tailieunhanh - The sat math section 6

Tham khảo tài liệu 'the sat math section 6', ngoại ngữ, anh ngữ phổ thông phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | THE SAT MATH SECTION 25. c. You have to factor this expression accord- ingly. Notice that there are only two terms and there is a subtraction sign between them. Sometimes that is a clue to try to factor using the difference of two perfect squares technique. However in this case 3x2 and 27 are not perfect squares. Therefore you have to try a different method. First notice that there is a common factor of 3 in both terms. Factor this term out of both terms. Once you do the expression is 3 x2 - 9 . The job is not done. You have to factor COMPLETELY Look at the expression x2 - 9 . This is a binomial with two perfect squares separated by a subtraction sign. Thus this binomial can be factored according the difference of two perfect squares. The expression now becomes 3 x 3 x- 3 . The answer is choice c. If you are not careful you may select one of the alternate choices. Remember factor completely and do not stop factoring until each term is simplified to lowest terms. 26. d. This is a word problem involving geometry and figures. The best way of solving a problem like this is to read it carefully and then try to draw a diagram that best illustrates what is being described. You should draw a diagram similar to the one below. You are trying to find out the height of the ladder as it rests against the house. This height is represented as x. The ground and the house meet at a right angle because you are told that it is level ground. This makes the diagram a right triangle. Thus in order to solve for x you have to use the Pythagorean theorem. Remember the Pythagorean theorem is a2 b2 c2 where c is the hypotenuse or longest side of a right triangle. It can also be written as leg 1 2 leg 2 2 hypotenuse 2. In this case the ladder is 5 feet from the house. This distance is leg 1 or a. The ladder is across from the right angle. This makes it the hypotenuse. The hypotenuse or c is 13 feet. Thus you have to solve for leg 2 or b the following way. 52 b2 132 25 b2 169 b2 144 b 12 feet