Answer Choices
2
6
sqrt(2)
sqrt(6)
Explanation for Question 15 From the Math (No Calc) Section on the Official Sat Practice Test 7
Question 15 says the expression one-third X squared minus two. 2 It can be rewritten as one-third times X minus K times X plus K, 3 where K is a positive, constant. What is the value of K? 4 So I'm just going to start by distributing. So from that I get one 5 third times X, which is one third X plus negative 6 one-third K or one third times. 7 Negative K. And then this has to be multiplied by X plus K. 8 So next I'm going to do one third X times X, 9 which is one third X squared, 10 plus one third X squared, 11 K plus negative one third, 12 a X K, 13 or sorry that last one should just be a X. 14 K should be X squared, K plus negative. 15 One-third K squared. 16 These two middle terms cancel out. 17 And that gives us one third X squared plus negative 18 one-third K squared is equal to one third 19 X squared minus two. So since these two terms 20 cancel out, we can rewrite this as negative one-third K squared is equal 21 to negative two. And from there we can solve for K. 22 So first I'm going to multiply both sides by negative three, 23 and that's going to give me K squared is equal to six and that 24 finally I can square both sides. 25 And that gives me K is equal to route six, 26 which is answer choice.