SAT Math Accelerator (Black Friday Special - $300 Off) : www.admissionhackers.com/sma 25 Concept List - www.admissionhackers.com/25concepts Parabola Concepts for SAT Math Part 1 - ua-cam.com/video/_Yst9VbRR7U/v-deo.htmlsi=GCDaBHCk3W2-egzb Part 2 - ua-cam.com/video/iQWA5bkI3Fc/v-deo.htmlsi=NmS8Hit8U1UFyUee 8 Practice Questions - ua-cam.com/video/wkLGsN6zeK8/v-deo.htmlsi=v1kvK96VdH8wGrqW
for circle questions like those, you can also just plug the entire equation into desmos and find out if any of the x values in the choices fall within the circle
Good point. For clarity, as long as the x-coordinate is one of the x-values of the circumference, it will work. Desmos works (and I admit, it's faster) for this question, but it's valuable to learn the equation method for other SAT questions. Thanks for sharing.
@@shlattrtI do too, good luck! If you haven’t figured it out already you can quite literally just type the exact equation into Desmos and it will graph the circle for you. Then from there the question can be a quick process of elimination. If you haven’t practiced using Desmos I highly recommend using some time you have left to check it out.
For the first one you literally enter the equation in desmos, then type in a moveable point like this: (answer choice, b) and move the point up and down with the slider for b until you can tell it intersects the circle. Clearly happens with (-14,b). This took me 15 seconds with zero risk of making a calculation blunder. Amazing how tutors these days barely lift a finger to teach students how to operate the greatest gift the college board ever provided on the SAT math.
An alternative method for the first question. The radius of the circle is 11, and the center of the circle is ( -4, 19). Hence by adding and subtracting the radius from -4, we can find the maximum and minimum values of a which will turn out to be 7 and -15 respectively. And only -14 lies within those values. P.S. drawing a quick sketch makes it much easier to understand.
For the circle question at 0:59, since they're only asking for the X-Coordinate, you could do -4 (X-coordinate of the center) ± 11 (radius, square root of the right side of the equation), and get that the X-Coordinate must be from -15 to 7, which only answer B fulfills.
Here we go again...for the third problem just enter a single point into a table in desmos, namely (5,-4) since that is given on line t. Then calculate the slope between the two points with desmos by doing (1 - - 4) / (-1 -5), which is -5/6. Line t must have slope 6/5 since tangents are perp. to radii. Then do a regression to get the line graphed for you by doing y_1 ~ 6/5 * x_1 + b. Then drag your mouse along the line until you find an answer choice on the line. Clearly at (10,2). This took about 1 minute.
For the second one you just enter a table in desmos and plug in three obvious points from the graph: (-1,-8), (-3,0), and (1,0). Then do a regression to have desmos solve for the missing constants b and c by typing y_1 ~ 2x_1^2 + bx_1 + c, then in the next line type bc and your answer (-24) is handed to you in less than 30 seconds with zero chance of making a calculation error.
Hello and thanks for commenting these solutions, I find them very helpful personally! Do you have a video or collection of videos on utilizing DESMOS to solve problems on the SAT math? I love using it but struggle to identify what types of problems are solvable with it.
for the first question (22), it would be much simpler and time-saving to just throw the circle equation into desmos and check for the possible x-intercepts.
For the second question, you can use the sum of roots and product of roots formula. Sum of roots is -b/a, and product of roots is c/a, so you just find the sum of the roots which is -2, and the product of the roots which is -3. Then you plug it into the formula. -b/2 has to equal -2, so b is 4. And c/-2 has to equal -3, so c is 6. Then you just multiply to get your answer of -24.
For the second question, it is also easy to do it by using the concept of sum and product of roots, since the roots of the equation are given in the graph (-3 and 1)
All 3 questions can be done fairly quickly in Desmos although the 3rd is not quite as intuitive. However, the first 2 are very easy and can be done in under 30 secs. No reason to spend 2-4 mins doing all the work by hand esp on #1.
