 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?