CHAPTER 6 / WHAT THE SAT MATH IS REALLYTESTING 251
- D Begin by simplifying ^3 −^2 by substitution:
But be careful not to pick (A) becauseNotice that the choices must be evaluated first be-
fore we can see which one equals 1/6. Notice that
choice (D) is- 1 Begin by simplifying ^^kby substitution:
Yikes! That doesn’t look simple! But think about
it: why is it that kcan’t be 0? Because division
by 0 is undefined, and kis in a denominator. But
notice that is also in a denominator, so
can’t be 0, either!Solving:Add :Multiply by k: k≠ 1
Then check by noticing that ^^1 is undefined:
^^1 =^(1 −1/1) =^0 = 1 −1/0, and 1/0 is undefined.1
1
−
k1
k1
1
−≠ 0
k1
1
−
k1
1
−
k∧∧ =−∧⎛
⎝⎜
⎞
⎠⎟=−
−
k
k
k1
1
1
1
1
1
∧65 1 56 16.=− =
∧16 1 6=− =− 5
∧ 16
∧∧3 2 1 13 1 12 2 3 12 16−=−()−−()=−=
Concept Review 4
− 2 n−(6 − 5 n) −n=− 2 n− 6 + 5 n−n= 2n− 6
3.
4.
5.
- Substitute y= 1 −xinto 2y+x=5 to get
2(1 −x) +x= 5
xx x x x^634 =× =6410
2
6
2
4
2
10
2
325
32 3 2
xx x 2
xx
xx
xx
xxx++
=++=++
21
2
4
22
4
xx 2x
xx
x+=+=
+
218
23
23 3
31
(^223)
2
x
xx
xx
xx
x
x
−
+−
=
()− ()+
()+ ()−
=
()−
()−− 1
Distribute: 2 − 2 x+x= 5
Simplify: 2 −x= 5
Subtract 2: −x= 3
Multiply by −1: x=− 3- 3 +m+n=n^2 +m^2
Subtract nand m: 3 =(n^2 −n) +(m^2 −m)
Substitute:- <<4>>
Substitute for <4>: =<(1 −4)^2 >
Simplify: =<(−3)^2 >
Simplify: =<9>
Substitute for <9>: =(1 −9)^2
Simplify: =(−8)^2
Simplify: = 64
nnmm^22
63
6
1
2
()− +−()
==
Answer Key 4:Simplifying Problems
SAT Practice 4
- E Subtract the equations: 3 y− 4 z= 6
- C Add the equations:
(a+b) +(a+c) +(b+c) = 3 + 5 +− 6
Simplify: 2 a+ 2 b+ 2 c= 2
Divide by 2: a+b+c= 1 - D Start by simplifying the expressions:
Substituting into the original equations givesSubtract 1:Divide the fraction:Simplify:Simplify:
b
c= 2
a
cb
a×= 2
a
cc
a
b=
4
2
a
ba
c== 24 anda
ba
c+= 13 and += 15ab
ba
bb
ba
bac
ba
cc
ca
c+
=+=+
+
=+=+
1
1
−+=( )
−=−
210
54
yz
yz