SAT Mc Graw Hill 2011

CHAPTER 7 / ESSENTIAL PRE-ALGEBRA SKILLS 273

Concept Review 1

1.−10 (Remember: “greatest” means farthest to the

right on the number line.)

2.−10/1, −20/2, −30/3, etc. (Fractions can be integers.)

3. If the original number is negative, then taking a
   square root doesn’t “undo” squaring the number.
   Imagine that the original number is −3. The
   square of −3 is 9, but the square root of 9 is 3. This
   is the absolute valueof the original number, but
   not the original number itself.


4. 22 (16 + 18 + 20 + 22 =76. Just divide 76 by 4 to
   get the “middle” of the set =19.)


5. Infinitely many (If you said 3, don’t assume that
   unknowns are integers!)


6. sum


7. difference


8. product


9. 21 ((12 ×3) −(12 +3) = 36 − 15 =21)

10.+(−6) 11. ×(1/4) 12.÷(−3/5) 13. ×(7/6)

14.+(6) 15. ×(4) 16. ÷(−5/3) 17. ×(6/7)

18.−13 (If you said −5, remember to do multiplica-

tion/division from left to right.)

19. 
    


20. 50
    21.− 4


21. Circle all numbers except and underline
    only 0, ,and 56/7 (=8).


22. PG-ER-MD-AS (Parentheses/grouping (left to
    right), exponents/roots (left to right), multiplica-
    tion/division (left to right), addition/subtraction
    (left to right))


23. Fraction bars (group the numerator and denom-
    inator), and radicals (group what’s inside)


24. 120 (It is the least common multiple of 5, 6, 8,
    and 12.)


25. Step 1: subtract 7; step 2: divide by 3; step 3: take
    the square root; x=3 or −3 (not just 3!)

25 ()= 5

− 7

Answer Key 1: Numbers and Operations

SAT Practice 1

1.C^5 ⁄ 2 is not^1 ⁄ 3 of an integer because

(^5) ⁄ 2 × 3 = (^15) ⁄ 2 =7.5, which is not an integer.
2.C 48 = 6 × 8
3.

4.D

Add 3:

Square: k= 121

5.B (4 ×3) +(2^1 ⁄ 2 ×2) = 12 + 5 = 17

6. 3 3 x+7 > 13 and x−5 < − 1
   3 x> 6 and x< 4
   x> 2 and x< 4

k= 11

k−= 38

C 1113 1112

11 2 1

()−−−()()−−−−()()()

=−−−()()()−−−−−()()()

=−()−−()

=− − −()

=− +

=−

11

13 12

21

21

1

7.D −5 is the least (farthest to the left on the num-

ber line) of all the integers that are greater than

(to the right on the number line of) −5.6.

8.A Dividing by^3 ⁄ 4 is equivalent to multiplying

by^4 ⁄ 3 :

x÷^3 ⁄ 4 ×− 2

=x×^4 ⁄^3 ×−^2

=x×−^8 ⁄ 3

9.4.5 6 x− 14 = 40

Add 14: 6 x= 54

Divide by 6: x= 9

(Don’t forget to find halfthe number!)

10.C 9,876 −1,023 =8,853

Don’t forget that 0 is a digit, but it can’t be the first

digit of a four-digit integer.

11.D You might “plug in” increasing values of xto see

whether the expressions increase or decrease. 1 and

4 are convenient values to try. Also, if you can graph

y=1/x^2 , ,and y= 10 −^1 ⁄xquickly, you might

notice that ,and y= 10 −1/x“go up” as you

move to the right of 1 on the x-axis.

yx=

yx=