The most difficult examples
- Parabola 3
Find the equation of a parabola with its focus at (0,2) and its vertex at the origin. ?
- 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.
- 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'.
- 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.
- Box and whisker plot
Construct a box and whisker plot for the given data. 56, 32, 54, 32, 23, 67, 23, 45, 12, 32, 34, 24, 36, 47, 19, 43
- 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.
- 10 pieces
How to divide the circle into 10 parts (geometrically)?
- 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
- The sum graphically
Draw a graphically sum of the all sides of 4-gon ABCD.
- Draw it!
Draw two lines c, d that c || d. On line c mark the points A, B. By point A lead perpendicular line to c. By point B lead perpendicular line to c.
- 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].
- 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.
- Equation with abs
Solve this equation with absolute value member: ?
- Series and sequences
Find a fraction equivalent to the recurring decimal? 0.435643564356
The length of the rectangle is 8 smaller than three times the width. If we increase the width by 5% of the length and the length is reduced by 14% of the width, the circumference of rectangle will be increased by 30 m. What are the dimensions of the rectan
Find x in modulo equation: 47x = 4 (mod 9) Hint - read as: what number 47x divided by 9 (modulo 9) give remainder 4 .
- 6 terms
Find the first six terms of the sequence. a1 = 7, an = an-1 + 6
The diameter of a circular plot is 14 dm. Find the circumference and area.
- Volume and area
What is the volume of a cube which has area of 361 cm2?
- Ratio iso triangle
The ratio of the sides of an isosceles triangle is 7:6:7 Find the base angle to the nearest answer correct to 3 significant figure.