SAT Mc Graw Hill 2011

CHAPTER 8 / ESSENTIAL ALGEBRA I SKILLS 315

SAT Practice 4: Working with Roots

1. The square root of a certain positive number is
   twice the number itself. What is the number?

(A) (B) (C)

(D) (E) 1

2. If what is one possible value of x?


3. If a^2 + 1 =10 and b^2 − 1 =15, what is the greatest
   possible value of a−b?
   (A) −3(B)− 1 (C) 3
   (D) 5 (E) 7


4. If , then y^3 =

(A) (B) (C)

(D) (E) 18

5. If x^2 =4, y^2 =9, and (x−2)(y+3) ≠0, then
   x^3 +y^3 =
   (A) − 35 (B) − 19 (C) 0
   (D) 19 (E) 35

4

3

2

3

4

9

2

9

3

2

y

y

=

1

2

xxx<<,

1

2

3

8

1

4

1

8

6. If mand nare both positive, then which of

the following is equivalent to

(A)

(B)

(C)

(D)

(E)

7. A rectangle has sides of length cm and

cm. What is the length of a diagonal of the

rectangle?

(A)

(B) a+ bcm

(C)

(D)

(E)

8. The area of square Ais 10 times the area of
   square B.What is the ratio of the perimeter of
   square Ato the perimeter of square B?
   (A) (B)
   (C) (D)
   (E) 40:1


9. In the figure above, if nis a real number greater
   than 1, what is the value of xin terms of n?
   (A)
   (B)
   (C)
   (D) n− 1
   (E) n+ 1

n+ 1

n− 1

n^2 − 1

10 :1 410 :1

10 : 4 10 :2

abcm

ab^22 + cm

ab+ cm

ab+ cm

b

a

8 n

6 n

4 n

6 mn

3 mn

218

2

mn

m

?

n

1

x

....

1 2 3 4 5 7 8 9

6

1

0 2 3 4 5 7 8 9

6

1

0 2 3 4 5 7 8 9

6

1

0 2 3 4 5 7 8 9

6