all right welcome back my name is jesse i am a tutor and a business owner in melbourne and i also sat at the gamsat in march of 2021 and scored one of the highest scores uh scoring 100 in section three and so what i've done is created this channel to basically make videos and free resources for other candidates that are sitting in gamsat because there's not enough high quality or hopefully this is high quality uh high quality resources that are also available for free at the same time hopefully these things you can get a lot of value out of you can improve your score as well i try to make them as kind of actionable and skills based as possible there are some content related stuff today's one is going to be looking mostly at skills looking at the skills of graph analysis i guess this comes more so from the maths domain of the test but you'll see it being used across biology questions chemistry questions and the physics questions as well running through some of the things that i used for reading graphs really really quickly and kind of cutting out a lot of the noise of the information of the stem and then we'll also go through all the different types of graphs that we commonly come across in it and some of the specific features and ways to kind of break them down and things to look for based on what i've seen acer actually assessing in the tests even though this is not going to be a substitute for actual physics chemistry or biology knowledge it is a reasoning based test and particularly for the bio questions a lot of it is just about being able to recognize patterns understand relationships and make conclusions and extrapolations from them as well all right so i've put already i wanted to pre-prepare the notes sometimes i scribble them on screen sometimes i'm a little bit messier than usual my handwriting is never great to begin with i figured i'd do it a little bit more neatly beforehand and then we'll scribble on here cool so the first thing is we've got just some general tips first thing is just scanning the axes right so always check whenever i get given a graph the first thing i do is go straight to the two axes and i try to understand what variables am i being given and then what are the units that are being used and then moving from there how to read the graph i don't actually try to draw any information from the graph when i'm reading i wait until the question at that point so all i'd be doing here is scanning through and getting a sense of what kind of scale i'm dealing with some of the common ones i'll leave off obviously linear scales which are just standard numbers we're going to start with if they give you a log scale so if they give you a log scale um say here i've done an example log of bacterial population one two three four five six and we've got ph which is technically another log scale but let's just leave it at that then immediately we need to understand what a log actually means so most of the time in gamsat you're dealing with standard logs anything else like natural logs or logs with different bases they will give you the approximated decimal for it if they're going to use the actual maths side of it itself otherwise you'll be using standard logs standard logs are expected that you'll know how to read and understand them so effectively a standard log is anything with a base a log with a base 10 of something right x we'll call it could be any variable the quick way to read them is when you're logging a number a standard log of a number however many zeros there are if there's a one in front however many zeros there are that is the log value so there are four zeros so the log ten of ten thousand is four right um if we were to be logging something that was not starting with a one say twenty thousand then what i would do is go well the log of ten thousand is four twenty thousand is above that um so it's going to be a little bit more than four but it won't be anywhere near five because five would represent a log of one hundred thousand five zeros so then i can estimate that and call that maybe 4.2 or something coincidence with the 20 000. estimation would be fine for anything beyond beyond that and so really what you're dealing with is when you're dealing with log scales is you're just looking at an order of magnitude so because we know that standard logs log 10 will put then it means this number just represents the order of magnitude or the number of zeros so one would really represent a one with one zero two would represent a one with two zeros and so on so you can see one represents the tens two represents the hundreds three the thousands and you could just keep going from there on that's the first one and then the next one is uh scale alterations so this is where they put in extra things like in the units they'll say in the thousands for example so if this says three that really means three thousand it's representing it in groups of a thousand or they might do something like this in exponential or scientific notation where they put times 10 to the power of 6 so that is millions effectively so i've put here the common prefixes n for nano 10 to the negative 9 standard units then mu for micro 10 to the negative 6 a millionth and then little m so for milly 10 to the negative three thousandth uh c centi ten to the negative two hundredth deci for a tenth k only lower case value for large numbers but k for kilo a thousand times um m for mega 10 to the six a million times in g for giga ten to the nine billion times right so look out for those because you may have to adjust the number the number on the scale won't represent the actual value that you need to use and that may be the trick in the question and then finally is broken scales so if you see either a double dash line or a little zigzag like that all that means is the scale is not continuous so you can't assume that at the axes that x or y is equal to zero you have to start the count so we might see for example if i get rid of those we might see something like this that says five and then you'll see it just do six seven eight it means that there is no data that exists below five so they didn't want to waste space having 0 to 5 shown so they've just kind of cut it there what that means