SAT Math Part 1 - Evaluating Functions and Solving Basic Equations - Algebra - Free Educational videos for Students in K-12

SAT Math Part 1 - Evaluating Functions and Solving Basic Equations - Algebra - By The Organic Chemistry Tutor

Transcript


00:0-1	this video is for those of you who are studying
00:02	for the S . A . T . Exam ,
00:04	it's going to focus on the math section of that
00:07	exam . Now this is just part one . So
00:10	be sure to check out the links in the description
00:12	section below for part two . Now this particular video
00:16	is going to focus on evaluating functions and solving equations
00:20	in future videos , I'm going to talk about trigonometry
00:25	, geometry problems , converting sentences into equations , averages
00:29	proportions , fractions percent and other topics that you're going
00:34	to be tested on . But let's focus on this
00:37	section of the S . A . T . Exam
00:40	. So let's start with number one by the way
00:42	for each of these problems , pause the video ,
00:45	try it yourself and then once you have the answer
00:48	, play the video to see if you have the
00:50	right solution . Let's start with this problem . If
00:54	G of X is equal to five X squared minus
00:58	four X plus two X cube . Then what is
01:02	G . F . So all we need to do
01:05	is evaluate the function , We need to replace X
01:09	with three . So instead of five X squared is
01:12	going to be five times three squared And instead of
01:16	four ax is gonna be four times street Now ,
01:22	3 to the second power . It's basically multiplying 2
01:26	, 3 together . Three times three is 9 .
01:28	four times 3 is 12 . Now what about 3
01:32	to the 3rd power ? So in this case we're
01:34	multiplying three threes together three times 3 is nine .
01:39	nine Times Street is 27 . So this is what
01:43	we now have Now , five times 9 is 45
01:51	and two times 27 , two times 20 is 40
01:55	Two times seven is 14 , 40 plus 14 is
01:58	54 , 45 -12 is 33 And 33 plus 54
02:07	. It's 87 . So d . Is the right
02:12	answer for this problem number two . In the function
02:17	H of X shown below K is a constant .
02:22	If HF three is 26 Then what is the value
02:26	of H of -3 ? So notice that were given
02:33	this information . That's going to be helpful in order
02:36	for us to calculate the value of kate . Once
02:39	we find the value of K We can replace X
02:42	with -3 And we could find the value of H
02:45	. of -3 . So focusing on this expression what
02:54	is exe X is the number inside of the function
02:58	? So accessory , That means h . of X
03:02	will be 26 . So let's begin by replacing X
03:06	with three . So this is gonna be 5/3 time
03:11	straight squared plus K . Time Stream -4 . Now
03:16	H . Of three that's equal to 26 . So
03:19	let's replace H . Of three with 26 now 5/3
03:26	times three squared three squared is nine . So we
03:30	have this so far . Now if you want to
03:33	you can add for to both sides so these will
03:36	cancel . And so we have 26 plus four which
03:39	is 30 now what about this ? 5/3 times nine
03:45	. Now you could do five times nine divided by
03:48	three . Or you could do nine divided by three
03:50	times five . I prefer the second method nine divided
03:54	by three history three times five is 15 . So
03:58	now we have this Now let's subtract both sides by
04:02	15 . Yes So 30 -15 is 15 And that's
04:09	going to equal three K . Now if we divide
04:12	both sides by three K . I mean by three
04:15	. Rather We get 15 divided by three which is
04:17	five . So Kay is five . Now let's just
04:26	write that here . So now that we have our
04:30	K . Value we could answer the question what is
04:33	the value of H . Of negative three ? So
04:38	let's replace X with -3 . And Let's replace K
04:44	with five negative three squared negative three times negative three
04:50	is positive nine . five times negative three is negative
04:55	15 . nine divided by three is 3 . three
04:59	times 5 is 15 . So we have 15 -15
05:03	and -4 . These two will cancel and so this
05:07	will give us negative four . So H of negative
05:10	three is negative four . So A is the right
05:13	answer number three . If our vax is equal to
05:19	three X squared plus four X . Monastery then which
05:23	of the following expressions Is equivalent to our of -4
05:28	X . So for this problem we simply need to
05:32	replace Acts with negative for Acts . So it's three
05:37	times negative four X squared and then four instead of
05:41	four X . We're going to replace Acts with negative
05:44	four X . So it's just direct substitution . Now
