1. A rectangular swimming pool 12m by 8m is surrounded by a concrete path of uniform width. If the area of the path is 224m², find its width

2. A surveyor wants to determine the height of a building. She measures the angle of elevation of the top of the building at two points 15m apart on the ground. The angles are shown in the figure below. Find the height of the building ( use a calculator, and round to one decimal place)

3. Cube A has 4 red faces and 2 white faces; cube B has 3 red and 3 white faces; cube C has 2 red and 4 white faces. The three cubes are tossed. What is the probability of 3 red faces uppermost?

4. Find the value of $\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+...+\frac{1}{\sqrt{24}+\sqrt{25}}=?$

5. A teacher wants to choose a captain and vice-captain among 12 soccer players. In how many different ways can he do so?

6. Express $\frac{-3x-1}{x^2+2x-3}$ as two separate fractions

7. Find the coordinates of the point of intersection of two functions: $y=|x-2|+1$ and $y=x^2+3$ in the second quadrant.

8. Given that the curve $y=x^2+(3k-1)x+(2k+10)$ has a minimum value greater than 0, which value of k guarantees this condition?

9. Lines BP and BE divide angle ABC into three same angles. Lines CP and CE divide angle ACB intro three same angles. Find angle BPC.

10. $1+2+2^2+3^3+......+$2²⁰⁰⁰