft to in we are given our conversion factor as 1T equal 12 in you'll first write down what you are converting in this case 6 ft then you'll bring your conversion factor you want to write it in a fraction form such that the feet will cancel out you basically want the bottom factor to be the same as the value you're converting so you can cancel here we will write 12 in over 1 ft the feet can cancel out we now have 6 * 12 in over 1 this will give us 72 in so 6 ft is 72 in convert 5 Y into in given the conversion factors 1 ft = 12 in and 1 yard = 3 ft you can have questions in which you must use multiple conversion factors here in order order to convert from yards to inches we have to convert from yards to feet first then we will convert from feet to inches let's look at it as usual we will write down what we are converting in this case 5 yards we multiply this by the converting Factor 3T over 1 yard the yard will cancel out 5 * 3 is 15 so we have 15 ft now we have to convert the 15 ft to inches we will multiply it by the conversion factor 12 in over 1 ft the feet will cancel out 15 * 12 is 180 so the 5 yards we started with is 180 in you could have done this entire conversion as one step by basically combining the two steps we just did we will start with the 5 yards then we will multiply it by the first conversion factor 3 ft over one yard The Yards will cancel out then we will multiply it by the second conversion factor 12 in over 1 ft the feet will cancel out we can see that we just have inches left we compute this on our calculator 5 * 3 * 12 this will give us 180 in as our answer find X in the diagram below the work here is being able to identify that this is angles on a straight line angles on a straight line adds up to 180° once you know that you will just add everything and equate it to 180 then solve the resulting equation so here we will add 75 + x + 20 + 25 = 180 we can add the numbers 75 + 20 + 25 to get 120 so we have x + 120 = 180 we can subtract 120 from both sides sides the 120 will cancel out 180 minus 120 is 60 so X is 60 find the measure of the angle below here the first thing you have to identify is that this is a right triangle because of this Mark here this means this angle is 90° we know that the sum of the interior angles of a triangle is 180° so we we can add 40 + 90+ B and this must be equal to 180 40 + 90 is 130 we have 130 + B = 180 one step equation subtract 130 from both sides to get b equal 50° there's a faster way to solve this but knowing how to solve it by adding everything and equating it to 180 is so important I don't want to even teach any other way this will ensure you get the answer correct no matter the twist what value of x will make the expression undefined 2x + 3 / x - 2 a x = 2 b x = -2 c x = 3 d x = -3 from this expression to be undefined the denominator must be zero you cannot have a zero denominator so we can say that x - 2 must be equal to Zer we solve for x add two to both sides of the equation the two will cancel out 0 + 2 is 2 so x = 2 therefore the correct answer is a find the angle X below you can have questions in which you'll need to use other properties of straight lines to get the interior angles of the triangle the two most common ones are vertical angles and angles on a straight line we've already done both in this question we can find angle B using the idea of vertical angles we know that vertical angles are equal so if this angle is 70° then the opposite angle B will also be 70° to find angle a we know that this is a straight angle angles on a straight line must be equal to 180° so if this is 120° then a will be 60° 60 + 120 is 180 now we add all our interior angles and equate it to 180 we have 70 + 60 + x = 180 I'm sure you can do this by now we solve it to get X = 50° there's another way we could have solved it once we knew the angle B is 70 in a triangle the exterior angle is equal to the sum of the two opposite interior angles so in this figure the exterior angle 120 is equal to the sum of the two opposite interior angle that's X and 70 so we can write 70 + x must be equal to 120 we solve for x to get X = 50° notice we got the same answer question 38 we are factoring the quadratic x^2 - 5x - 6 in question 17 we multiplied two binomials to get one trinomial the idea of factorization is basically reversing the process finding out what multiplied to get x^2 - 5x - 6 you will find two numbers that multiply to get the constant in this case the -6 the two numbers must also add up to get the coefficient of the X which is -5 this takes some trial and error and Depends mainly on how good your multiplication is the two numbers here will be -6 and 1 -6 * 1 will be -6 -6 + 1 will be -5 after finding these numbers all you'll do is to put them in parenthesis with the X and you are done so we have x - 6 and x + 1 this method Works only if there's no number in front of the X squ in math we say the coefficient of the x squ is one please check out ultimate g.com for other cases of factoring and factorizations here we are supposed to find the area of the green shaded portion questions like this is also very common the work here is to find the areas of the two shapes and subtract it we starts