# Examples for secondary school students

#### Number of problems found: 2059

- Remuneration

Total remuneration for workers is 47 000 CZK. The second worker received 20% more than the first and third 4000 CZK less than a second employee. How many CZK each received? - Forces

Forces with magnitudes F1 = 42N and F2 = 35N act at a common point and make an angle of 77°12'. How big is their resultant? - Acceleration 2

if a car traveling at a velocity of 80 m/s/south accelerated to a velocity of 100 m/s east in 5 seconds, what is the cars acceleration? using Pythagorean theorem - Right triangle - ratio

The lengths of the legs of the right triangle ABC are in ratio b = 2: 3. The hypotenuse is 10 cm long. Calculate the lengths of the legs of that triangle. - US GDP

Consider the following dataset , which contsins the domestic US gross in millions of the top grossing movie over the last 5 years. 300,452,513,550,780 I. Find the Mean of the Dataset II. Find the Squared deviation of the second observation from the mean I - Two-digit number

Digit sum of thinking two-digit natural number is 11. When it exchanging a sequence of digits, given a number which is 27 less than the thinking number. Find out which number I think. - Bank account CZ

We will deposit CZK 6,600 into the bank for 1 year with an interest rate of 2.5%. The interest tax is 15%. How many crowns will we receive after one year? - Rectangular plot

The dimensions of a rectangular plot are (x+1)m and (2x-y)m. If the sum of x and y is 3m and the perimeter of the plot is 36m. Find the area of the diagonal of the plot. - Dollars

Mama split 760 dollars Jane, Dane and Eva as follows: Jane got three times more than Dane and Dane and got 40 more than Eva. How much does get each of them? - Square

Suppose the square's sides' length decreases by a 25% decrease in the content area of 28 cm^{2}. Determine the side length of the original square. - Pyramid

Pyramid has a base a = 3cm and height in v = 15 cm. a) calculate angle between plane ABV and base plane b) calculate angle between opposite side edges. - Diameters of circles

How many percent of the area of a larger circle is a smaller circle if the smaller circle has a diameter 120 mm and a larger one has a diameter 300 mm? - The book

If one day you read p pages, you will read the book 24 days. If you read each day 10 pages more, you would read a book in 16 days. How many pages have the book? - Rotary cone

Rotary cone whose height is equal to the circumference of the base, has a volume 229 cm^{3}. Calculate the radius of the base circle and height of the cone. - Spherical cap

From the sphere of radius 11 was truncated spherical cap. Its height is 6. What part of the volume is a spherical cap from the whole sphere? - Rectangle

In a rectangle with sides, 6 and 3 mark the diagonal. What is the probability that a randomly selected point within the rectangle is closer to the diagonal than to any side of the rectangle? - Rhombus diagonals

In the rhombus ABCD are given the sizes of diagonals e = 24 cm; f = 10 cm. Calculate the side length of the diamond and the size of the angles, calculate the content of the diamond - Diagonals of the rhombus

How long are the diagonals e, f in the diamond, if its side is 5 cm long and its area is 20 cm^{2}? - Two workers

Two workers work together and perform the job in 12 hours. If one has done half the work and then the second worker next half of the work it will take 25 hours. How long would it take job them separately? - Block or cuboid

The wall diagonals of the block have sizes of √29cm, √34cm, √13cm. Calculate the surface and volume of the block.

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