1
The midpoints of the sides of a regular hexagon ABCDEF are joined in order to form a smaller regular hexagon.
What fraction of the area of ABCDEF is enclosed by the smaller hexagon?

2
Find the inverse function of \( f(x) = \frac{2x – 3}{3x + 1} \).

3
The diameter of the circle was increased by a factor of \( 2\frac{1}{4} \). How did its area change?

4
\( \sqrt{x+2} = 2 – \sqrt{x} \)

5
Solve for x.
\( 4 – 6sin^2(3x) = 2.5 \)

6
Graph.
\( y = 5 – 2sec(x – \frac{\pi}{2}) \)

7
\( \sqrt{2x + 3} + 2 = \sqrt{6x + 7} \)

8
Graph.
\( f(x) = \frac{4x^2 – x – 5}{2x^2 – 8} \)

9
\( log_{\frac{1}{9}} (27\sqrt{3}) = \)

10
The midpoints of the sides of a regular hexagon ABCDEF are joined in order to form a smaller regular hexagon.
What fraction of the area of ABCDEF is enclosed by the smaller hexagon?

Explaining.

1
Factorize.
\( 3x^7 – 5x^6 – 12x^5 = \)

2
The diameter of the circle was increased by a factor of \( 2\frac{1}{4} \). How did its area change?

3
What is the domain of \( f(x) = -\frac{4}{\sqrt{4 – 9x^2}} \)?

4
The midpoints of the sides of a regular hexagon ABCDEF are joined in order to form a smaller regular hexagon. What fraction of the area of ABCDEF is enclosed by the smaller hexagon?