SAT Mc Graw Hill 2011

CHAPTER 6 / WHAT THE SAT MATH IS REALLYTESTING 255

3. 1.8 Key formula: The Pythagorean theorem:
   c^2 = a^2 + b^2. Key theorem: In similar triangles, cor-
   responding sides are proportional. Notice that the
   figure has two right triangles, and they are similar.
   The hypotenuse of the bottom triangle is 5 because
   32 + 4^2 = 5^2. Therefore, the hypotenuse of the top
   triangle is 8 −5 = 3. Since the two triangles are
   similar, the correspondingsides are proportional:

Cross-multiply: 5 h= 9

Divide by 5: h= 1.8

3

53

=

h

Concept Review 5

1. The Pythagorean theorem: In a right triangle, if
   cis the length of the hypotenuse and aand bare
   the lengths of the two legs, then c^2 =a^2 +b^2
   (Chapter 10, Lesson 3).


2. The zero product property: If a set of numbers has
   a product of zero, then at least one of the numbers
   is zero. Conversely, if zero is multiplied by any
   number, the result is zero (Chapter 8, Lesson 5).


3. The parallel lines theorem: If a line cuts through
   two parallel lines, then all acute angles formed
   are congruent, all obtuse angles formed are con-
   gruent, and any acute angle is supplementary to
   any obtuse angle (Chapter 10, Lesson 1).


4. The rate formula: distance (or work)=rate×time
   (Chapter 9, Lesson 4).


5. The average (arithmetic mean) formula:
   Average=sum÷number of things(Chapter 9,
   Lesson 2).
   6. The definition of the median: The “middle num-
   ber” of a set of numbers when they are listed in
   order. If there are an odd number of numbers, the
   median is the “middle number,” and if there are
   an even number of numbers, it is the average of
   the two middle numbers (Chapter 9, Lesson 2).
   7. The definition of the mode: The number that ap-
   pears the most frequently in a set (Chapter 9,
   Lesson 2).
   8. The circumference formula: Circumference= 2 πr
   (Chapter 10, Lesson 5).
   9. The circle area formula: Area=πr^2 (Chapter 10,
   Lesson 5).


6. The triangle area formula: Area=base×height/2
   (Chapter 10, Lesson 5).

Answer Key 5:Connecting to Knowledge

SAT Practice 5

1. C Key formula: Average=sum÷number of things.

So if xis the average of kand 10, then.

And if yis the average of kand 4, then y=.

The average of xand y,then, is

2. D Key formulas: Number of cars=rate×time,and

Since xis the number of cars

and yis the time in hours, the rate is x/ycars per

hour. Using the first formula, then, the number of

cars that would pass in zhours is

You should notice, too, that simply plugging in

values for x, y,and zcan make the problem easier

to think about. Say, for instance, that x=10 cars

pass every y=2 hours. In z=4 hours, then, it

should be clear that 20 cars should pass by. Plug-

ging these numbers into the choices, you will see

that (D) is the only one that gives an answer of 20.

xy z

xz

y

()cars per hour()hours=

rate

number of cars

time

=.

kk

kk k k

+

+

+

=

+

+

+

=

+

=

+

10

2

4

2

2

10

4

4

4

214

4

7

2

k+ 4

2

x

k

=

+ 10

2

3 feet

4 feet

8 feet

3 feet h feet

5 feet