sat virtual reality ii explanations phần 1 pot

Section (Math) SAT Virtual Reality II 1 A Here we have a basic algebra question The important thing to remember here is that when solving an algebraic equation, you have to the same thing to both sides of the equation You’re given an equation with 4x + on the left side of the equal sign and the question stem asks about 4x + What you have to to 4x + to make it look like 4x + 8? Right, just add But since you’ve added to the left side of the equation, you have to add to the right side of the equation also, since you have to DO THE SAME THING TO BOTH SIDES! Adding to the right side of the equation gives you 26 + 6, or 32, answer choice (A) A more mathematical way of expressing what we just did is to write it out like this: 4x + = 26 +6 +6 4x + = 32 E You have to know a few facts about geometry here, and if you don’t, you might want to some review in your Math Reference Book First, you have to know that the word “bisects” means “cuts in half.” So, if line EX bisects angle BXD, it cuts angle BXD into two equal halves The diagram shows that angle BXE is 30˚, and since it is half of angle BXD, angle BXD must equal 60˚ Now that we’ve found the degree measure of angle BXD, we can find the degree measure of angle CXB Angles CXB and BXD are supplementary angles because they from line segment CXD So angle CXB plus angle BXD equals 180˚ Since angle BXD is 60˚, angle CXB equals 180˚ – 60˚ or 120˚ C Here you have to know an important concept that appears fairly often on the SAT — that when two quantities multiplied together equal 0, one or both of those quantities is equal to What that means in this question is that either x – = or x + = or they both equal If x – = 0, what does x equal? Just add to both sides of that equation to get x = And the same thing for x + = to get x = –5 So (x – 2)(x + 5) = when x = or x = –5, choice (C) You could also have solved this one by backsolving, or trying each answer choice in the question You need to find all the possible values of x that make the given equation true There are four numbers mentioned in the answer choices, in various combinations They are –5, –2, 2, and If x = –5, is the equation true? Yes, the equation is then (–5 – 2)(–5 + 5) = (–7) × = So, choice (A) is a possibility, but you can’t be sure if it’s right because you’re looking for ALL the values of x that make the equation true However, since –5 does work, the answer choice must contain –5, so it must be (A) or (C) What about 2? (2 – 2)(2 + 5) = × = 0, so if section one Even if you’ve forgotten most of what you ever learned about geometry, you can eliminate two answer choices by just eyeballing the figure Figures are drawn to scale on the SAT, so you can assume that the angle measurement is about what it looks like You should know what a 90-degree angle looks like — the corner of this piece of paper Angle CXB in the figure is clearly greater than 90˚, so choices (A) and (B) can be eliminated So you could guess among answer choices (C), (D), and (E) x is 2, the equation is also true Therefore, the correct answer choice must have both and –5 so it’s choice (C) If you try plugging –2 or into the equation, you’ll see that they don’t work section one C Inequalities are very similar to equations The only difference between them is that if you multiply or divide both sides of an inequality by a negative number, you must reverse the sign Here you have inequalities, which you can solve the same way as you would solve an equation In the first inequality you can subtract from both sides: a+2>5 –2 –2 a>3 The second inequality is similar It can be solved by adding to both sides: a–4 c (that’s just a way of saying that the sum of any two sides is greater than the third) Then adding a to both sides of the inequality gives us a + a + b > c + a, or 2a + b > c + a But if 2a + b is greater than c plus something, then 2a + b is also greater than c and thus can’t be equal to c, so choice (C) is wrong Choice (D) has similar problem, since it reduces to c = a + b + 1, and we know that c is less than a + b, so it can’t be equal to more than a + b Choice (D) is wrong, so we’d better hope that choice (E) works (E) reduces to c = a + b – 1, which looks good We know that c is less than a + b, so it could equal less that a + b, and choice (E) is correct 25 C What this question is really asking is — how many pairs of teams can you make from a group of teams? One way to it is to just create those pairs yourself Let’s call the teams A, B, C, D, E, F, G, and H You then have to pair up every team with every other team Starting with team A, you can create the pairs AB, AC, AD, AE, AF, AG, and AH You’ve created pairs of teams by pairing up team A with each of the other teams You can the same with team B, except that you don’t pair team B up with team A, since you’ve already done that (The pair BA would be the same as the pair AB.) So you just pair team B up with the teams that come after it in the alphabet to create BC, BD, BE, BF, BG, and BH, for a total of more pairs Do you see a pattern here? We created pairs starting with team A, with team B, so we’ll get more from C, from D, from E, from F, and then when we finally get to team G, there’ll only be one team left, team H, to create a new pair So, the total number of pairs of teams is + + + + + + = 28 Since each pair of teams plays games, the total number of games is × 28, or 112, choice (C) section one 24 E ... thought it was –6, but –6 is less than –5 .1 (It is to the left of –5 .1 on the number line) So 5 .1 – –5 .1 = – (–5) = + = 11 , choice (B) 23 C SAT Virtual Reality II 10 This is a complicated triangles... between ᎏ and ᎏ 4 12 A SAT 53 57 Virtual Reality II ᎏ = 13 ᎏ and ᎏ = 14 ᎏ , so the average must be greater than 13 ᎏ and less 4 4 than 14 ᎏ There’s only one answer choice that fits, 14 , choice (E)... but just for the fun of it you can try the other 3: (C) (D) (E) 14 + 2(6) = 14 + 12 = 26 14 + 2(7) = 14 + 14 = 28 14 + 2(9) = 14 + 18 = 32 not a multiple of not a multiple of not a multiple of