05:49	what is negative for X squared ? So this is
05:52	basically negative four x Times another -4 x -4 times
05:59	negative four is positive 16 X times X . He
06:03	needs to add the exponents , one plus one is
06:05	two . So we're going to get three . Yeah
06:11	Times positive 16 x squared Now four times negative for
06:16	that's negative 16 and we can carry over the X
06:22	. Now the last thing we need to do is
06:23	multiply three x 16 . three times 16 is 48
06:29	. So are of -4 x is equal two 48
06:36	X squared minus 16 . X minus tree . Therefore
06:40	answer choice C . Is the correct answer number four
06:46	. Consider the function G . Of X is equal
06:49	to six over X plus C . What is the
06:53	value of C ? If the point to come ?
06:56	A seven lies on a graph of G Fx .
07:03	So let's focus on The .2 comma seven . So
07:09	that tells us that Access to Y is seven .
07:15	So this means that GF two is equal to seven
07:19	. So what we're going to do is we're going
07:21	to replace X with seven in that function . So
07:24	GF two , it's going to be 6/2 plus C
07:30	. Now we know that GF two is equal to
07:33	seven . So let's replace GF two of 7 .
07:36	So we have seven is equal to six divided by
07:40	two , which is three plus C . Now let's
07:44	attract both sides by three . seven . Monastery is
07:47	four . So in this problem we can see that
07:51	C is equal to a value of for so D
07:55	is the answer number five . Given the functions F
08:00	of X and G of x , What is the
08:02	value of G . 4 ? So let's plug in
08:06	four into this expression . So it's gonna be four
08:11	squared -2 times before minus five . Now four squared
08:18	is 16 F . Before we need to plug it
08:21	into that function . So it's going to be 3-4
08:26	And then replace X with four And then -2 .
08:32	Now 3/4 times for the force will cancel . So
08:36	that's just gonna give us 3 -2 . 3 -2
08:42	is one . and so we have 16 -2 which
08:46	is 14 And 14 -5 is nine . So in
08:51	this example G . F four has a value of
08:54	nine which means E . is the right answer .
08:58	Now for those of you who truly value this video
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09:24	page . Also , when you get a chance to
09:27	check out the links in the description section below this
09:29	video , because I'm going to post some other resources
09:32	that you might find helpful . So let's get back
09:36	to the video number six . If G F X
09:40	plus two is equal to X squared minus three X
09:43	plus seven , Then what is the value of GF
09:47	5 ? Go ahead , take a minute and try
09:52	this problem . Now , the first thing we need
09:54	to determine is the value of X . What is
09:58	X Is actually equal to 5 ? It turns out
10:03	that in this problem is something else . We need
10:07	to write G . 05 as being G Of three
10:11	Plus 2 . The reason being is we have X-plus
10:16	two inside of G . Yeah . So notice that
10:22	the two is the same , which means that X
10:24	has to be equal to three . So what we're
10:28	going to do is we're going to replace acts with
10:30	three in this problem . So it's going to be
10:32	three squared minus three times three plus seven . three
10:37	squared is nine , Three times three is also nine
10:40	. And so these two numbers will cancel . Thus
10:44	GF five is equal to seven . So in this
10:47	problem you need to determine X based on what you
10:50	see here . So what you could do is set
10:53	five equal to X plus two . Subtract on both
10:56	sides by two , You'll get that X . Is
10:59	equal to three . And then once you have the
11:01	X . Value , you can now plug it in
11:03	to the formula or to the function rather . So
11:06	for this problem answer choice D . Is the right
11:08	answer number seven . What is the value of acts
11:13	in the equation shown below ? So here we have
11:17	two fractions separated by an equal sign . When you
11:21	see this , you need to cross multiply . So
11:25	for over seven times x Is the same as for
11:30	X divided by seven . You can view this as
11:32	X over one And this is equal to 8/5 .
11:39	So first we're going to multiply four x by five
11:44	And that's gonna give us 20 x . And then
11:47	we're gonna multiply seven times eight , Which is 56
11:53	. Now let's divide both sides by 20 . So
11:57	now we need to reduce the fraction , So how
12:01	can we reduce 56/20 while both numbers are even ,
12:06	so We can divide the top and the bottom by
12:09	two Half of 56 is 28 . Half of 20
12:14	is 10 . Now we still have even numbers ,
12:18	So we could divide both numbers again by two ,
12:21	28 , divided by two is 14 , Half of
