Maths practice for 14 year olds - page 138 of 375

Number of problems found: 7494

The sum
The sum of the squares of two immediately following natural numbers is 1201. Find these numbers.
Balloon buoyancy force
The balloon filled with hot air has a volume of 1440m³. How large a buoyancy force acted on the balloon in the air with a density of 1.3 kg/m³?
Pharmacist
The pharmacist had a 12 liter vessel of herbal lotion, which contained a 30% active ingredient. Her assistant poured 18 liters of herbal lotion, containing 45% of the active ingredient, into a container. What percentage of herbal lotion was produced?
Triangle angle
For the interior angles of a triangle, the angle β is twice as large, and the angle γ is three times larger than the angle α. Is this triangle right?
The bun
The bun costs CZK 2, and the rolls CZK 3.5. Hanka bought 22 pieces of bread, bought only buns and rolls, and paid CZK 65. how many rolls did she buy, and how many rolls?
Muesli
You want to mix your own muesli on a specialized website. 200 g of muesli base costs 170 CZK. You want to add cornflakes in chocolate to the basics. 50g of this ingredient costs 13 CZK. How much do you pay for a 150g mixture when both components weigh the
Camel hump
There are one-humped and two-humped camels in the caravan going through the desert. The guide counted 28 heads and 45 humps. How many humpback camels are in the caravan?
Balloon flight
From the pilgrimage, Nikola has a balloon on a two-meter-long string, the end of which is held 60 cm above the ground. The balloon floats diagonally from Nikola and is 145 cm horizontally away from her. How high is the balloon from the ground?
Concert ticket
Noah wants to save $60 to purchase a concert ticket. If he has saved $45 so far, what percentage of his goal has he saved? What percentage remains?
A trapezoid
A trapezoid with a base length of a = 36.6 cm, with angles α = 60°, β = 48°, and the height of the trapezoid is 20 cm. Calculate the lengths of the other sides of the trapezoid.
Tower distance
How far from the lookout tower, 48 m high, did the tourist stand if he saw its top at an angle of 40°?
Mrs Perry
Mrs. Perry shares 25 biscuits between Gemma and Zak in a ratio of 1:4. How many biscuits have each?
Route option
From Zubrohlava to Bobrov, there is one asphalt road, two forest roads, and one bike path. Find the number of ways we can get from Zubrohlava to Bobrov and back. List all options.
Pyramid complete
A regular quadrilateral pyramid is given: a = 27 mm, w = 21 mm (wall height). Calculate the height, volume, and surface area of the pyramid.
Roof material
In the form of a pyramid with a square floor plan, the house's roof has dimensions of 12 x 12 m, at the highest point, a height of 2 m. How much roofing do we need to buy? Count on a 10% reserve.
Pyramid of Giza
The Great Pyramid of Giza is shaped like a regular quadrangular pyramid. The base edge is 227 m long, and the pyramid is 140 m high. What is the weight of the stone needed to build this pyramid if the weight of 1 m³ of stone is 2.5 t?
Truncated pyramid
Find the volume and surface area of a regular quadrilateral truncated pyramid if base lengths a1 = 17 cm, a2 = 5 cm, and height v = 8 cm.
Truncated pyramid
Find the volume of a regular 4-sided truncated pyramid if a1 = 14 cm, a2 = 8 cm, and the angle that the side wall with the base is 42 degrees.
Grade 2
At the end of the year, the class teacher bought a mug and sweets for her students. One mug cost 15 CZK, a chocolate bar cost 12 CZK, and a wafer cost 9 CZK. The boys received a mug and chocolate, and the girls received a mug and a wafer. How many crowns
Grandmother money distribution
Jana and Tomáš received a total of 105 CZK from their grandmother. Jana got a third more than Tomáš. How many crowns did everyone receive?

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