is if you had a graph that was doing this you cannot assume that this here is actually the true y-intercept right because this does not represent x equaling 0 because the scale is broken unless it were to state it that way so this would not be the x-intercept or the y-intercept and then slopes and gradients this is the next feature i look for so once i've scanned the axes then i might look at all right what's the slope doing a lot of questions are relating to slopes and gradients and these are effectively just rates so remember that the slope represents the rate of change of something and it's always the rate of change of y against x or y per x per x so we could say the vertical axis if you prefer it that way per whatever the horizontal axis is right so linear graphs or straight lines implies that the gradient or the slope is constant and so therefore we can use some of our mathematical rules rise over run or using it from actual coordinate points as well and actually map it out more importantly though they often don't get you to actually do calculations you might do rough estimation of them but more than likely you'll just be ranking different graphs based on their steepness so if something is steep it has a high rate flat low rate and when i say steep doesn't necessarily mean steep positive it can mean steep and negative as well so this would be a maximum or a very high rate of increase and this would be a very high rate but of decrease in something right so look out for that flatter is where they're going to sit almost horizontal right so this would be a lower a lower gradient or a lower slope overall cool and i'll just change this here that should be that's high as well so a high decrease this is a high increase like that whereas this is a low increase and then this is a low decrease or slow decrease then exponential growth and decay is not linear so we've got two different types so growth common example would be cell population size and so we'll see this curve upwards like a plane taking off although more like a jet i guess planes wouldn't want to go vertical um and if we map it out we can see that for every standard jump to the right each time doesn't matter what that actual interval is as long as it's consistent we can see that the rise each time is getting bigger so here it was this big if i then drag this across you can clearly see it's about two and a half times bigger so it means that it's steepening up as it goes it means the gradient is changing and increasing which means the rate is also non-linear and it's not standard or it's not consistent or constant the rate is growing so that would mean it's going faster and faster so again if that's cell population and then this is time that would mean that the population is growing at a faster and faster rate every uh period of time we can also do that from tangents so you can draw straight lines that just touch the graph once and you can keep drawing tangent lines at different points and you can see that they're steepening up as you go then exponential decay looks like the complete opposite that one slopes down like a slide and the same thing if we take even incremental jumps to the right we can see that the jump down gets less and less each time so this would be something like radioactive decay for example if it had 100 of the sample there let's call this one half-life i'll just do one half l then it would drop by 50 percent right down to 50 but in the next half-life that it goes across it's going to drop by half of what is there so that is 25 of the original and then they're 12 and a half percent and so on it'll approach zero over time uh and then s-curves so these come up more in chemistry questions um and biochemistry kind of related questions so we see them in ph titrations uh or acid-base titrations and you get the equivalence point in the middle where the gradient is at its steepest point so that's why i'm mentioning it because it relates to gradients still and you can see the gradient starts off very very low it then becomes very positive and then it becomes less positive but still positive so if you've got a question relating to rates or rate of change or speed or anything like that what i would do is my notation was i would either use numbers so i'd go well here the gradient is zero then i might say oh it's one then it's two then it's three then it's four then it's ten and then it starts to soften off again eight seven five four well it's a little bit wonky let me try that again 10 it might be symmetrical then 4 3 2 1 0 like that to understand what it's doing and i can see that it's still always positive i might use tangent lines i can see that no matter what always pointing upwards to the right so they're always positive and then the other option i might use is notation just with little pluses so i'd go 0 and then i'd put a little plus because it's just positive and a slightly bigger plus then an even bigger plus and then a really big plus and then a less big plus and then smaller again like that and back to zero like that to help understand the relative size of the slope and then the other thing to think about is the curvature as well so what's the rate of change of the rate of change for anyone who's done calculus you will not have to use calculus in this at all that's well well beyond the maths uh kind of topics or expectations in gamsat but it is good to understand what curvature means from a qualitative perspective so here the curvature is positive through this region because the gradient is increasing over time whereas here the gradient is decreasing through this section so here the curvature is actually negative meaning that it's still increasing but at a lower and lower rate or it's increasing less and less each time a simple way to think about it though to understand any kind of curvature is just to go what is the gradient doing here what is the gradient doing here and what's it doing in between it is increasing so that is a positive curvature what is the gradient doing from here to here technically this would be infinite right but we're not going to go there um here it's back to zero so from here here it is decreasing so that is a negative curvature like that cool same thing so