Maths practice for 14 year olds - page 164 of 376

Number of problems found: 7501

Motorcyclist and a car
The passenger car left at 7:00 and was heading east at a speed of 60 km/h. A motorcyclist left the same place and headed north at 40 km/h. What will be their air distance at ten o'clock?
Ski lift height
What height difference does the 2.5 km long ski lift overcome when the horizontal distance of the entry and exit station is 1200 meters?
Garden diagonal length
The garden has a square shape, and its area is 8,100 m². It will be divided by a sidewalk connecting the two opposite garden peaks. How long will this trail be?
Class boy girl
There were 24 pupils from the whole class on the school trip. Out of 4/7 of all girls, ¼ did not go. Since all the boys went, there were an equal number of boys and girls on the trip. How many students are there in the class? How many boys are there?
Track surface fitting
The circular running track has a diameter of 130 meters. Can a rectangular surface with dimensions of 12m and 50m be grassed inside the circle?
Spherical segment
Calculate the volume of a spherical segment 18 cm high. The diameter of the lower base is 80 cm, and the upper base is 60 cm.
Cuboid edges
Calculate the volume and surface of a cuboid whose edge lengths are in the ratio 2:3:4 and the longest edge measures 10cm.
Percentage comparison
How much is 20% of number 200 less than 30% of number 300?
Right angle
In a right triangle ABC with a right angle at the apex C, we know the side length AB = 24 cm and the angle at the vertex B = 71°. Calculate the length of the legs of the triangle.
Sound speed calculation
Calculate the speed of sound in the air a) at a temperature of t = 20 °C b) at a temperature of t = 27 °C
Triangle in a square
In a square ABCD with side a = 6 cm, point E is the center of side AB, and point F is the center of side BC. Calculate the size of all angles of the triangle DEF and the lengths of its sides.
Hostel room calculation
Fifty-one students are accommodated in the tourist hostel in 15 four-bed and three-bedrooms. How many rooms are there if there are 2 spaces left after housing? a) There are four-bed rooms. b) There are three-bed rooms.
Bike cost
The father gave his son € 100 to buy a bicycle, which was 40% of the total amount of the bicycle. How much did the bike cost?
The cable car
The cable car is 2610 m long and rises at an angle of 35°. Calculate the height difference between the lower and upper station of the cable car.
Triangle height construction
A. Construct ∆ABC such that c = 55 mm, α = 45 °, β = 60 °. B. Draw any acute triangle and construct its heights.
Sailing
Solve the following problem graphically. The fishing boat left the harbor early morning and set out to the north. After 12 km of sailing, she changed course and continued 9 km west. Then, When she docked and reached the fishing grounds, she launched the n
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.
Traffic sign
There is a traffic sign for climbing on the road with an angle of 7%. Calculate at what angle the road rises (falls).
Fighter
A military fighter flies at an altitude of 10 km. The ground position was aimed at an altitude angle of 23° and 12 seconds later at an altitude angle of 27°. Calculate the speed of the fighter in km/h.
The right triangle
In the right triangle ABC with a right angle at C, we know the side lengths AC = 9 cm and BC = 7 cm. Calculate the length of the remaining side of the triangle and the size of all angles.

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