ALL OF GRADE 9 MATH IN 60 MINUTES!!! (exam review part 3) - Free Educational videos for Students in K-12 | Lumos Learning

ALL OF GRADE 9 MATH IN 60 MINUTES!!! (exam review part 3) - Free Educational videos for Students in k-12


ALL OF GRADE 9 MATH IN 60 MINUTES!!! (exam review part 3) - By Lumos Learning



Transcript
00:0-1 Yeah , Here's the final part to grade nine .
00:01 Math in an hour . So it's kind of going
00:03 to end up taking a little bit longer an hour
00:04 to get through all three . But this is definitely
00:06 the shortest section . I should be able to do
00:07 this section in under 10 minutes . This section is
00:09 on geometry . So the geometry section , um ,
00:12 I'm just gonna quickly go through these topics for part
00:14 three of grade nine math in an hour . So
00:17 this has been the last year you would have done
00:19 . You probably would've started by reviewing parallel line theorems
00:21 . You probably already know these from grade eight ,
00:24 but parallel line themes . Basically , if you have
00:26 two parallel lines , we can tell the parallel because
00:28 these little arrows here we have two parallel lines that
00:30 are cut by a transfer cell . Um , there
00:33 are some theorems we can use to find unknown angles
00:35 . So first theorem is the alternate into your angles
00:39 theorem , and that tells us if we have this
00:41 Z pattern , the angles inside the Z are equal
00:45 to each other . Also , there's the F pattern
00:47 . We call those corresponding angles the corresponding angle theorem
00:51 the angles inside the f are also equal to each
00:54 other . And lastly , we have the C pattern
00:56 we call those co interior angles and the angles inside
01:00 of a C . They're not equal to each other
01:01 , but they do add to 1 80 so we
01:04 can use those three theorems in combination with supplementary angles
01:07 and , um , opposite angles . Remember , opposite
01:09 angles like this angle here in this angle here are
01:12 equal to each other . We can use these theorems
01:14 to be able to figure unknown angles if we have
01:16 parallel lines . So if we have here two parallel
01:19 lines , this tells us they're parallel . Um ,
01:22 let's find these three unknown angles using our parallel line
01:25 theorems . Well , first of all , here's A
01:27 is opposite from the 75 degrees , and we know
01:30 opposite angles are equal . So I know is equal
01:32 to 75 degrees , and we could stay off the
01:35 side here . They're opposite angles . And that's how
01:36 we know . Um , what's find ? Let's find
01:40 the next will be . Look at this F pattern
01:44 here . I've got an F pattern . I know
01:46 angles inside the F pattern are equal to each other
01:48 , so I know B is equal to 75 degrees
01:53 as well . And there's lots of ways I could
01:55 know what angle C is . Um , I could
01:57 see an F pattern here , so I know a
01:59 is equal to see . Um I know B and
02:02 C are opposite , so I know B and C
02:03 are equal to each other , or I can look
02:05 at the Z pattern here , so they're alternate interior
02:08 angles . These two angles are equal , so I
02:10 know , see is also equal to 75 degrees .
02:15 Next thing you would have looked at probably is Pythagorean
02:17 theorem . Pythagorean theorem can only be used when you
02:20 have a right triangle in a right triangle is a
02:22 triangle has one angle equal to 90 degrees , and
02:25 we can tell because there's this little rectangle inside marking
02:28 off that there is a 90 degree angle , Um
02:33 , in a right triangle , one of the sides
02:35 we call the hypothesis . How do we know which
02:37 side that is ? Well , it's always the longest
02:40 side of the right triangle , and if you can't
02:42 tell which one is the longest we know , it's
02:43 always decide that is opposite from the right angle .
02:47 It's always the side across from the right angle and
02:50 what is Pythagorean theorem . Pythagorean theorem tells us that
02:54 the sum of the squares of the shorter two sides
02:56 so the square of the shorter two sides . If
03:00 we add up those areas , it should equal exactly
03:05 the area of the square of the larger side .
03:08 Algebraic Lee speaking . We say a squared plus B
03:10 squared equals C squared where A and B represent the
03:13 shorter two sides and we sometimes call those the legs
03:16 and the C represents the longest side . We call
03:18 that the high pot news , so Pythagorean theorem to
03:21 sum of the squares of the shorter two sides .
03:23 So a squared plus B squared is equal to the
03:25 square of the longer side . C squared well ,
03:27 to practice using Pythagorean theorem , it can be used
03:30 to find an unknown side of a right triangle as
03:33 long as we know two of the other sides .
03:35 So for this triangle here we have our right angle
03:38 here , which makes the side opposite that right angle
03:42 are hypotenuse and we always use the letters C for
03:44 the hypotenuse and we use the letters A and B
03:48 for the shorter two sides . Doesn't matter which is
03:50 which , but we know that the figurine theorem is
03:52 true for all right . Triangle . So a squared
03:54 plus B squared equals C squared . We can use
03:57 this formula to figure out the unknown side sea by
03:59 plugging into our Formula nine squared . Plus 12 squared
04:04 gives us C squared for evaluate . Nine squared plus
04:08 12 squared . We would get to 25 . That's
04:10 what C squared is equal to . But to figure
04:12 what C is equal to , we have to isolate
04:14 . See by moving the square to the other side
04:15 . The opposite of squaring is square rooting . So
04:18 I have to square root 2 . 25 to get
04:21 me c squared up to 25 . What times itself
04:24 is equal to to 25 . Well , that's 15
04:27 , so c equals 15 . So we would say
04:29 c equals 15 and we are in meters . So
