The ship is designed for 450 passengers and 16

The book "Unified State Examination: 3000 Problems with Answers in Mathematics" is an excellent collection that is needed for focused training. A large number of tasks, the conditions of which are repeated periodically, are a good way to deal with the exam in mathematics.

However, an attentive reader will probably notice that the tasks proposed in the collection sin with a certain one-sidedness. Or at least a bad group. For example, among the 16 tasks discussed below, there is not a single task for interest. But interest is perhaps the most important topic in tasks B1. Without them, there is nothing to do on the exam.

In fairness, it should be noted that somewhere in the 70s, interest still begins. But why aren't they in the beginning?

A task. The cheese costs 8 rubles 60 kopecks. What is the largest number of curds you can buy for 50 rubles?

To begin with, we will translate everything into rubles. We have: 8 rubles 60 kopecks - this is 8.6 rubles. Now we divide 50 rubles by the price of one cheese:

Since the problem requires finding the greatest   the number of curds, the last step is to round the number in less   side. This is quite logical, because no one will sell us 35/43 cheese. Do not believe me - go to the store and take an interest.

A task. The ship is designed for 500 passengers and 15 crew members. Each lifeboat can accommodate 80 people. What is the smallest number of boats on the ship, so that, if necessary, they could accommodate all passengers and all crew members?

First we find how many people are on the boat: 500 + 15 \u003d 515. To find out how many boats are needed, you need to divide the total number of people by the capacity of one boat. We have:

Since you need to find lowest value, the result is rounded up. We get 7 boats. It is easy to notice that 6 boats are not enough: judging by the fraction, in this case 7 · 5 \u003d 35 people will drown.

A task. In a pack of 500 sheets of A4 paper. Over a week, 1,800 sheets are spent at the office. What is the smallest amount of paper you need to buy at the office for 6 weeks?

Find how many sheets are spent in the office for 6 weeks. It’s simple: if 1800 sheets are consumed per week, then in 6 weeks - 1800 · 6 \u003d 10800 sheets. Divide this number by the number of sheets in one pack:

Similar to the previous task, we need to find the smallest number of packs. Therefore, we round up - we get 22.

A task. Anya bought a monthly bus ticket. She made 45 trips in a month. How many rubles did she save if a ticket costs 560 rubles and a one-time trip costs 19 rubles?

Apparently, Anya bought a ticket for 560 rubles. Well, let's see how much it will take to travel if she did not buy a travel card.

So, 1 trip costs 19 rubles. Consequently, 45 trips cost 45 · 19 \u003d 855 rubles. It turns out that Anya had to pay 855 rubles, and paid only 560. Savings: 855 - 560 \u003d 295 rubles. Here is the math.

A task. The patient is prescribed a medicine that needs to be drunk 0.5 g 3 times a day for 8 days. In one pack of 8 tablets of 0.25 g of medicine. What is the smallest number of packs enough for the entire course of treatment?

First, find out how many grams of the medicine the patient will drink in these 8 days. If you take 0.5 grams each time, then 0.5 · 3 \u003d 1.5 grams per day will come out. Then 8 · 1.5 \u003d 12 grams will be released in 8 days.

Now let's see how many grams are contained in one package. According to the condition, there are 8 tablets of 0.25 grams, i.e. 8 · 0.25 \u003d 2 grams.

Total, in each package 2 grams, and you need 12 grams. We find the required number of packages: 12: 2 \u003d 6. Everything, you can safely run to the pharmacy and purchase 6 packages.

A task. To prepare a marinade for cucumbers, 1 g of water requires 16 g of citric acid. Citric acid is sold in bags of 10 g. What is the smallest number of such bags that a housewife needs to buy to make 9 liters of marinade?

Find out how much acid is needed for 9 liters. If for every liter you need 16 grams, then for 9 liters you need 9 · 16 \u003d 144 grams. Not weak, right?

But in each bag - only 10 grams of acid. And you need 144 grams. Therefore, you need 144: 10 \u003d 14.4 → 15 sachets. We round up, as no one will sell us 0.4 bags. As you can see, the rule again applies: if you need to find the lowest value, round up.