by finding in the area of the rectangle this is the length time the width so we will have 5 * 7 which is 35 next we find the area of the triangle we know that it's the base times the height over two the base is three and the height is four we have 3 * 4 / 2 this will give us 6 so the area of the Shaded portion will be 35 - 6 this will be 29 we are looking at a similar problem we want to find the area of the green shaded portion again all we have to do is to find the areas of the two shapes and subtract them here we have a circle of radius 5 inscribed in a square the formula for finding the area of a circle is piun * R 2 where R is the radius so we have 5^ 2 * piun this will give us 25 Pi the value of pi is approximately 3.14 so we have 25 * 3.14 which is 78.5 now we find the area of the square the area of a square is the length squared we have not been given the length but we can find it since this is the radius if we extend it to touch the other side of the square we will have the diameter the length of the diameter will be the same as the length of the square the diameter is 2 * radius which is 2 * 5 the diameter is therefore 10 so the length of the square is also 10 now we find the area the area will be 10 squared this will give us 100 finally we subtract the two areas to get the area of the Shaded portion we have 100 - 78.5 the area of the Shaded portion is therefore 21.5 question 41 calculate two exponent 3 * 16 do not use a calculator this was the first question on our GED math 2021 video and most students weren't able to solve it because they were not familiar with negative exponents so let's look at it here we'll be solving it two different ways method one this first method just requires that you know that 16 can be written as 2 exponent 4 2 exponent 4 is 2 * 2 * * 2 * 2 this is 16 once you know that then you can replace the 16 with two exponent 4 now we have 2 exponent -3 * 2 expon 4 in math if you have two numbers multiplying and the bases are the same you can simply add the exponent they both have the base of two so we can simply add the exponents so here we will have two exponent -3 + 4 -3 + 4 is is the same as 4 - 3 which is 1 so we have two exponent 1 any number exponent one is the same number so 2 exponent 1 is simply two this is our answer let's look at method two method two first we have to know that we can move a number with an exponent from the numerator to the denominator or denominator to numerator by changing the sign of of the exponent example if you have 2 * 7 expon -4 over 3 we can move the 7 exponent -4 from the numerator to the denominator if we do that we have to change the exponent -4 to exponent pos4 so we have 2 over 3 * 7 exponent pos4 the 7 exponent -4 in the numerator BEC 7 exponent pos4 in the denominator notice that there's this two in the numerator and three in the denominator if you are not given any values in either one or both you can use one this is not a necessary step it can serve as a guide let's go to our question we have two exponent -3 * 16 here we do not have a denominator so we can use one so we'll have 2 exponent -3 * 16 / 1 we know we can move the 2 exponent -3 to the denominator to become 2 exponent 3 3 notice that the exponent -3 became exponent POS 3 1 * 2 exponent 3 is simply 2 exponent 3 so we have 16 over 2 expon 3 2 expon 3 is 2 * 2 * 2 which is 8 we have 16 / 8 this will give us two as our final answer Burke's Home Store rents lawnmowers for $10 plus $6 per hour Jake paid $64 to rent the lawnmower for how many hours did he rent the lawnmower this is also another very common kind of twep geds word problem here all our three values are in dollars so you have to find the group in a different way I call it the revolving so again we will have our total here the total is $64 this is the total amount of money Jake paid for the lawnmower the group which we are calling calling the revolving is the value that keeps happening usually per day or per hour or each day or something like that is with it so here we have $6 per hour so this will be six we also know the group has the X finally we have what is left or the fixed value here it is $10 we can write the two-step equation for it we have 6 x + 10 = 64 we subtract 10 from both sides the 10 will cancel out 64 - 10 will be 54 so we have 6X = 54 next we will divide both sides by 6 this will cancel out 54 divided by 6 is 9 therefore x equal 9 so Jake rented the lawnmower for 9 hours please you don't have to write all these on the GED test we are using it for teaching purpose you can just identify your total fixed and revolving values and solve the resulting two-step equation also if you know what you're doing you could have solved this in less than 10 seconds input 64 - 10 / 6 on your calculator to get nine as the answer what we did was the total minus the fixed divided by the revolving we are supposed to calculate this without using a calculator let's bring our order of operations again we will perform the operations within the parenthesis first we notice that there's parenthesis within parenthesis in this case we will perform the inner one first so we have 3 + 2 to get 5 we now have parenthesis 28 - 5 * 5 all 2quared - 5 using the order of