# The most difficult examples

1. Percent change If the length of a rectangle is increased by 25% and the width is decreased by 10%, the area of the rectangle is larger than the area of the original rectangle by what percent?
2. Parabola 3 Find the equation of a parabola with its focus at (0,2) and its vertex at the origin. ?
3. Straight lines Draw two lines c, d so that c || d. On line c mark points A, B, from point A start perpendicular to line c, from point B perpendicular to line c.
4. Regular octagon Draw the regular octagon ABCDEFGH inscribed with the circle k (S; r = 2.5 cm). Select point S' so that |SS'| = 4.5 cm. Draw S (S '): ABCDEFGH - A'B'C'D'E'F'G'H'.
5. Draw a trapezoid Draw a trapezoid if given a = 7 cm, b = 4 cm, c = 3.5 cm, diagonal AC = 5cm. Solve as a construction task.
6. Right triangle Draw a right triangle ABC if |AB| = 5 cm |BC| = 3 cm, |AC| = 4 cm. Draw Thales circle above the hypotenuse of the triangle ABC.
7. 10 pieces How to divide the circle into 10 parts (geometrically)?
8. Three points Mark three points E, F and G in the plane not lie on one line. a) Draw a line segment FG b) Construct halfline (ray) EG c) Draw a line EF
9. The sum graphically Draw a graphically sum of the all sides of 4-gon ABCD.
10. Square ABCD Construct a square ABCD with cente S [3,2] and the side a = 4 cm. Point A lies on the x-axis. Construct square image in the displacement given by oriented segment SS'; S` [-1 - 4].
11. Photo enlarge Mark wants to enlarge a 4-inch by 6-inch photo so that it has a height of 15inches. Use a ratio table to determine the new width of the photo.
12. Medians and sides Determine the size of a triangle KLM and the size of the medians in the triangle. K=(-5; -6), L=(7; -2), M=(5; 6).
13. Four circles 1) Calculate the circle radius if its area is 400 cm square 2) Calculate the radius of the circle whose circumference is 400 cm. 3) Calculate circle circumference if its area is 400 cm square 4) Calculate the circle's area if perimeter 400 cm.
14. Volume and area What is the volume of a cube which has area of 361 cm2?
15. Snowman 3 During the last winter carnival, the local college students built a 30- foot snowman out of 109 tons of snow. How much snow will be needed to build a 36- foot snowman this year?
16. Series and sequences Find a fraction equivalent to the recurring decimal? 0.435643564356
17. Study For 7 hours study, she scored a 75 so if she made 93 how many hours would she need to study?
18. Equation with abs Solve this equation with absolute value member: ?
19. Money 6 Lita had some money. She spent 1/2 of it on a hand bag and 1/3 of the remainder of the blouse. She had 260.00. How much money did she have at start?
20. Photocopier A photocopier enlarges a picture in the ratio 7:4. How many times will a picture of size 6cm by 4cm be enlarged to fit on a 30cm by 20 cm page?

Do you have an interesting mathematical example that you can't solve it? Enter it, and we can try to solve it.

To this e-mail address, we will reply solution; solved examples are also published here. Please enter e-mail correctly and check whether you don't have a full mailbox.