12:25	10 is five . So the answer is B 14/5
12:33	. Number eight . If three times y plus four
12:38	plus five Times two Y . Monastery is equal To
12:44	10 y plus three . Then what is the value
12:48	of Why ? So in this equation all we need
12:52	to do is simply soft . So let's rewrite the
12:57	equation first . Now the first thing you need to
13:07	do is distribute let's distribute three to why and to
13:12	four three times . Why is street wide three Times
13:17	Voice 12 . Now let's do the same thing with
13:21	the five . So we have five times to why
13:25	? That's 10 y . five times 3 is 15
13:32	. If we subtract both sides by 10 Y ,
13:35	the bees will cancel . Now We can combine like
13:39	terms 12 plus negative 15 , That's going to be
13:45	-3 . So this is what we now have .
13:49	Now Let's add 3 to both sides . 3-plus 3
13:55	is six . Our next step is to divide both
14:00	sides by three . six , divided by three is
14:04	too So why Is equal to 2 ? Which means
14:09	B is the right answer number nine A four x
14:15	plus seven Is equal to 31 . Then what is
14:19	the value of 5 ? X -8 ? So what
14:24	we need to do in this problem is we need
14:26	to solve for X in this equation . Now once
14:30	we have the value of X We can plug it
14:33	in into that expression . And let's calculate the value
14:36	of five X -8 . So let's start with this
14:42	equation , Let's begin by subtracting both sides by seven
14:50	. 31 -7 is 24 . Next Let's divide both
14:54	sides by four . So 24 divided by four is
14:59	6 . So now that we have the value of
15:02	X , let's plug it into that expression . So
15:06	we have five X -8 . So it's gonna be
15:09	five times 6 -8 . five times 6 is 30
15:14	And 30 -8 is 22 . So answer choice is
15:19	the right answer number nine , A four X plus
15:24	seven is equal to 31 . Then what is the
15:28	value of 5 ? X modest 8 ? So we're
15:32	given a linear equation and an algebraic expression . What
15:38	we need to do is calculate the value of X
15:41	by solving the linear equation . And then once we
15:45	have that , once we have the value of X
15:48	we could plug it in to the algebraic expression .
15:52	And that's going to give us the value Of five
15:55	X -8 . So let's begin by solving the equation
16:01	on the left . The first thing we need to
16:04	do is some try both sides by seven . Mhm
16:09	. 31 -7 is 24 . Next We need to
16:14	divide both sides by four . 24 , divided by
16:19	four is 6 . So X Is equal to six
16:25	. Now let's take that value and plug it into
16:28	this expression . So let's replace X with six .
16:34	five times 6 is 30 And 30 -8 is 22
16:40	. So therefore answer choice A . Is the correct
16:45	answer number 10 . Given the equation shown below ,
16:52	what is the value of 12 divided by X plus
16:57	Torri . Now this problem is very similar to the
17:01	last problem . Were given an equation in which we
17:05	need to solve and once we get the value of
17:08	X , we need to plug it into this expression
17:11	to calculate the value of 12 over X plus three
17:18	. Now , how should we solve this particular equation
17:23	? What do you think we need to do Whenever
17:26	you see two fractions separated by an equal sign ,
17:31	you need to cross multiply . So we're gonna multiply
17:35	too By four x -9 And then we're gonna multiply
17:40	three By X- Plus four . So let's distribute to
17:47	two , X -9 . So two times 4 x
17:51	is a tax and then two times negative nine .
17:56	That's going to be negative 18 On the right side
18:00	we have three times acts And three times 4 ,
18:04	which is 12 . Now let's subtract both sides by
18:09	three X and at the same time Let's add 18
18:14	to both sides . So these will cancel now .
18:20	eight x monastery x is five x . 12 plus
18:25	18 is 30 . Now , our next step is
18:29	to divide both sides by five , 30 divided by
18:33	five is 6 , so X is equal to six
18:39	. Now that we have the value of X ,
18:43	we can take it and plug it into that expression
18:47	. So this is going to be 12 Over 6-plus
18:51	3 . 12 divided by six is too two Plus
18:56	3 is five . So as we can see here
19:01	, answer choice is the correct answer . So that's
19:04	basically it for this video . Now , be sure
19:07	to check out the links in the description below .
19:10	As I'm going to post part two at that location
19:13	when it's available . Thanks for watching .

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SAT Math Part 1 - Evaluating Functions and Solving Basic Equations - Algebra is a free educational video by The Organic Chemistry Tutor.

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