hemoglobin dissociation curves you can also get these operate in the same way but with these ones you'll often look a little bit more at concepts of shifting the curve so we might have two species or two different conditions being shown and the hemoglobin saturation against the partial pressure of oxygen in the blood uh or partial pressure of oxygen in the air or wherever it's being measured and so we often look at this point in the center which is usually the 50 saturation level as a comparison and we look at it shifting and we look at what the change in the pressure is you can see that both the gradient and the axes become the key tools that you use to break down graphs overall and so in this case a shift to the right i've put here what would this actually mean what does a shift to the right actually mean to saturate 50 of the hemoglobin in the in the red blood cells you need a higher partial pressure oxygen which means that is not a good outcome it means you're requiring much higher pressure of oxygen in order to saturate the exact same level which means that the ability to take on or saturate the hemoglobin is lower in this case than standard if it's shifted left that's a good thing that means that you can saturate with less oxygen pressure which means it's easy to saturate overall cool um we often don't really talk much about the kind of plateau ends there and there uh then area under the curve so these are a little bit more physics based so a simple way to think of what the area under the curve represents rather than just memorizing every single graph and what the area might represent is think of well area of a box or a rectangle is length times width so the area of a graph regardless of the shape even though you may have to do calculations area is some version of length times width so if we think of the x and the y axis as our length and width dimensions whatever they are will give you it'll calculate the variable that the area represents so if for example this was a speed time graph for physics about something moving then i go okay speed times time is length times width that's the area and what's speed times time it's distance so now i know that the area under the graph is going to be total distance and that might help me answer a question like that if i wanted to then get average speed i know that average speed is total distance divided by time so i can take the area divided by the interval and then i've got my average speed instead like that so i'll get rid of that so it's not confusing and you can do that with literally any variable you'll find some of them have variables or units that don't really make any sense and in that case you won't be asked about the area of that particular graph it really only comes up in physics more than anything that's it for all of the skills right then we've got graph types so the first one you should already be pretty familiar with is standard line graph so this is just looking at analyzing two variables usually an x variable a y variable of some sort on the two axes so for example say here we've got whim wing flap frequency of some kind of bird or insect and air temperature using this because i'm sure you've probably seen something similar in acer material they seem to love air temperature and birds flapping their wings and their velocities and things uh there seems to be a real trend there and let's say all of these different lines here are separate graphs you wouldn't normally be given all of these on the one just overlaid them to save time and look at the different features of them you can see that the let's start with the red one it's linear so what that means is that there's a linear and a positive relationship meaning as air temperature increases the wing flap frequency increases at a constant rate we can make that assumption and a lot of graph reading is about being able to make assumptions to answer qualitative questions rather than technically reading the graph or calculating gradients and things like that it's just understanding what something like the gradient or the variables actually tell you let's do the blue one so the blue one the light blue one says that the wing flap frequency for this particular species is very high and then as temperature goes down it actually drops off it decays exponentially as well and so this is exponential decay and so therefore we can assume that as air temperature increases the change or the drop in wing flap frequency is less and less each time because we understand that the mechanics of how exponential decay works so it's often recognition of the shape itself and understanding the mathematical relationships from a qualitative perspective then the green one has a plateau in it so what this would suggest is that it prefers lower temperatures or sorry it doesn't prefer lower temperatures does not like lower temperatures does prefer higher temperatures for higher frequency but it gets to a point where about here it effectively flattens out and what that means is that there's no longer any benefit or any increase in wing flap frequency beyond a particular temperature that would be a plateau in that case unaffected then we have plateau plateau i don't know i'll leave it to people who know french or something like that to spell that one i think it's that way uh and then the dark blue so this one is our s-curve so this would suggest that you get the most benefit or the most increase in wing flap frequency in this kind of middle region of air temp it's not very responsive at low temperatures and it's not very responsive at high temperatures you can see we're starting to get qualitative analysis out of it so that's our s-curve and then the pink one means that it's completely unaffected by air temperature right there's no gradient the gradient is zero so that means that the wing flap frequency remained constant regardless of the fluctuation in air temp so that is we'll just say zero gradient which we can make the assumption then that temp is unrelated to frequency for that particular species of that particular graph and then a slightly different one i thought i'd do this on a separate axis is a kind of distribution curve so here we have enzyme activity over ph range and so what