@@NtS785 Yes. Create a table and type in the 3 highlighted points (-2, 6) (-1, 8) (0, -6). Do a quadratic regression y1~ax1^2 + bx1 + c. It will give you values for a, b, c. Type b*c (or just do it in your head).
@@AbdullahKhan-lq1fn Not sure if this is the best way but its how I did it. Use the center point to create circle equation (x+1)^2 + (y-1)^2 = a and add a slider for constant a. Create a table and type in point (5,-4). Using the slider test values for a until the edge of the circle lines up with the point. Do linear equation regression y1=mx1+b. Then I just tested each of the answer choices by adding them to the table to see which one created a tangent.
For the last question I think using point slope form would be better. If you like only having y on the left then u can simply add over the y1 so u get y = m(x-x1) + y1. It makes it a lot easier bc then u can plug it into desmos as a function without needing to solve for b
Question 1 is a head-solver (no plugging in, no Desmos). Circle has a center at (-4,19) and a radius of 11. Therefore, no x-value can be less than -4 - 11 or greater than -4 + 11. Only -14 (choice B) satisfies
For the first question, there are a couple ways to look at it. The way you presented it is one way for sure, but there are two other ways to do it that are much faster in my opinion. First, the cheater way: Desmos. Just type the equation into desmos and it will give you the circle. Then punch in different x-values and see which one intersects the circle. This is the best way to do it just because it is so fast, even if it really feels like cheating. Second, the other smart/conceptual way. This is an easy way to grasp the question's concept. You know from the circle equation that your point is (-4, 19), and your radius is √121 = 11. So the range of possible x-values will be a max of ±11 from its center, -4. Thus the range of possible x-values that fall on the circle is -15 < x < 7. We're looking for a, which is just the same as x here. So any choice that is smaller than -15 or greater than 7 automatically falls out of the circle's x-range. Thus, -14 is the correct answer.
For the second question ,we can use desmos point table and put the x and respective y values and then use regression If u know wht regression is then ud know that if u plug in the eqn they would automatically give u value for b and c
for the first question, input the equation in desmos. just visualize yourself which point can be inside the circle. No need to go through any calculation.
There is another method to solve first question , first we make graph of centre point then we know the radius of circle which is 11 . there is possible value of x is between -4+11 , and -4-11 so we got that
I enjoyed your solution to the 2nd Problem 7:08 I used Vietta's formula Sum of Roots/Solutions = -b/a Product of Roots = c/a Find c and b and then Multiply I would have used ur method. Wanted to Try this formula out
You can also enter the circle equation into desmos and eyeball it or enter x= -16 which lets you create a slider from -16 to 19 with step 1. Drag the slider around to see which x value actually works. It seems that the digital SAT loves to reinforce that an (x,y) ordered pair satisfies the equation that it is a solution for. Love the way you did the circle question and the way you emphasized the logic. ACT used to include these questions often.
@@jaywestg9248 Your comment is not true. Perhaps you typed the equation wrong. x=-14 perfectly intersects the circle at two points. YT won't allow me to share the desmos link, but if you look up Tutorllini's video about sharing desmos, then you'll know how to access my graph with this info nk42lfi0co
Before you start solving the questions, i tried them and I got answers to all of them without even knowing the formulas. With the help of DESMOS i got the answers in 20-40 seconds...
@@shlattrt I typed the equations on the graph and pointed the options on the x-axis like this (-16,0) (-14,0) (11,0) (19,0) and labeled them. then i saw that X-Coordinate must be from -15 to 7 so only -14 can be placed on circle and others are outside of the circle. ngl, I don't remember any formulas but i used my brain and some tricks and Desmos, i got like 700+ in math practice test.
I want to do good but only two weeks are left ,I haven’t prepped for my exams and I don’t have time and I don’t want to give it more than once I’d love advice from anyone
for the last q, couldn't you have just used the inverse of slope from the centre of the circle to the point of tangent instead of finding the entire line ? as both the point of tangent and the new point would need to have the same slope ?
