Maths practice for 14 year olds - page 37 of 368

Number of problems found: 7356

Relay
A relay race will be run by the class team of Kate, Alice, Michaela, and Erica. Determine how many different running orders are possible, given that each of them can run in any position.
Police on time
A boat carrying smugglers has left the shore and is travelling at 85 km/h. After 10 minutes, a police boat starts chasing it at 110 km/h. International waters, where the possibility of apprehending the smugglers ends, begin 30 km from the coast. Will the
Map - route
A map has a scale of 1:40,000. How many centimetres will a route of 4.8 km be shown as on the map?
Tanker 3
A full fuel tank weighs 4,500 kg. If we pump out 30% of the gasoline, it will weigh 3,900 kg. How many kilograms does the empty tank weigh?
Gardener 5
A gardener bought 17 apple trees and 11 pear trees and paid a total of €111.65. How much did 1 pear tree cost, given that its price was 35 cents higher than the price of 1 apple tree? How much would the gardener pay for 28 apple trees and 15 pear trees?
Determine the surface area
Find the surface area of a cone of height 30 cm whose slant side makes an angle of 60° with the base plane.
Beads
We have 4 beads: one green, one yellow, and 2 pink. In how many possible ways can we string them onto a string?
Calculate
A cone has a base diameter of 16 cm and a slant height of 10 cm. Calculate its surface area and volume.
Mirror
The dimensions of a mirror are 750 mm × 700 mm, and the mirror is to be tilted 8° away from the wall. How many centimetres must the bottom of the mirror protrude from the wall?
Quadrilateral - irregular
Find the length of side d = |AD| in quadrilateral ABCD: a = 35 m, b = 120 m, c = 85 m, angle ABC = 105°, angle BCD = 72°.
Prizes - competition
For the prizes for the three best competitors a sum of money in crowns was prepared. The first competitor got half of this sum. The second competitor got 300 crowns. The third competitor got the rest of the prepared amount, which was three times less crow
Rhombus 48
A large rhombus is composed of four identical smaller rhombuses, each with an area of 42 m² and an angle alpha of 60°. What is the perimeter of the large rhombus?
Double the number of apples
Adam and Ben were picking apples. Together they picked 77 kg of apples. How much did each collect, given that Adam collected 5 kg more than twice what Ben collected?
Observation tower
An observation tower is covered with a roof in the shape of a regular quadrilateral pyramid with a base edge of 8 m and a height of 6 m. 60% of the roofing needs to be replaced. How many m² of new roofing material need to be bought?
Sweets
There are 12 sandwiches on a plate: 5 with poppy seeds and 7 with jam. How many cheese sandwiches must be added so that the probability of randomly selecting a poppy seed sandwich is 20%?
Penny and rolls
For one hundred crowns I need to buy exactly one hundred pieces of pastry at the following prices: rolls at 0.50 crowns each, bread at 10 crowns each, and buns at 3 crowns each. How many of each should I buy? (The Slovak koruna was the currency in Slovaki
Calculate
The circumference of a sphere is o = 87 cm. Calculate its volume. Express the result in litres and round to the nearest whole number.
Peter 28
Peter bought shares of a foreign company for a total of €3,000. Today their value is 50% lower. By what percentage must the price of these shares increase from today for their total value to return to the original €3,000?
In a football
In a football tournament of eight teams, where each team played each other exactly once, points were awarded as follows: the winner received 3 points, the loser received 0 points, and in the event of a draw, each team received 1 point. At the end of the t
Traffic accidents
Of the total number of traffic accidents, 80% occur within built-up areas and 20% outside them. If the number of traffic accidents within built-up areas were reduced by 40%, by what percentage would the total number of traffic accidents decrease?

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