operations we have to perform the operation in parenthesis we'll notice that the operation in parenthesis also has multiple operations that's subtraction and multiplication we will use the order of operation to work that out we know we have to do multiplication before subtraction so we have 5 * 5 which is 25 then we have 28 Minus 25 which is 3 now all these has been simplified to three we now have 3 exponent 2 - 5 from the order of operations we will do the exponent next 3 exponent 2 is 9 we have 9 - 5 finally we'll do the subtraction 9 - 5 is 4 so we have four as our final answer a car travels at a speed of 60 MPH if it travels at that speed for 5 hours what will be the distance it has traveled the formula for finding distance is given on the GED formula sheet distance equals rate time time the rate is the same as the speed for this question it is 60 MPH the time is 5 hours we just put these values in the formula and solve distance equals 60 * 5 so the distance traveled will be 300 mil please you should be able to manipulate formulas to get different values in the formula you should be able to find the rate given the distance and time you should also be able to find the time given the distance and rate graph a line with Y intercept -3 and x intercept 6 we know the Y intercept is a point on the Y AIS this value is -3 we Loc at it and plot our point the x intercept is six we know that the x intercept is a point on the X AIS we locate our point six on the x axis and plot the point finally we draw a line through those two points and we are done in a class of 10 students seven are girls and the rest are boys the average height of the girls is 5 in and the average height of the boys is 6 in what is the average height of all the students in the class to find the average height of the whole class we must first find the total Heights of the girls and the boys first for the height of the girls we multiply the average height of the girls by the total number of girls in the class that is 7 times the average height of the girls 5 in which gives us 35 in now for the boys we do same to get the total number of boys in the class we have to subtract the number of girls in the class that is seven from the total number of students 10 which gives us three now three times the average height of Boys 6 in gives us 18 in now the average equals the total height over the number of students that is 35 in + 18 in all over 10 which gives us 53 over 10 that is 5.3 in write 887 mil 344,000 in scientific notation to have a scientific notation we want to move the decimal point behind the first nonzero digit in this case it will be behind the eight when you have a whole number or a number without a decimal point the decimal point is behind we have our decimal point here so we will move this point 1 2 3 4 5 6 7 points to the left to get it behind the 8 this is represented as 10 ^ 7 this is because we moved seven times to the left we write our 8.73 44 * 10 ^ 7 notice we left out the zeros in our answer this is how we write scientific notations we could have been required to round it up to one decimal place we learned that earlier so this will be 8.7 * 10 ^ 7 what is the equation of the line that passes through the point 0 -3 and has a slope of -2 for questions like this there are two simple ways of solving it we can use the slope intercept form of the equation of the line or the point slope form of the equation of the line since we've been given a point in a slope it is preferable to use the point slope form of the equation of the line the formula for the point slope slope form of the equation is given as y - y1 = M in parenthesis x - X1 please note that this formula will be provided on the GED from the question our X1 value is zero and our y1 value is -3 our slope m is -2 now we substitute the values into our equation and we have y - -3 = -2 into parentheses x - 0 y - -3 can also be written as y + 3 now we deal with the parenthesis -2 * X gives us - 2x and -2 * 0 is still 0 so we leave it we have y + 3 = -2X to make the Y stand alone we subtract 3 from both sides of the equation the ne -3 cancels out pos3 giving us Y = -2x - 3 so this is the equation of the line what is the value of the expression 3x² + 3x + 2 y when x = 4 and Y = 5 in this expression the value of x is four hence all the X in the expression are to be replaced with four also the value of y is given as five hence anywhere that there is y we have to replace it with 5 therefore we can have 3 * 4^ 2 + 3 * 4 + 2 * 5 by order of operation we have to perform the exponent first 4^ 2 which is 4 * 4 is 16 now we have 3 * 16 + 3 * 4 + 2 * 5 3 ultied 16 is 48 3x 4 is 12 and 2x 5 is 10 we add 48 + 12 + 10 this will give us 70 as the value of the expression the chart below represents the yearly number of enrollment in a business school in New York how many students enrolled from 2017 to 2021 line charts are common on the GED math science and social studies this is simply an addition question we will add the number of students that enrolled from 2 2017 to 2021 we have 4,000 + 8,000 plus 2,000 + 6,000 + 9,000 this will give us 29,000 students we will end this video here please watch our other videos for more thank you