Examples for 9th grade - page 4
- Movement
From the crossing of two perpendicular roads started two cyclists (each at different road). One runs at average speed 24 km/h, the second at average speed 26 km/h. Determine the distance between them after 35 minutes cycling. - Gimli Glider
Aircraft Boeing 767 lose both engines at 45000 feet. The plane captain maintain optimum gliding conditions. Every minute, lose 1870 feet and maintain constant speed 212 knots. Calculate how long takes to plane from engines failure to hit ground. Calculate - Short cut
Imagine that you are going to the friend. That path has a length 270 meters. Then turn left and go another 1810 meters and you are at a friend's. The question is how much the journey will be shorter if you go direct across the field? - Scale
Swimming pool is long 110 m and 30 m wide. The plan of the city is shown as a rectangle with area 8.25 cm2. What scale is the city plan? - Cone A2V
Surface of cone in the plane is a circular arc with central angle of 126° and area 415 dm2. Calculate the volume of a cone. - Cubes
One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 254 cm2. - River
From the observatory 14 m high and 32 m from the river bank, river width appears in the visual angle φ = 20°. Calculate width of the river. - Cube diagonal
Determine length of the cube diagonal with edge 33 km. - Transforming cuboid
Cuboid with dimensions 10 cm, 17 and 17 cm is converted into a cube with the same volume. What is its edge length? - Regular 5-gon
Calculate area of the regular pentagon with side 7 cm. - Rhombus
Calculate the perimeter and area of rhombus whose diagonals are 2 cm and 6 cm long. - Logs
Trunk diameter is 52 cm. Is it possible to inscribe a square prism with side 36 cm? - Right triangle Alef
The area of a right triangle is 294 cm2, the hypotenuse is 35 cm long. Determine the lengths of the legs. - Sphere
Surface of the sphere is 2820 cm2, weight is 71 kg. What is its density? - Proof PT
Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it. - No. of divisors
How many different divisors has number ?? - Rectangle
In rectangle with sides 3 and 10 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 ABCD
Rhombus ABCD, |AC| = 97 cm, |BD| = 35 cm. Calculate the perimeter of the rhombus ABCD. - 7 heroes
5 heroes galloping on 5 horses behind. How many ways can sort them behind? - Diagonal
Calculate the length of the diagonal of the rectangle ABCD with sides a = 8 cm, b = 7 cm.
From the crossing of two perpendicular roads started two cyclists (each at different road). One runs at average speed 24 km/h, the second at average speed 26 km/h. Determine the distance between them after 35 minutes cycling.
Aircraft Boeing 767 lose both engines at 45000 feet. The plane captain maintain optimum gliding conditions. Every minute, lose 1870 feet and maintain constant speed 212 knots. Calculate how long takes to plane from engines failure to hit ground. Calculate
Imagine that you are going to the friend. That path has a length 270 meters. Then turn left and go another 1810 meters and you are at a friend's. The question is how much the journey will be shorter if you go direct across the field?
Swimming pool is long 110 m and 30 m wide. The plan of the city is shown as a rectangle with area 8.25 cm2. What scale is the city plan?
Surface of cone in the plane is a circular arc with central angle of 126° and area 415 dm2. Calculate the volume of a cone.
One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 254 cm2.
From the observatory 14 m high and 32 m from the river bank, river width appears in the visual angle φ = 20°. Calculate width of the river.
Determine length of the cube diagonal with edge 33 km.
Cuboid with dimensions 10 cm, 17 and 17 cm is converted into a cube with the same volume. What is its edge length?
Calculate area of the regular pentagon with side 7 cm.
Calculate the perimeter and area of rhombus whose diagonals are 2 cm and 6 cm long.
Trunk diameter is 52 cm. Is it possible to inscribe a square prism with side 36 cm?
The area of a right triangle is 294 cm2, the hypotenuse is 35 cm long. Determine the lengths of the legs.
Surface of the sphere is 2820 cm2, weight is 71 kg. What is its density?
Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it.
How many different divisors has number ??
In rectangle with sides 3 and 10 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 ABCD, |AC| = 97 cm, |BD| = 35 cm. Calculate the perimeter of the rhombus ABCD.
5 heroes galloping on 5 horses behind. How many ways can sort them behind?
Calculate the length of the diagonal of the rectangle ABCD with sides a = 8 cm, b = 7 cm.- «
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