Examples for secondary school students

Number of problems found: 2059

  • Dodecagon
    clocks Calculate the size of the smaller of the angles determined by lines A1 A4 and A2 A10 in the regular dodecagon A1A2A3. .. A12. Express the result in degrees.
  • Cuboid diagonals
    kvadr_diagonal The cuboid has dimensions of 15, 20 and 40 cm. Calculate its volume and surface, the length of the body diagonal and the lengths of all three wall diagonals.
  • Motorbike circuit
    motorbike2 On a 2,550 m long circuit, two motorcycles go at such speeds that they meet every minute if they go against each other and run every 5 minutes if they go in the same direction. Find their speeds.
  • Controller
    std_dev Output Controller of the company in the control of 50 randomly selected products found that 37 of them had no defect 8 has only one flaw, three had two defects, and two products had three defects. Determine the standard deviation and coefficient of variat
  • Transforming cuboid
    cube Cuboid with dimensions 6 cm, 10, and 11 cm is converted into a cube with the same volume. What is its edge length?
  • Euler problem
    euler Someone buys a 180 tolars towels. If it was for the same money of 3 more towels, it would be 3 tolars cheaper each. How many were towels?
  • Right isosceles triangle
    euclid_theorem_1 Right isosceles triangle has an altitude x drawn from the right angle to the hypotenuse dividing it into 2 equal segments. The length of one segment is 5 cm. What is the area of the triangle?
  • Three workshops
    workers_24 There are 2743 people working in three workshops. In the second workshop works 140 people more than in the first and in third works 4.2 times more than the second one. How many people work in each workshop?
  • Rhombus and diagonals
    kosostvorec_2 The a rhombus area is 150 cm2 and the ratio of the diagonals is 3:4. Calculate the length of its height.
  • Bank
    money_3 Paul put 10000 in the bank for 6 years. Calculate how much you will have in the bank if he not pick earned interest or change deposit conditions. The annual interest rate is 3.5%, and the tax on interest is 10%.
  • Barrel with water
    sudy_5 The water barrel has a weight of 52 kg. When we pour a quarter of the water, the weight of the barrel is reduced to 40 kg. Determine the weight of the empty barrel.
  • Percent change
    rectangles 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?
  • Triangle and its heights
    triangle_2 Calculate the length of the sides of the triangle ABC, if va=5 cm, vb=7 cm and side b is 5 cm shorter than side a.
  • Money
    money_17 Peter has 2x more money than Michael. But if Peter gave Michael € 16 Michael would have 3.5 times more money than Peter. Determine how much money was originally Peter and how much Michael.
  • Embankment
    nasyp The railway embankment 300 m long has a cross section of an isosceles trapezoid with bases of 14 m and 8 m. The trapezoidal arms are 5 m long. Calculate how much m3 of soil is in the embankment?
  • Working together
    workers Two people will do the work in 12 days. They worked together for 8 days. Then only one worked for 10 days. How many days would each of them do the work if he worked alone?
  • Hexagonal pyramid
    hex_pyramid Please calculate the height of a regular hexagonal pyramid with a base edge of 5cm and a wall height of w = 20cm. Please sketch a picture.
  • There
    triangle_rt_taznice There is a triangle ABC: A (-2,3), B (4, -1), C (2,5). Determine the general equations of the lines on which they lie: a) AB side, b) height to side c, c) Axis of the AB side, d) median ta to side a
  • The hiker
    tourist The hiker will travel 40% of the route on the first day 1and/3 of the rest od second day. Last day 30 km. What was the length of the 3-day trip? How many kilometers did he walk each day?
  • Trapezoid
    lichobeznik_3 trapezoid ABCD a = 35 m, b=28 m c = 11 m and d = 14 m. How to calculate its area?

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