A task. A taxi driver drove 6,000 km in a month. The cost of 1 liter of gasoline (in the city) is 22 rubles. The average consumption of gasoline per 100 km is 10 liters. How many rubles did a taxi driver spend on gas this month?

Let's see how much a taxi driver costs every 100 km. Since the consumption of gasoline per 100 km is 10 liters, and each liter costs 22 rubles, we get 10 · 22 \u003d 220 rubles. That is how much a taxi driver spends for every 100 km of travel.

Now we find the total costs. So, for 100 km you have to pay 220 rubles. And how much should I pay for 6000 km? Obviously, 60 times more (6000: 100 \u003d 60). Total, we get the final price: 60 · 220 \u003d 13,200 rubles. Yes, 13,200 rubles for gasoline per month! What do you want?

A task. In the summer camp, each participant relies on 40 g of sugar per day. There are 160 people in the camp. How many kilogram packs of sugar will be needed for the entire camp for 6 days?

So, everyone needs 40 grams per day. Only 160 people, they need 160 · 40 \u003d 6400 grams of sugar. And so for 6 days. Total sugar consumption: 6 · 6400 \u003d 38400 grams.

Well, how many kilogram packs do you need to buy to provide these 38,400 grams? Recall that 1 kg is 1000 grams. Then everything is simple: 38400: 1000 \u003d 38.4 → 39 packs. Again, since you want to find the smallest value, round off the result.

A task. The summer camp has 245 children and 29 teachers. The bus accommodates no more than 46 passengers. How many buses are required to transport everyone from the camp to the city?

On buses, you need to accommodate everyone: both children and caregivers. Only 245 + 29 \u003d 274 people. But only 46 people can be pushed into one bus. Find how many buses are needed:

Round up to accommodate all passengers. Otherwise, someone will have to walk.

A task. In the summer, a kilogram of strawberries costs 80 rubles. Mom bought 3 kg 500 g of strawberries. How many rubles of change should she receive from 1000 rubles?

So, mom bought 3 kg and 500 grams of strawberries. We translate this into kilograms - we get 3.5 kg. According to the condition, 1 kg of strawberries costs 80 rubles. So, 3.5 kg of strawberries cost 3.5 · 80 \u003d 280 rubles.

That is what mother had to pay. But, alas, she took out a banknote of 1000 rubles from her shabby Soviet wallet. Therefore, the cashier had to give her change (I would not give in the place of the cashier). Delivery amounted to 1000 - 280 \u003d 720 rubles.

A task. A birthday is supposed to give a bouquet of an odd number of flowers. Tulips cost 70 rubles apiece. Vanya has 300 rubles. Of the largest number of tulips, he can buy a bouquet for Masha's birthday?

So, the whole month Vanya saved on paid dinners, and as a result he saved up as much as 300 rubles, which he is now going to spend on tulips for Masha. Since each tulip costs 70 rubles, Vanya will be able to buy 300: 70 \u003d 4 tulips. And he will have 20 more rubles.

But 4 tulips should not be given, so Vanya will buy only 3 tulips, spending 3 · 70 \u003d 210 rubles on them. He successfully drinks the remaining 90 rubles with friends after school.

A task. Pavel Ivanovich bought an American car, on the speedometer of which speed is measured in miles per hour. The American mile is 1,609 m. What is the speed of the car in kilometers per hour if the speedometer shows 26 miles per hour? Round the answer to an integer.

If 1609 meters are in one mile, then 26 · 1609 \u003d 41,834 meters in 26 miles. We are asked to answer in kilometers. There are 1000 meters in every kilometer, so 41 834 meters is 41 834: 1000 \u003d 41.834 kilometers. We round to an integer - we get 42 km. Note: it is the standard rounding that works here: no “largest” and “smallest” ones, as in previous tasks.

A task. In a pack of 500 sheets of A4 paper. 1300 sheets are consumed per week at the office. What is the smallest number of packs of paper you need to buy at the office for 7 weeks?

Well, such a problem was solved above (see). Therefore, I will be brief:

1. Total sheets: 1300 · 7 \u003d 9100;
2. Packs required: 9100: 500 \u003d 18.2 → 19.

Since you need to find the smallest number of packs, round the number up.

