The sat math section 6 ppsx

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 expres￾sion 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 expres￾sion 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 sim￾plified to lowest terms.

26. d. This is a word problem involving geometry

and figures. The best way of solving a prob￾lem 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 tri￾angle. 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

The answer is choice d.

Note: You could easily solve this equa￾tion if you recognize that this right triangle is

a Pythagorean triplet. It is a 5-12-13 right tri￾angle and 12 feet had to be the length of leg 2

once you saw that 5 feet was leg 1’s length and

13 feet was the length of the hypotenuse.

27. b. You can outline all the possibilities that can

occur. First, you have either boys or girls at

the party. You also know that they are either

wearing a mask or not wearing a mask.

Therefore, you can start outlining the possi￾ble events.

You are told that 20 students did not

wear masks. In addition, you know that 9 boys

did not wear masks. Therefore, calculations

tell you that 11 girls did not wear masks.

Now, if 11 girls did not wear masks and

7 girls did wear masks, then 18 girls attended

the party.

5 feet

x feet

13 feet

–THE SAT MATH SECTION–

167

5658 SAT2006[04](fin).qx 11/21/05 6:44 PM Page 167