04:32 I should write meters beside that here . What if
04:35 the missing side is one of the legs ? So
04:37 once again , right angle opposite . That is a
04:39 hypothesis that c So our legs are here and here
04:43 . If I used to Failure and theorem a squared
04:45 plus B squared equals c squared . My unknown this
04:48 time is the B . So I could start by
04:51 rearranging the formula , or I could plug in and
04:53 then rearrange I'm gonna plug in first . So I
04:56 know A is 5454 squared plus B squared equals C
05:01 squared +90 C . Is 10.3 . And now what
05:04 I'm going to want to do is isolate the B
05:06 squared by moving the 5.4 square to the other side
05:09 so I b squared equals 10.3 squared minus 5.4 squared
05:16 d squared . If I evaluate that , I get
05:19 76.93 and then if I take sorry , that's B
05:23 squared to get B , I have to actually square
05:27 root to 76 93 and that gives me an approximate
05:35 answer . I should write approximately here because I've rounded
05:38 this answer . If I evaluate that , I get
05:41 8.77 8.77 all right , And what units are we
05:49 in centimetres ? Okay , so that's Pythagorean theorem .
05:53 The next thing you probably looked at is three dimensional
05:57 shapes getting surface area and volume of three D shapes
06:00 . I'm sure you remember what the difference between volume
06:02 surface area , so let's just go into a couple
06:04 of quick calculations . Let's start with a couple of
06:06 different prisms . Um , here's a rectangular prism .
06:08 It's a rectangular prism because the base of it is
06:12 a rectangle . Let's find the volume of this rectangular
06:15 prison . It's a volume of any prism is actually
06:18 just equal to area of days multiplied by the height
06:25 of the prison . And since the base of this
06:27 shape is just a rectangle , let's find the area
06:30 of the rectangle by doing its length times its width
06:33 so length , times width and multiply that by the
06:35 height of the entire prison . So L W H
06:39 is the volume of this rectangular prism . We could
06:43 get that formula from our Formula Page Rectangular prism volume
06:47 area based on site , which is length , times
06:49 , weight , times site . So if we evaluate
06:51 this volume equals nine times seven time 16 , we
06:57 would figure out volume is 1000 and eight centimetres .
07:03 Cute member of volume is always in units Cube .
07:08 Here we have a triangular prison . Let's find the
07:10 volume of this as well . Members always area base
07:12 times height , so the base is a triangle .
07:14 So I'm gonna need to find the area of that
07:16 triangle area of a triangle is base times height divided
07:18 by two . And we call the base of the
07:20 triangle of the triangle B , and we call the
07:22 height of the triangle . Actually call it El because
07:24 we need to use H for the height of the
07:26 prison . So we're going to have to do the
07:28 times all divided by two , and then multiply that
07:30 by h . So our formula for volume of of
07:32 a triangular prism is B l h divided by two
07:36 . If we plug that into our formula 23 times
07:41 34 times H , which is 4.8 , divide the
07:47 entire product by two . And if we do that
07:51 , I'll just write my answer below . Here we
07:54 get 18 768 m . Cute . And lastly ,
08:03 I have a sphere . So this one is not
08:06 a prism . Um , but for a sphere ,
08:08 let's instead of finding volume this time , let's find
08:11 let's find the surface area this time . Surface area
08:14 for a sphere , it's four pi r squared .
08:16 We can look at our Formula page surface area four
08:19 pi r squared . So we're gonna find the surface
08:21 area of this sphere for pie . Our square .
08:26 Remember , R stands for the radius , which is
08:28 a distance from the center of the sphere to the
08:30 edge . If it gave us the diameter , we
08:33 would have to divide it by two . But it
08:35 gives us the radius in this question , so just
08:37 plug in our radius . So four pi times 28
08:42 squared and make sure you press the pie button on
08:44 your calculator . Don't use 3.14 Approximate value calculator stores
08:48 many more digits for its pi value , so you
08:51 know more accurate answer if you actually use the pie
08:53 button on your calculator . So if we do four
08:56 pi times 28 squared , make sure if you're doing
08:59 this step by step , you're following bed Mass .
09:02 But if you're typing it on a scientific calculator ,
09:05 it'll do the correct order of operations here for you
09:07 , and we will get 98 52 0.3 In this
09:15 case , we are in millimeters squared . Remember Surface
09:19 area . It's always in units squared volume . It's
09:22 always in units . Cute . So 9008 . 52.3
09:28 millimeters squared . So probably lastly in your geometry course
09:33 you would have done some optimizing measurements . I'm not
09:36 gonna have time to get through that because I think
09:37 I'm already over an hour . But these are the
09:40 main concept you would have done in geometry . Some
09:42 service area volume , calculations , um , without your
09:45 into your room and parallel line theorems . So that's
09:50 it for grade nine . Math in an hour .
09:51 Hopefully , you watched all three parts and you're ready
09:54 for your math exam ? Um , yeah , and
09:57 that's it .
Summarizer

DESCRIPTION:

Here is a great exam review video reviewing all of the main concepts you would have learned in the MPM1D grade 9 academic math course. The video is divided in to 3 parts. This is part 3: Geometry. In this video you will review parallel line theorems, pythagorean theorem, and volume/surface area of three dimensional shapes.

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ALL OF GRADE 9 MATH IN 60 MINUTES!!! (exam review part 3) is a free educational video by Lumos Learning.

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