Examples for secondary school students - page 126 of 231
Number of problems found: 4613
- Paper money distribution
The four friends received money for collecting paper as follows: Mirko received a quarter of the entire amount, Robo received a third of the remaining money, and Boris received half of the second remaining money. Peter had 1.50 euros left. How many crowns - Three Day Hike Distances
Pupils walked a total of 30 km during the three-day trip. On the first day, they ran twice as much as on the third day, and on the second day, they ran 6 km more than on the third day. How many km have they traveled each day? - Final exam
There are five learners in a class that has written a final exam. Aleta scored 55%, Vera scored 36%, and Sibusiso scored 88%. If Thoko scored 71% and the class average was 63%. What was Davids's score as a percentage? - Clogging
How much distilled water must the pharmacist add to 30g of a 30% hydrogen peroxide solution to obtain a 3% solution for clogging? - Diamond diagonals
Find the diamond diagonal's lengths if the area is 156 cm² and the side is 13 cm long. - Matrix determinant change
We have a matrix of order n ≥ 3. If we add the last column to each column (including the last), how does its determinant change? - Light bulb resistance
The resistance of a 40W light bulb is 10 Ohms. What voltage source is connected to it? What current is flowing through it? - Wage variance deviation
A statistician monitored the variance of monthly wages and found its value to be 640,000. Determine the standard deviation of salaries if there is a one-off increase: a) about CZK 1,800, b) about 5%. - Three friends Cuba, Matthew, and their friend Adam found a brigade during their weekend weekends because they wanted to make a joint trip to the Alps that they planned for spring break. Cuba enjoyed the skiing trip very much, so he was not lazy to get up and went to th
- Vinegar mixing
When we mix 70g water with 50g 8% vinegar, how many percent of the vinegar solution do we produce? - Aircraft Carrier Acceleration
The runway of the aircraft on the mother ship is 49m long. Calculate the aircraft's acceleration so that its speed when leaving the ejection device reaches 252km/h. - Two trains
Through the bridge, long l = 240m, the train passes through the constant speed at time t1 = 21s. A train running along the traffic lights at the edge of the bridge passes the same speed at t2 = 9s. a) What speed v did the train go? b) How long did a train - Number machine modifications
The Numerometer has invented as the number machine that changes numbers until it makes them single-digit numbers. He still makes the change according to the same rule. For example: from the number 87312, after six modifications, he gradually made the numb - Temperature and volume
The pool with a length of l = 50 m and a width of s = 15 m has a depth of h1 = 1.2 m at the shallowest part of the wall. The depth then gradually increases to a depth of h2 = 1.5 m in the middle of the pool. = 4.5 m walls in the deepest part of the pool. - Substitution method
Solve a goniometric equation: sin4 θ - 1/cos² θ=cos² θ - 2 - Families 2
Seven hundred twenty-nine families have six children each. The probability of a girl is 1/3, and the likelihood of a boy is 2/3. Find the number of families having two girls and four boys. - Survey women respondents
In the survey, 2/3 of those who correctly answered the question were women. 4/5 of all respondents answered the question correctly. How many women answered correctly if a total of 900 respondents participated in the survey? What proportion of all responde - Shopping vegetables
John and his mother were shopping. My mother bought 2 kg of peaches and 5 kg of potatoes and paid CZK 173. The neighbor bought 3 kg of peaches and 4 kg of potatoes and paid CZK 186. How much did 1 kg of peaches and 1 kg of potatoes cost? - Television quality probability
In the department store, they have 100 televisions, of which 85 are of first quality, and 15 are of second quality. The first ten buyers received a premium TV. What is the probability that the eleventh is sold a second-rate TV? - Exercise Books Division Ways
How many ways can three children divide five small and six large exercise books? Admittedly, some get nothing.
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