Maths practice for 14 year olds - page 46 of 376

Number of problems found: 7503

Bell copper tin
Nine kilograms of bell metal contain 7 kg of copper, the rest of which is tin. How much copper and how much tin were used to cast five bells? Each of the two larger bells weighed 535kg, and each of the remaining three smaller ones weighed 286kg.
Bronze copper tin
Bronze is an alloy of copper and tin in a ratio of 1:4. How much copper does a bronze piece of jewelry weighing 25 g contain?
Buy and sell
The selling price is 5.75 EUR, and the buying price is 4 EUR. By what percentage was the price increased?
Circle chord construction
Two line segments of different lengths are given. Construct a circle k so that both line segments are its chords.
Central angle
A circle k with a center at point S and a radius of 6 cm is given. Calculate the size of the central angle subtended by a chord 10 cm long.
Bouquet flower percentage
The spring bouquet consists of 13 daffodils and 8 tulips, and the other 30% are freesias; how many flowers are there in total?
The balance - the lever
For the lever to be balanced, the arms' lengths must be inversely proportional to the weight ratio of the weights suspended on these arms. Complete the data: 30 cm, 10 cm, 4 kg, and m₂ kg.
Original model
When drying, the modeling mass loses 36% of its original volume. If the cube's volume is 5.12 dm³ after drying, what was the original length of the edge?
Cable division parts
The master gave the apprentice the task of dividing the 28 m long electric cable into two parts so that the second part was 2.5 times larger than the first. How long were the cable sections supposed to be?
Canister water morning
In the morning, 6 liters more water was in the green canister than in the blue one. In the afternoon, the gardener poured 1 liter of water from the green canister into the blue one. There was then twice as much water in the green canister as in the blue o
Triangle area angle
The area of a right triangle ABC is 346 cm², and the angle at vertex A is 64°. Calculate the lengths of the overhangs a and b.
Isosceles triangle and cosine
Using the cosine theorem, prove that in an isosceles triangle ABC with base AB, c=2a cos α.
Triangle hypotenuse circle
In a right-angled triangle ABC with a right angle at the vertex C, the magnitudes of the hypotenuses are given ta=5, tb=2√10. Calculate the side sizes of triangle ABC and the circle's radius described by this triangle.
Triangle circle radius
Given is an isosceles triangle whose base is 8 cm, and the sides are 15 cm long. Calculate the area of the triangle and the radius of the inscribed and circumscribed circle.
Class grade average
There are 30 students in the class. Five had a mark three — other twos and ones. The average grade was 1.9. How many students got mark one?
Car braking force
A car of mass m=1t moves at a speed v0=54 km/h. What braking force must be exerted to bring the car to a stop in 10 seconds, and how far will the car travel in this time?
Tetrahedron water level
A container shaped like a rotating cylinder with a base radius of 5 cm is filled with water. If a regular tetrahedron with an edge of 7 cm is immersed in it, how much will the water level in the container rise?
Basketball point throws
In the basketball game, the players threw 37 times, including 2-pointers and 3-pointers, for a total of 82 points. How many were 2 points, and how many were 3 points?
Dimensions of an aquarium
The large aquarium is shaped like a cuboid and has dimensions in the ratio 5: 7: 4. The sum of the lengths of all edges is 96 dm. How many liters of water will be in the aquarium if it is filled to four-fifths?
PIN probability number
The mobile PIN has 4 characters. What is the probability that the PIN contains the number 7 and ends with the number 5?

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