# Examples for 8th grade

#### Number of problems found: 2723

- Red diplomas

He numbers of students with honors in 2013 and 2014 are in ratio 40:49. How big is the year-on-year percentage increase? - Resistance

A resistor having an electrical resistance of 1.5 k ohms passes an electrical current of 0.1 A. Calculate what voltage is between the terminals of the resistor. - One million

Write the million number (1000000) by using only 9 numbers and algebraic operations plus, minus, times, divided, powers, and squares. Find at least three different solutions. - Luggage and air travel

Two friends traveling by plane had a total of 35 kg of luggage. They paid one 72 CZK and second 108 CZK for being overweight. If only one paid for all the bags, it would cost 300 CZK. What weight of baggage did each of them have, how many kilograms of lug - Folded square

ABCD is a square. The square is folded on the midpoint of AB and A is folded onto the fold, creating a shaded region. The perimiter of the shaded figure is 75. Find the area of square ABCD - Call of Duty

Game Call of Duty in CTF (Capture the Flag) opposes the British and the Germans, whose bases are 15 km apart. A German soldier stole the British flag and hid it with it in a secret place between the bases. If the British soldiers set out at a speed of 14 - Workers

Two workers will construct the stage at the festival in 54 hours. Organizers need to shorten the assembly time by 42 hours. How many workers must the assembly company send? - Trapezoid

How long are the trapezoid bases with area 24 cm^{2}and height 3 cm. One base is 3 times longer than the shorter. - Reminder and quotient

There are given numbers A = 135, B = 315. Find the smallest natural number R greater than 1 so that the proportions R:A, R:B are with the remainder 1. - Copper parts

From copper cast were made 3 parts. At first consumed one third of casting, the second 2/3 of rest and the third weighed 18 kg. What is the weight of original copper cast? - Hectares of forest

12 workers plant 24 ha of forest in 6 days. In how many days will 15 people and 12 people plant the same area? - Right triangle

Calculate the length of the remaining two sides and the angles in the rectangular triangle ABC if a = 10 cm, angle alpha = 18°40'. - Two rectangular boxes

Two rectangular boxes with dimensions of 5 cm, 8 cm, 10 cm, and 5 cm, 12 cm, 1 dm are to be replaced by a single cube box of the same cubic volume. Calculate its surface. - Father and sons

After15 years will father many years as his two sons together now. There is a six-year difference between the brothers, and the older one celebrated fifty years three years ago. How old is their father now? - Eight palm

There grows 8 palms by the sea. At the first sitting one parrot, on second two, on third sits four parrots on each other twice the previous parrots sitting on a previous palm. How many parrots sitting on eighth palm? - Surface area of the top

A cylinder is three times as high as it is wide. The length of the cylinder’s diagonal is 20 cm. Find the surface area of the top of the cylinder. - ATC camp

The owner of the campsite offers 79 places in 22 cabins. How many of them are triple and quadruple? - Slant height

The slant height of cone is 5cm and the radius of its base is 3cm, find the volume of the cone - Pentadecagon

Calculate the content of a regular 15-sides polygon inscribed in a circle with radius r = 4. Express the result to two decimal places. - The bakery

The bakery baked 325 cakes from 25kg flour. How many kg of flour do they need to bake 195 pieces of such cakes?

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