Maths practice for 14 year olds - page 36 of 368

Number of problems found: 7356

Large 2
A large gear has 72 teeth, a medium gear has 56 teeth, and a small gear has 27 teeth. How many revolutions will the smallest gear make when the largest gear turns 120 times?
Calculate 449
Calculate the size of the angle formed on a clock face by the lines connecting the centre to the positions at 7:12 and 1:24.
Daniel 3
Daniel and Eve earned 180 euros together. Daniel earned 70 euros more than Eve. How much did Daniel earn, and how much did Eve earn?
Three friends 10
Three friends Peter, Thomas, and George earned 4,000 CZK from part-time work. Peter earned three times more than Thomas, and George earned 500 CZK more than Thomas. How much did each of them earn?
In a regular 5
In a regular triangular prism ABCV, the angle between the lateral face and the base plane is α = 45°. Determine the angle between the lateral edge and the base plane.
Matej 2
Matthew, Mark, Miles, and Matt had a total of 205 football player cards with signatures. Mark has four times more than Matthew. Matt had twice less than Mark. Miles had 20 fewer cards than Matthew. How many cards did each of them have?
In the domestic
In a domestic express train, there are 1st and 2nd class carriages. There are twice as many 2nd class carriages as 1st class carriages. Each carriage has 10 compartments. Each 1st class compartment has 6 seats, and each 2nd class compartment has 8 seats.
5D decimal
How many five-digit numbers contain exactly 2 fours and exactly 3 sevens in their decimal notation?
Average time
Determine the weighted average time required in minutes per product, given that 6 workers each take 8 minutes, 15 workers each take 12 minutes, 5 workers each take 10 minutes, and 9 workers each take 13 minutes.
Construct 22
Construct a rhombus ABCD if the diagonals are f = 7 cm and e = 5 cm.
Between terminals
A resistor is connected to a 220 V source. A current of 220 mA flows through the resistor. Determine the current that flows through the resistor when it is connected to a 24 V voltage source.
The tower
From a window 8 m above the horizontal plane, the top of a tower can be seen at an elevation angle of 53°20′, and its base at a depression angle of 14°15′. How high is the tower?
Two Sections
A sphere with a radius of 5 cm was divided into two spherical caps. The height of the smaller cap is 1 cm. Determine the volume of the smaller cap to the nearest hundredth of a cm³.
To the cinema 2
On Tuesday, 20 more visitors came to the cinema than on Monday. On Wednesday, half as many visitors came as on Tuesday. There were a total of 175 visitors over these three days. How many visitors came on each day?
HAMMER 4
Determine in how many ways the letters of the word HAMMER can be rearranged so that some group of consecutive letters in the rearrangement forms the word CAL.
Members 2
The members of a housing cooperative elected a seven-member board. In how many ways can a chairman, vice-chairman, treasurer, and secretary be chosen from among them?
Books in Slovak and English
Vera has 4 Czech and 3 English books. She wants to arrange them on a shelf so that the Czech books come first and the English books second. In how many ways can this be done?
Birthday boy 2
In how many ways can seven people be seated around a table if the birthday boy must sit at the head?
HAMMER 3
Determine in how many ways the letters of the word HAMMER can be rearranged so that some group of consecutive letters in the rearrangement forms the word WATER.
Base RR odd
The base of a prism is an isosceles trapezoid ABCD with bases AB = 12 cm and CD = 9 cm. The angle at vertex B is 48°10′. Determine the volume and surface area of the prism if its height is 35 cm.

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