Explanation for Question 4 From the Math (No Calc) Section on the Official Sat Practice Test 9
Okay. Question four reads the front of a rollercoaster car is 2 at the bottom of a hill and is 15 feet above the ground. 3 If the front of the rollercoaster car rises at a constant rate of eight 4 feet per second, which of the following equations gives the height H in feet 5 of the front of the rollercoaster car, as seconds after it starts up the 6 hill. So let's do a quick little sketch. 7 This is a word problem, and it can sometimes help to visualize what is 8 physically going on. So let's call this point. 9 Let's imagine that this is the front of the rollercoaster car. 10 It's at the bottom of a hill and it's 15 feet above 11 the ground. So let's say that this is the ground. 12 This is the front of the car. It's 15 feet from the ground, 13 but it's at the bottom of a hill that goes up like this. 14 If the front of the rollercoaster car rises at a constant rate of eight 15 feet per second, which the final equations gives the height of the front of 16 the car. Okay. So we know that it's rate up this hill is going 17 to be eight feet per second. 18 And hopefully this is starting to look a little bit like a graph in 19 the X, Y plane. So we can see that it's initial height is 15 20 feet, and let's call that our Y intercept. 21 And then we can see that it's rate of height gained essentially 22 is eight feet per second. So let's call that our slope. 23 And then with those two components, we can write an expression that looks much 24 like that classic slope intercept form Y equals MX plus B, 25 but this time our, why is H the total height. 26 So if H equals MX plus B, except 27 the X here is actually going to be S the number of seconds. 28 So we have H is equal to the slope, 29 which is eight feet per second times. 30 The number of seconds, which is S plus that 15 feet that starts 31 off with sort of H equals eight times us plus 15. 32 And that is going to get us answer choice a.