For the second question can you also do it by figuring out the y int from graph for c value and then use a point from the graph say (-2,-6) and then plug it into the equation provided for the b value and then multiply it together(b and c)?
1. Create a table with the 2 given points 2. Linear regression on those points: y1~mx1 + b; this gives you the slope of the radius to the point of tangency, m = =-.83333333333 3. Create a new table with 5, -4 4. Linear regression on that new table (the 1 point) with the slope entered as the opp recriprocal of the value from 2 above: y2~(1/.8333333333)x2 + b 5. Look at which points are on the graph or you can type in the points and see if they fall on the line.
I have a video on how to use desmos to do that type of question (linear regression for a line tangent to a circle). It is great that John teaches the fundamentals in case College Board makes some un-Desmosable questions.
Hi John... I took a bluebook practice test yesterday and I got 740 in maths (5 questions incorrect). But when I compared my score with a practice test I had taken earlier, I saw that I had gotten a 780 in that test with the same amount of incorrect answers. What do you think could be the reason for this?
Hello, it’s because the questions on mdoule 1 are worth more than questions on module 2, of you have before gotten 2 questions wrong on module 2 it will result in 800-2(10)= 780 but now maybe you have got 2 questions wrong on module 1 which can result in 800-2(30)= 740 Hope this helps
The test is adaptive. Bomb an easy question, lose more marks. Solve a tough one, win a lot more marks. Some questions do not even carry marks (generally the toughest ones). Bomb those, lose nothing. Try to solve the easiest questions first, and try not to bomb them.
in order to do that question on desmos there is alot of steps that are required like creating a table, its actually easier to just learn that the tangent line is perpendicular to the radius
It's REALLY easy to do in Desmos. It includes one of the top Desmos skill I'd recommend learning. It's called linear regression. Once you know that, you basically know quadratic regressions as well. I have videos on both, but I think it's rude for me to post them here. It's my video on lines tangent to a circle.
Man, your solutions are so confusing. You just need to start solving based on fundamental concepts. And if you do that, then you easily determine where the center of a circumference is - it is at (-4;19), then you know the radius is 11. Then, imagine the circumference centered at (-4;19) with radius 11. The border x coordinates will be at -15 and 7. You immediately throw choices (A), (C), and (D) away. The only (B) is in this domain of [-15, 7]. But if you want to be extra confident, just plug choice (B) into that equation, and you will find out the corresponding "y" value. Your method of solving these types of problems could mislead and take extra time, which is not a good strategy for an SAT framework.
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SAT Math Accelerator (Black Friday Special - $300 Off) : www.admissionhackers.com/sma
25 Concept List - www.admissionhackers.com/25concepts
Parabola Concepts for SAT Math
Part 1 - ua-cam.com/video/_Yst9VbRR7U/v-deo.htmlsi=GCDaBHCk3W2-egzb
Part 2 - ua-cam.com/video/iQWA5bkI3Fc/v-deo.htmlsi=NmS8Hit8U1UFyUee
8 Practice Questions - ua-cam.com/video/wkLGsN6zeK8/v-deo.htmlsi=v1kvK96VdH8wGrqW
for circle questions like those, you can also just plug the entire equation into desmos and find out if any of the x values in the choices fall within the circle
Good point. For clarity, as long as the x-coordinate is one of the x-values of the circumference, it will work.
Desmos works (and I admit, it's faster) for this question, but it's valuable to learn the equation method for other SAT questions. Thanks for sharing.
bro can u show me how to do that i have my exam in 3 days
@@shlattrt same omg!! just started to study:)
@@shlattrtI do too, good luck! If you haven’t figured it out already you can quite literally just type the exact equation into Desmos and it will graph the circle for you. Then from there the question can be a quick process of elimination. If you haven’t practiced using Desmos I highly recommend using some time you have left to check it out.
can you explain how did you solve last question?
