SAT Mc Graw Hill 2011

334 MCGRAW-HILL’S SAT

Concept Review 1:

New Symbol or Term Problems

For questions 1–6, translate each expression into its simplest terms, using the definition of the new symbol.

The following definition pertains to questions 1–3:
For any real number x,let §xbe defined as the greatest integer less than or equal to x.

1. §−4.5 = __

2. §−1.5 +§1.5 = __

3. = __

The following definition pertains to questions 4–6:
If qis any positive real number and nis an integer, let q@ nbe defined by the equation.

4. 8 @ 3 = __


5. 9 @ (k−1) = __


6. x^2 @ 0 = __


7. If qis any positive real number and nis an integer, let q@ nbe defined by the equation.

If y@ 2 =64, what is the value of y?

8. For any integer nand real number x,let x^ nbe defined by the equation x^ n=nxn−^1. If y^ 4 =−32, what is
   the value of y?


9. For any integer n,let Ωnbe defined as the sum of the distinct prime factors of n.For instance, Ω 36 =5, because
   2 and 3 are the only prime factors of 36 and 2 + 3 =5. What is the smallest value of wfor which Ωw=12?

qn q

n

@ =

+ 1

qn q

n

@ =

+ 1

§§ 15 + 17