we're more interested in here are the turning point right so turning points represent maximums and minimums that is our key feature anything where it's zero means the activity is nothing and it's not working very well but we just want to understand what the position of that is and that will then tell you something about the optimum ph for that particular enzyme and so these are the three things that i'd be looking for when i get a two variable graph is slope are there turning points and are there any points where it plateaus or flattens out as well and understanding what that means in the context of the question the next one is comparative line graphs these ones do catch a lot of people out i know i got tricked by a lot of the axes and things in my practice on these so i've tried to mock up a simple example of this this is where you have three or more variables to deal with so although you're limited to just the x and the y axis they can then create these fanning lines that bring in a third variable in this case i've gone with oxygen oxygen saturation of blood against temperature and velocity and so pretty much what you want to do here is wait for the question to guide you on what you're actually looking for and it may say something about like you know 4 20 oxygen saturation right so it's holding that variable constant what that means is stick on the 20 line and don't look at anything else then it might say at a temperature of 10 degrees or something and it might be here and you go up and then it asks you for the velocity and you can read out like that or vice versa right so the idea is that you hold one of the three variables constant and then you test the relationship between the remaining two the graph is there to just disguise it and confuse you into thinking you have to be paying attention to more variables if they're just getting you to locate a point then they may just give you information about all three and you literally just kind of map it and point to it those are probably the easier ones and you won't see many of those if instead they're saying for a particular temperature that is where we would use a vertical line and hold the temperature constant at whatever temperature it is and then what we can do is we can test the impact of one variable on the other so if i want to increase velocity and see what that does to oxygen saturation and i effectively just bounce from low i always go from low to high i always try to increase one variable and then see what happens to the other so low to high velocity what does that do to oxygen saturation at this particular fixed temperature it starts down here so it starts at 100 and then it seems to jump as i jump up the line because i'm following the orange arrow i'm bouncing onto new oxygen saturations and i can see that's a decrease so now i know there's a negative relationship between velocity and oxygen saturation like that i could do the same thing if i wanted to hold velocity constant so say this was a bird flying at 20 meters per second or something that's crazy fast but we'll go with it 20 maybe that's here i would now hold this constant instead and let me just highlight that hold this constant and i might want to see what the temperature does to the oxygen saturation so in that case i'm going to increase the temperature at this fixed velocity and now what's going to happen is i'm going to start at 20 and then i can see that as i run along the red line it's jumping to higher and higher oxygen saturations so that means there's a positive relationship between temperature and oxygen saturation in that case you can also reverse it so you can look at like what's the impact of oxygen saturation on velocity as well although there may be a bit of like cause and effect relationship that's being reversed there but um so at a particular temperature i might hold the temperature constant here and then if i ink if i that would be decreasing it that way so i might go this way so i want to again increase the oxygen saturation and see what happens to velocity so i have to basically bounce from here to here here to here and here to here so as i increase oxygen saturation velocity i'm on this axis here goes down so there's a negative relationship between them which we proved before anyway there was a negative relationship velocity to oxygen sat so reversing it would have the exact same effect as well cool and so this is what i refer to when i talk about vertical line testing horizontal line testing and so on um another way to do it is you can actually take the the line itself and you can kind of drag across like this and you can see what happens to each of the variables then we also have some other ones like this so in this case all linear three different species uh and we're looking at water salinity in ppms this might be fish in parts per million and then velocity in meters per second maybe swimming velocity so you can use concepts from something called linear programming if you were trying to work out uh the ranges over which you had the fastest species the quickest way to do it is just kind of scan along the top end here so we can go like this and i'll switch colors each time as soon as you switch lines switch colors i mean obviously you wouldn't have that luxury in the real thing but there we go and then you can just map who's better at what so basically the fastest swimmer from here to here say this was eight degrees and this was 12 degrees from zero through eight the fastest swimming species is species c from eight through twelve the fastest species is i follow the yellow line species b and then species a is better in higher temperatures so on they might have a question about like tropical water or this or that and yeah well probably the green species a swims fastest like that and this is how we can kind of very very quickly break down the graph intersections you could do the same thing for lower you can see on the lower end one of the species does not get involved so you could use this as a reasoning as to which species is on average the fastest swimmer and so that would be the one that does not get involved so up here that would be species b seems to never really be at minimum velocity so that would probably