Explanation for Question 10 From the Math (Calc) Section on the Official Sat Practice Test 8
So question number 10 is telling us that we are filling up this glass 2 right here with water, and they want to know what a graph of the 3 height of the water level would look like over time. 4 If we fill up this glass at a constant rate. 5 And so this question is actually pretty subtle, 6 right? Because when we see constant rate, our initial thought might be a linear 7 graph because if something goes up constantly and the rate never changes, 8 that's kind of like saying the slope never changes. 9 And so if you're thinking about a constant rate, usually it's safe to assume 10 that this graph is linear, but in this case that's not going to work 11 a is not going to be our correct answer. And we get that by 12 looking closely at the shape of the cup. 13 So if you look at the shape of the glass, we see we have 14 a small diameter at the bottom and a big diameter at the top. 15 And the consequences of this is that when we pour water into the glass, 16 we're going to gain height quickly at the bottom. 17 So again, height fast at the bottom, but then once we get to the 18 top, the water has to cover more horizontal distance before it can build upwards. 19 So we actually gain height more slowly at the top of the cup. 20 And now the graph that shows that relationship gaining height quickly, 21 and then leveling off and gaining height more slowly is going to be see, 22 right? We see a real quick burst here at the beginning. 23 And then things start to level off showing that slower growth of height. 24 He actually shows the opposite relationship. It shows slow growth of the height initially, 25 and then fast at the end, which we know can't be the case because 26 we have the larger diameter at the top of the cup. 27 So B doesn't make sense. And then finally D is perhaps the easiest 28 one to eliminate because the shows that the height of the water never changed. 29 And we know that can't be the case because we've added water to the 30 cup. So our best answer is going to be C.