For the first one you literally enter the equation in desmos, then type in a moveable point like this: (answer choice, b) and move the point up and down with the slider for b until you can tell it intersects the circle. Clearly happens with (-14,b). This took me 15 seconds with zero risk of making a calculation blunder. Amazing how tutors these days barely lift a finger to teach students how to operate the greatest gift the college board ever provided on the SAT math.
An alternative method for the first question. The radius of the circle is 11, and the center of the circle is ( -4, 19). Hence by adding and subtracting the radius from -4, we can find the maximum and minimum values of a which will turn out to be 7 and -15 respectively. And only -14 lies within those values. P.S. drawing a quick sketch makes it much easier to understand.
For the circle question at 0:59, since they're only asking for the X-Coordinate, you could do -4 (X-coordinate of the center) ± 11 (radius, square root of the right side of the equation), and get that the X-Coordinate must be from -15 to 7, which only answer B fulfills.
same thing I did here bro . I got B ..but what I watched on.. boom!!. I saw that I was wrong
Another valid method! Thanks for sharing.
Here we go again...for the third problem just enter a single point into a table in desmos, namely (5,-4) since that is given on line t. Then calculate the slope between the two points with desmos by doing (1 - - 4) / (-1 -5), which is -5/6. Line t must have slope 6/5 since tangents are perp. to radii. Then do a regression to get the line graphed for you by doing y_1 ~ 6/5 * x_1 + b. Then drag your mouse along the line until you find an answer choice on the line. Clearly at (10,2). This took about 1 minute.
For the second one you just enter a table in desmos and plug in three obvious points from the graph: (-1,-8), (-3,0), and (1,0). Then do a regression to have desmos solve for the missing constants b and c by typing y_1 ~ 2x_1^2 + bx_1 + c, then in the next line type bc and your answer (-24) is handed to you in less than 30 seconds with zero chance of making a calculation error.
Hello and thanks for commenting these solutions, I find them very helpful personally! Do you have a video or collection of videos on utilizing DESMOS to solve problems on the SAT math? I love using it but struggle to identify what types of problems are solvable with it.
@@huylequang6623 Just type in the search 20 SAT Math Questions You Can Annihiliate Using Desmos
for the first question (22), it would be much simpler and time-saving to just throw the circle equation into desmos and check for the possible x-intercepts.
That's what I did. I just made the equation, x=a, and set a range of values a could be. I then tested each value, and only b fulfilled the answer.
@@R4PT0Rhe circled a and b. Is b the correct answer
For the second question, you can use the sum of roots and product of roots formula. Sum of roots is -b/a, and product of roots is c/a, so you just find the sum of the roots which is -2, and the product of the roots which is -3. Then you plug it into the formula. -b/2 has to equal -2, so b is 4. And c/-2 has to equal -3, so c is 6. Then you just multiply to get your answer of -24.
Yes vieta’s formula
For the second question, it is also easy to do it by using the concept of sum and product of roots, since the roots of the equation are given in the graph (-3 and 1)
All 3 questions can be done fairly quickly in Desmos although the 3rd is not quite as intuitive. However, the first 2 are very easy and can be done in under 30 secs. No reason to spend 2-4 mins doing all the work by hand esp on #1.
Can u explain how #2 can be put in desmos?
@@NtS785 Yes. Create a table and type in the 3 highlighted points (-2, 6) (-1, 8) (0, -6). Do a quadratic regression y1~ax1^2 + bx1 + c. It will give you values for a, b, c. Type b*c (or just do it in your head).
@@jwmathtutoring thank uuuu
bro how to put q3 in desmos
@@AbdullahKhan-lq1fn Not sure if this is the best way but its how I did it. Use the center point to create circle equation (x+1)^2 + (y-1)^2 = a and add a slider for constant a. Create a table and type in point (5,-4). Using the slider test values for a until the edge of the circle lines up with the point. Do linear equation regression y1=mx1+b. Then I just tested each of the answer choices by adding them to the table to see which one created a tangent.
