## SAT SUBJECT TEST MATH LEVEL 2

## PART 2

## REVIEW OF MAJOR TOPICS

## CHAPTER 1

Functions

###

1.2 Polynomial Functions

### INEQUALITIES

Given any algebraic expression *f(x*), there are exactly three situations that can exist:

**1.** for some values of *x*, *f(x*) < 0;

**2.** for some values of *x*, *f(x*) = 0;

**3.** for some values of *x*, *f(x*) > 0.

If all three of these sets of numbers are indicated on a number line, the set of values that satisfy *f(x*) < 0 is always separated from the set of values that satisfy *f(x*) > 0 by the values of *x *that satisfy *f(x*) = 0.

**EXAMPLE**

**Find the set of values for x that satisfies x^{2 }– 3x – 4 < 0.**

Graph *y *= *x*^{2 }– 3*x *– 4. You need to find the *x *values of points on the graph that lie below the *x*-axis. First find the zeros: *x *= 4, *x *= –1. The points that lie below the *x*-axis are (strictly) between –1 and 4, or –1 < *x *< 4.

**EXERCISES**

1. Which of the following is equivalent to 3*x*^{2 }– *x *< 2?

(A)

(B)

(C)

(D)

(E)

2. Solve *x*^{5} – 3*x*^{3 }+ 2*x*^{2 }– 3 > 0.

(A)

(B) (–1.90,–0.87)

(C)

(D) (–0.87,1.58)

(E)

3. The number of integers that satisfy the inequality *x*^{2 }+ 48 < 16*x *is

(A) 0

(B) 4

(C) 7

(D) an infinite number

(E) none of the above