be the all-rounder overall and then finally as well you can look at points of intersection so this is where not only are the variables equal but it also means that there's a point of indifference yeah so if there was a choice between two species we would be indifferent in our choice it's a good way to think of it i'm not really sure what the context of that would be but keep in mind point of intersection is also a point of indifference and then vertical separation so vertical separation you're looking at the deviance or the uh the difference between them so if for example they said at what temperature are species a and b most different from one another in terms of their velocities i'd effectively be going all right well species a which is this line here and species b i think i said or species c let's go with species c i can't remember where are they most different so i'd be looking at this vertical separation because that is the difference clearly through this middle section they're very very close together further away they've got larger larger differences so visually it looks like either at 0 degrees down here or all the way up here looks about equivalent let's just call that 30 degrees at extreme temperatures they seem to differ most they seem to be more similar in kind of middle run temperatures of maybe 15 degrees then we have distribution curves so distribution curves i mentioned those before with enzyme activity so you can also have them in physics questions relating to wavelength of light and the absorbance of that light and a couple of different examples the only things you really want to look for here are the position of the maximum point and the spread of the data as well the spread of the graph so you can if you want to compare the absolute values or positions just go for the maximums this would be x1 this would be x2 so clearly the blue graph has a higher wavelength of absorbance spread analysis is about how wide the the graph is so in terms of which one is more adaptable to absorbing different types of light that would be the blue graph so it seems to be the winner all around if that was to be a good trait it's much much wider through kind of the majority of it also and the same thing if i do it with the red it's clearly not spanning as big of a range of wavelengths so it's a little bit more specific those are the only things you need in any kind of distribution bell curve and then grouped bar charts so we're all familiar with bar charts i think but group bar charts is some tricks to reading these really really quickly so the first thing is you can isolate a group so if the question is just in relation to one group focus just on that group and ignore everything else it's often just about pulling out the right information without getting overwhelmed by the amount that's in front of you so say this was some kind of experiment about plants and you've got those in light those in dark those in a bit of both and then we've got two variables negative will mean that the variable is absent and then positive would mean the variable has been added so effectively two independent variables with one control group being this here and then you've got a bunch of experimental groups repeated and then we're seeing the impacts on survival rate in percentage we don't need another any more context to that so if we got a question about those in light and comparing the impacts of the variables stick here and then look at what's happening so from the control we can see that adding variable 2 cause an increase adding variable one cause an increase which technically i guess should go from here to here so both variables caused an increase individually however it caused a decrease when you add both as well so there's some kind of connection there and you could answer a question just on that so that is group isolation then um probably should have done that in red let me color code this that should be in red let's do it in blue now so connecting the tops so i've kind of done that there um if i wanted to understand the relationship between them then you can see i just did this and that helps me just understand increase decrease that kind of thing and then error bars i haven't got those shown on here but as long as we know how to read them an error bar might look like that it's a relative accepted deviance around our data based on some error margins within our calculations so it means that although we've measured it to this point it may actually in fact sit up to this high or a little bit lower as well and there'll be some confidence interval associated with that as long as you understand that taller error bars means less trustworthy data and shorter error bars means much more reliable and trustworthy data like that and then isolating specific bars so you might instead want to do an analysis of this variable the light presence right and so what you would have to do is to hold everything else constant is isolate one of them so for example you could take the control and then it's effectively staying flat and then from here here oh actually that's not it decreasing and then we can understand a relationship there for the control in that case it means that um light or dark makes no impact mixing the two seems to not be good for survival rate for whatever reason wouldn't make any sense for a plant but i've just made this data up if we do another one and again i've not stuck to my color coding let's go to purple we might do for example the the second bar here where the second variable has been added so what happens as we add or take light away it seems to not have any impact again and then there's a slight decrease so we've got a consistent relationship then i might go for this one so what about when we add just the third variable that one seems to be completely different right so that one seems to be impacted and then there's the same old decrease so we can start to understand then that any changes in this group probably due to the first variable because the third bar which had the first variable added without the second one explained it and the second bar explained that the second variable had no significant impact relative to the control and that allows you then to isolate