Examples for secondary school students - page 130 of 237

Number of problems found: 4730

Repairing
Three employees earned a total of € 469 for repairing the equipment. They split the money so that the first got 20% more than the second and the third 15% more than the second. Thus, everyone got a total of € 469.
Math test
Obelix filled out a mathematical test in which he answered 25 questions. For every correct answer, he received 5 points. For each wrong answer, he had 3 points deducted. Obelix gained 36% of all points in the test. How many questions did he solve correctl
The Hotel
The Holiday Hotel has the same number of rooms on each floor. Rooms are numbered with natural numerals sequentially from the first floor; no number is omitted, and each room has a different number. Three tourists arrived at the hotel. The first one was in
Paper money distribution
The four friends received money for collecting paper as follows: Miro received a quarter of the entire amount, Rob 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 d
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 who wrote a final exam. Aleta scored 55%, Vera scored 36%, and Sibusiso scored 88%. Thoko scored 71%, and the class average was 63%. What was David's score as a percentage?
Clogging
How much distilled water must the pharmacist add to 30 g 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 40 W light bulb is 10 Ohms. What voltage source is connected to it? What current is flowing through it?
Cell division
At the end we could have something simpler and a bit (at least mathematically) more fun... At the beginning there was nothing... But no, here we have at the beginning one single cell. This cell is not just any ordinary cell, it is special, because there i
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 after a one-off increase of: a) CZK 1,800, b) 5%.
Three friends
Cuba, Matthew, and their friend Adam worked at a part-time job over the weekend to fund a joint trip to the Alps planned for spring break. Cuba worked diligently and earned 11,000 CZK. Matthew, however, earned only one-third of the arithmetic mean of Adam
Vinegar mixing
When we mix 70 g water with 50 g 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 49 m long. Calculate the aircraft's acceleration so that its speed when leaving the ejection device reaches 252 km/h.
Two trains
Through the bridge, long l = 240 m, the train passes through the constant speed at time t1 = 21 s. A train running along the traffic lights at the edge of the bridge passes the same speed at t2 = 9 s. a) What speed v did the train go? b) How long did a tr
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.

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