For the last question I think using point slope form would be better. If you like only having y on the left then u can simply add over the y1 so u get y = m(x-x1) + y1. It makes it a lot easier bc then u can plug it into desmos as a function without needing to solve for b
Question 1 is a head-solver (no plugging in, no Desmos). Circle has a center at (-4,19) and a radius of 11. Therefore, no x-value can be less than -4 - 11 or greater than -4 + 11. Only -14 (choice B) satisfies
For the first question, there are a couple ways to look at it. The way you presented it is one way for sure, but there are two other ways to do it that are much faster in my opinion.
First, the cheater way: Desmos. Just type the equation into desmos and it will give you the circle. Then punch in different x-values and see which one intersects the circle. This is the best way to do it just because it is so fast, even if it really feels like cheating.
Second, the other smart/conceptual way. This is an easy way to grasp the question's concept. You know from the circle equation that your point is (-4, 19), and your radius is √121 = 11. So the range of possible x-values will be a max of ±11 from its center, -4. Thus the range of possible x-values that fall on the circle is -15 < x < 7. We're looking for a, which is just the same as x here. So any choice that is smaller than -15 or greater than 7 automatically falls out of the circle's x-range. Thus, -14 is the correct answer.
For the second question ,we can use desmos point table and put the x and respective y values and then use regression
If u know wht regression is then ud know that if u plug in the eqn they would automatically give u value for b and c
for the first question, input the equation in desmos. just visualize yourself which point can be inside the circle. No need to go through any calculation.
There is another method to solve first question , first we make graph of centre point then we know the radius of circle which is 11 . there is possible value of x is between -4+11 , and -4-11 so we got that
I enjoyed your solution to the 2nd Problem 7:08
I used Vietta's formula
Sum of Roots/Solutions = -b/a
Product of Roots = c/a
Find c and b and then Multiply
I would have used ur method. Wanted to Try this formula out
That's a valid method. Good work!
Thank you, Father
😂😂
@@YasminaMuzaffarova hey!! he's more present in my education than my dad LOL
@@fvehed same)
u can use a desmos graphing calculator which is less time-consuming and more efficient.
for the graph equestion you can put the values on desmos and use the slider value until you get it right
thats what i did its alot faster
You can also enter the circle equation into desmos and eyeball it or enter x= -16 which lets you create a slider from -16 to 19 with step 1. Drag the slider around to see which x value actually works. It seems that the digital SAT loves to reinforce that an (x,y) ordered pair satisfies the equation that it is a solution for. Love the way you did the circle question and the way you emphasized the logic. ACT used to include these questions often.
I tried it doesn’t work. -14 is far left from the circle
@@jaywestg9248 Your comment is not true. Perhaps you typed the equation wrong. x=-14 perfectly intersects the circle at two points. YT won't allow me to share the desmos link, but if you look up Tutorllini's video about sharing desmos, then you'll know how to access my graph with this info nk42lfi0co
Before you start solving the questions, i tried them and I got answers to all of them without even knowing the formulas. With the help of DESMOS i got the answers in 20-40 seconds...
how can u do the first question on desmos
@@shlattrt I typed the equations on the graph and pointed the options on the x-axis like this (-16,0) (-14,0) (11,0) (19,0) and labeled them. then i saw that X-Coordinate must be from -15 to 7 so only -14 can be placed on circle and others are outside of the circle.
ngl, I don't remember any formulas but i used my brain and some tricks and Desmos, i got like 700+ in math practice test.
@@shlattrtwrite the equation and check the biggest and smallest x value. you’ll understand if you write the equation.
@@shlattrt enter the formula in and test y= as the different answer choices, option B will work because its the only one that hits the circle
How did you solve the third question in desmos?
taking the test in less than 12 hours wish me luck
for the first question ,what is the positive value to add to 100 to get 121. pls can you kindly tell me the positive value
in the last question ig the correct answer is d,using desmos
finally.thanks for video
I want to do good but only two weeks are left ,I haven’t prepped for my exams and I don’t have time and I don’t want to give it more than once I’d love advice from anyone
me too bro i’m scared 😂
Ur videos are so helpful, they are thorough and easy to follow!❤ well explained thank u
for the last q, couldn't you have just used the inverse of slope from the centre of the circle to the point of tangent instead of finding the entire line ? as both the point of tangent and the new point would need to have the same slope ?
