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?