Examples for secondary school students - page 123 of 237
Number of problems found: 4730
- Sheep and cows
There are only sheep and cows on the farm. Sheep are eight more than cows. The number of cows is half the number of sheep. How many animals live on the farm? - STRESSED word
Each letter in STRESSED is printed on identical cards, one letter per card, and assembled in random order. Calculate the probability that the cards spell DESSERTS when assembled. - Direction Vectors Points
A (5; -4) B (1; 3) C (-2; 0) D (6; 2) Calculate the direction vector a) a = AB b) b = BC c) c = CD - Classroom
Of the 26 pupils in the classroom, 12 boys and 14 girls, four representatives are picked to the odds of being: a) all the girls b) three girls and one boy c) there will be at least two boys - Spherical cap
A spherical cap is placed on a cylinder of height 4.6 cm such that the area of the curved surface of the cap is 20 cm². Determine the radius r of the sphere from which the cap was cut. - Triangle Side Lengths Probability
We have the numbers 4, 6, 9, 13, and 15. What is the probability that these will be the lengths of the sides of the triangle? (Consider only scalene triangles.) - Balance Scales Immersed Bodies
At the end of one arm of the equilibrium scales, which are in equilibrium, a lead body with a volume V1 is suspended in the air. At the end of the other arm is an aluminum body with a volume of V2. The balance arms have sizes l1 and l2, lead density h1 = - Football card distribution
Thomas was to distribute 259 cards with pictures of football players among three friends. And each subsequent friend had to get 2x more cards than the previous one. How many cards did the other friend receive? - Three workplaces
How many ways can we divide nine workers into three workplaces if they need four workers in the first workplace, 3 in the second workplace, and 2 in the third? - The father wanted
A father wanted to divide his inheritance equally among all his sons and ordered: the eldest son would receive 1,000 CZK and one eighth of the remainder; the second would receive 2,000 CZK and one eighth of the new remainder; the third would receive 3,000 - Triangle 42
Triangle BCA. Angles A=119° B=(3y+14) C=4y. What is the measure of triangle BCA=? - The pool - optimization
A block-shaped pool with a volume of 200 m³ is to be built in the recreation area. Its length should be 4 times the width, while the price of 1 m² of the pool bottom is 2 times cheaper than 1 m² of the pool wall. What dimensions must the pool have to make - Table Tennis Tournament Matches
Eight players took part in the table tennis tournament. The tournament system allows players to play with each other only once. How many matches will take place in this tournament? - Egg Incubator Hatch Percentage
92% of the eggs hatched in the incubator. 168 eggs remained unhatched. How many eggs have initially been in the incubator? - Square Lounge Drunken Shopper
After a long dinner, a man named Edward is lying inside a lounge in the shape of square ABCD, in such a position that triangle DEC is equilateral. A second person, Frank, is lying on edge BC with |EB| = |EF|. What is the size of angle CEF? - Restaurant
At "The untameable boar" they had thirty tables before the brawl, marked with natural numbers 2 to 31. Just two tables belonged to the lounge. So that the staff could find out at inventory which two they are, they used a trick. On the door of the lounge t - Hyperbola equation
Find the hyperbola equation with the center of S [0; 0], passing through the points: A [5; 3] B [8; -10] - Coordinates of square vertices
The ABCD square has the center S [−3, −2] and the vertex A [1, −3]. Find the coordinates of the other vertices of the square. - Prism diagonal
The body diagonal of a regular square prism has an angle of 60 degrees with the base, and the edge length is 10 cm. What is the volume of the prism? - Four-Digit Lock Codes
How many four-digit codes on the wheel lock can we create from the digit 0,1,2,3,4,5,6,7,8,9 if it is true that we cannot repeat the numbers?
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