For the second question can you also do it by figuring out the y int from graph for c value and then use a point from the graph say (-2,-6) and then plug it into the equation provided for the b value and then multiply it together(b and c)?
i think 1st one was the trickiest
1st question i just plugged in desmos and -14 was the only one on the circle
Show us how we can use Desmond on the tangent question, please!
How are they still allowing Desmos on the SAT's, when AI tools exist?
1. Create a table with the 2 given points
2. Linear regression on those points: y1~mx1 + b; this gives you the slope of the radius to the point of tangency, m = =-.83333333333
3. Create a new table with 5, -4
4. Linear regression on that new table (the 1 point) with the slope entered as the opp recriprocal of the value from 2 above: y2~(1/.8333333333)x2 + b
5. Look at which points are on the graph or you can type in the points and see if they fall on the line.
I have a video on how to use desmos to do that type of question (linear regression for a line tangent to a circle). It is great that John teaches the fundamentals in case College Board makes some un-Desmosable questions.
its so cool way to get high mark .thanks alot .
can i use desmos to solve all of these?
Did John just call himself an "average Joe?" 13:27 Yeah, right. 😂😂😂
Hi John... I took a bluebook practice test yesterday and I got 740 in maths (5 questions incorrect). But when I compared my score with a practice test I had taken earlier, I saw that I had gotten a 780 in that test with the same amount of incorrect answers. What do you think could be the reason for this?
Hello, it’s because the questions on mdoule 1 are worth more than questions on module 2, of you have before gotten 2 questions wrong on module 2 it will result in 800-2(10)= 780 but now maybe you have got 2 questions wrong on module 1 which can result in 800-2(30)= 740
Hope this helps
The test is adaptive. Bomb an easy question, lose more marks. Solve a tough one, win a lot more marks. Some questions do not even carry marks (generally the toughest ones). Bomb those, lose nothing. Try to solve the easiest questions first, and try not to bomb them.
i think vertex form is easier for question 2
got them all right wish me luck am my test is in 21 days
John I would like to know if using your program can get a +700 if on my last SAT, I got a 650
If you're ready to put in the work with the program, I guarantee you'll get 700+, or I'll give you a refund.
i love your videos,and i solved all the three
da kerm kada
bro are you just in youtube or are you selling sat math tutor
and if you are a tutor how can i be your student
There's an online course. You either score 700+ or get a refund.
You can learn more about it here : www.admissionhackers.com/sma
@@JohnSAT are you guarantee my score are right around 600 right now
@@AlperG35 absolutely. we do it all the time.
Is the first circle question not -14?
it is
my test is tomorrow 😭😭😭
you are the cutest thank you
I really miss your video
can someone explain how to do q3 in desmos
in order to do that question on desmos there is alot of steps that are required like creating a table, its actually easier to just learn that the tangent line is perpendicular to the radius
It's REALLY easy to do in Desmos. It includes one of the top Desmos skill I'd recommend learning. It's called linear regression. Once you know that, you basically know quadratic regressions as well. I have videos on both, but I think it's rude for me to post them here. It's my video on lines tangent to a circle.
Good afternoon, John.
pov ur running out of content
8:14
Man, your solutions are so confusing. You just need to start solving based on fundamental concepts. And if you do that, then you easily determine where the center of a circumference is - it is at (-4;19), then you know the radius is 11. Then, imagine the circumference centered at (-4;19) with radius 11. The border x coordinates will be at -15 and 7. You immediately throw choices (A), (C), and (D) away. The only (B) is in this domain of [-15, 7]. But if you want to be extra confident, just plug choice (B) into that equation, and you will find out the corresponding "y" value.
Your method of solving these types of problems could mislead and take extra time, which is not a good strategy for an SAT framework.
🔥🔥🔥
ez done 3/3