individual elements and then understand the relationship as well so isolating specific bars then we have stacked bar graphs so again just being mindful that to read them you're actually just looking for the widths of each section so if you the green one for example relatively easy just connect the tops and bottoms like that and you can clearly see that it's getting bigger so there's an increase overall if we look then at the purple though and we connect tops and bottoms look at the width of it don't look at the actual direction that the graph is going in and you can see here the first two are effectively running parallel to each other which means there's no change and then here they're cinching in so that means that there's a decrease and then cinching and again decrease so no change here but then decrease and decrease through there so a general decrease um whereas a general increase here and then this one we can just go right across the top there and we've already done a lot of the work we can see that seems to be a bit discontinuous or it seems to be a bit inconsistent it decreased then increased and so on you can get qualitative analysis just like that really really quickly sinusoidal graphs again more of a physics thing you'll see them in ac voltage sound waves any kind of transverse waves as well uh harmonics glottal pulse we saw that in some of the practice material and respiratory volumes as well from some physiology all we need to again understand is just some of the key features we're looking for amplitude which is the deviation from the center to the maximum or the deviation from the center to the minimum but not the whole way across the whole way across is two times the amplitude so be very careful about that unless it specifically defines the amplitude as being maxed to min that's not a standard thing though and then the period of the graph is the width of it before it starts repeating its sections so if i was to continue this graph you would see a complete carbon copy of that section and then it would just just do this it would just keep repeating and so we can chop it up into repeating cycles and the width of that is one period and if this is measuring time then frequency is one divided by the time interval of one of those periods so if this was 10 seconds for example then it frequency would be one on 10 and that is measured in hertz like that and those are the two things you can usually answer the questions just based on qualitative analysis of those two features of the graph and then finally so then we've got these pseudo-ternary phase diagrams used a lot in chemistry and maybe in some biochem type stuff as well looking at effectively the composition of a compound into three different groups you can have more complex ones with pentagons and that kind of thing i've not seen those being used in gamsat they could but the principles are the same so what you want to do first is make sure that you use a known point that they give you to understand how to read the graph if they don't give you that you can usually work it out by picking a random point try not to pick one in the center try to pick one where the numbers won't all be the same so i've picked one here and effectively you can just branch out in three directions and you have to go to all three walls of the triangle until the proportions uh add up and they should also not run in the same direction as each other so that one can't work you can see i've already run myself into a problem i can't go this way i can go that way but then that hits that wall so that's not going to work and you effectively just learn how to get it to there we go hit all three walls and then you check point two point four and point four that all adds up to one hundred percent effectively so that means this is the way that i'm gonna read it i'm gonna leave that on there and on the scratch paper i'll just scribble down a triangle with just a line so just like this without all the detail and just go like that oh a little bit wrong like that so i remember how to read it and so then they might talk about well if something is uh to have you know uh point four of class one point two of class two and then something of class three i don't know if this is going to work then i would go okay well that would mean i'll go a different color pink class 1 0.4 then class 2.2 oh i've picked that one there we go and then the third one left i have to go in this direction points me at 0.4 again you can do it in a different way so let's say this is uh 0.6 and this is 0.2 then i would go 0.6 0.2 so i'd line it up and i just run a line right across like that and then uh 3 this would have to be the leftovers which would also have to be 0.2 and then i can see there they actually don't cross which means that is actually not a possible compound in that case and this is effectively how you read them most of the time they'll get you just to find the point or read the axes off of a given point to know the proportions of three different compounds or three different uh ingredients in a chemical compound there we go so that is pretty much everything that's like my rundown of all the things i may have missed some graphs but i've gone through all of the material uh how to think about what i've seen in past exams and stuff as well there may be some things particularly the bar graphs you may be able to use that in section one they sometimes have some qualitative analysis in section one with some graphs so that might be helpful there as well but uh yeah hopefully this is helpful uh general tips scan the axes check for the scales check they're not alternating them or changing them think about what is the slope and what is that telling me area under the graph as well are the three key things then in terms of all of the different graphs they each have unique features something that you can probably make a cheat sheet on have that with you and practice and then start to remove that as well as you get more and more comfortable with them and maybe adapt that cheat sheet based on mistakes that might happen as well cool all right um i think this one has gone on longer than i wanted it to so i'm going to cut it there and then i will see you in the next one [Music] you