Examples for secondary school students - page 138 of 230

Number of problems found: 4597

Calculate 6539
Calculate the magnitude of the angle formed by the lines p and q, which connect 1, 6 (line p), and 5, 8 (line q) on the clock face.
Kilometers 6535
Two cyclists rode from Prague to Poděbrady. Determine the average speed of each of them if you know that they traveled 56 km and that the slower one lost two kilometers to the faster one every hour so that he arrived in Poděbrady 30 minutes later.
Solid cuboid
A solid cuboid has a volume of 40 cm³. The cuboid has a total surface area of 100 cm squared. One edge of the cuboid has a length of 2 cm. Find the length of a diagonal of the cuboid. Give your answer correct to 3 sig. Fig.
Determine 6533
A total of 256 tickets were sold for the concert. CZK 2,800 was collected for tickets under the stage, and CZK 2,160 for tickets to the corridors. Determine the price of tickets under the stage and on the corridors, if you know that the ticket under the p
Ornamental 6532
The gardener is to plant 6 ornamental trees. There are 8 different types of trees available. Two trees, A and B, will be planted on the left edge. How many ways can a gardener do this if all the saplings planted are to be different?
Circumference of a triangle
The circumference of the triangle is 104 cm. One side is 6 cm longer and 8 cm shorter than the third. Find the lengths of its sides.
Together 6519
One worker makes 15 parts per hour, the other 12, and the third 10. How many hours did each work when they worked together for 15 hours?
Identical 6517
The arranger is to display three identical beige, two identical green, and one black coat in the shop window. How many ways can it do that?
Bottles
The must is sold in 5-liter and 2-liter bottles. Mr. Kucera bought a total of 216 liters in 60 bottles. How many liters did Mr. Kucera buy in five-liter bottles?
Equation 6513
Solve the equation (y + 5 / y-3) + (y + 3 / y-5) = 3
Area of garden
If the width of the rectangular garden is decreased by 2 meters and its length is increased by 5 meters, the area of the rectangle will be 0.2 ares larger. If the garden's width and length will increase by 3 meters, its original size will increase by 0.9
Determines 6508
The product of the two numbers is 504. When one of them increases by six, the product increases to 720. It determines both factors.
Bridge cards
How many bridge hands are possible containing 4 spades, 6 diamonds, 1 club, and 2 hearts?
Dimensions of a cylinder
We rolled a cylinder shell with a volume of 18 / π dm³ from a rectangle with an area of 6 dm². Calculate the dimensions of the rectangle.
Cube, cuboid, and sphere
Volumes of a cube and a cuboid are in a ratio of 3:2. Volumes of a sphere and cuboid are in a ratio of 1:3. At what rate are the volumes of a cube, cuboid, and sphere?
Subsequent 6477
We will put 900 bags in nine rows, with five fewer in each subsequent one. How many are in the first place?
Evaluation of expressions
If a²-3a+1=0, find (i)a²+1/a² (ii) a³+1/a³
Expression with powers
If x-1/x=5, find the value of x⁴+1/x⁴
Speed of car
The car went to a city that was 240 km away. If his speed increased by 8 km/h, it would reach the finish one hour earlier. Determine its original speed.
Cancel fractions
Compress the expression of factorial: (n+6)!/(n+4)!-n!/(n-2)!

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