A task. In a pack of 500 sheets of A4 paper. During the week, 1,100 sheets are spent at the office. What is the smallest amount of paper you need to buy at the office for 6 weeks?

Similar to the previous task:

1. Total sheets: 1100 · 6 \u003d 6600;
2. Packs required: 6600: 500 \u003d 13.2 → 14.

According to the rules, the result is rounded up.

A task. The ship is designed for 850 passengers and 25 crew members. Each lifeboat can accommodate 80 people. What is the smallest number of boats on the ship, so that, if necessary, they could accommodate all passengers and all crew members?

Such a task already existed (see), only the numbers are different. Therefore, consider a short solution:

1. Total number of people: 850 + 25 \u003d 875;
2. Boats Required: 875: 80 \u003d 10.9375 → 11.

We round up, otherwise someone will be left without a boat.

A task. The ship is designed for 600 passengers and 20 crew members. Each lifeboat can accommodate 80 people. What is the smallest number of boats on the ship, so that, if necessary, they could accommodate all passengers and all crew members?

We solve similarly to the previous task:

1. Total number of people: 600 + 20 \u003d 620;
2. Boats Required: 620: 80 \u003d 7.75 → 8.

The result is rounded up.

Job Source: Decision 2936.-3. USE 2017 Mathematics, I.V. Yashchenko. 36 options.

Exercise 1.   The ship is designed for 450 passengers and 16 crew members. Each lifeboat can accommodate 40 people. What is the smallest number of boats on the ship, so that, if necessary, they could accommodate all passengers and all crew members?

Decision.

1st method.   The total number of people on board is 450 + 16 \u003d 466. Since each boat accommodates 40 people, 466: 40 \u003d 11.65 is required, that is, 12 boats are needed.

2nd method.   You can see that the first 440 people will fit in 11 boats. There are still 466-440 \u003d 26 people who are accommodated in the 12th boat.

Task 2.   The diagram shows the average monthly air temperature in Yekaterinburg (Sverdlovsk) for each month of 1973. Months are indicated horizontally, and vertically - temperature in degrees Celsius. Determine from the diagram below how many months the average monthly temperature was more than 14 degrees Celsius.

Decision.

The height of the bars indicates the monthly average temperature. In the task, it is required to calculate the number of columns exceeding 14 degrees. The figure shows that these are the columns of the months of June, July and August, that is, 3 months.

Answer: 3.

Task 3.   On a checkered paper with a cell size of 1x1, a rhombus is depicted. Find its area.

Decision.

The area of \u200b\u200bthe rhombus is calculated through the lengths of its diagonals and by the formula

The figure below shows the diagonals of the rhombus with red lines, and it can be seen that the length of one diagonal of the cell, the length of the second - of the cells.

The proposed manual contains tasks that are as close as possible to real examination tasks, but distributed by thematic blocks; this will make it possible to gradually work out a particular topic, identify gaps and eliminate them, generalize and systematize what has been studied.
The collection contains answers to all test cases. In addition, samples of forms used at the exam for recording answers to decisions are given.
The manual is intended for teachers to prepare students for the math exam, and students - high school students and applicants - for self-study and self-control.

Examples.
The ship is designed for 450 passengers and 30 crew members. One lifeboat can accommodate 70 people. What is the smallest number of boats needed to accommodate all passengers and crew members if necessary?

Notebook costs 6 rubles. What is the largest number of such notebooks that can be bought for 200 rubles, provided that when buying more than twenty notebooks, the buyer receives a 10% discount on the cost of the entire purchase?

In one pack of 500 sheets of A4 paper. Over a week, 1,600 sheets are spent at the office. What is the smallest number of bundles of paper you need to buy at the office for 3 weeks?

CONTENT
Thematic training exercises 5
Level 5 quests
B1 5
B2 6
B3 12
B4 16
B5 19
B6 20
B7 22
B8 23
B9 28
B10 29
B11 31
B12 32
B13 34
B14. 35
Quests from C 37
C1 37
C2 38
C3 40
C4 41
C5 42
C6 44
Benchmark tests 46
Description of the Unified State Examination Forms in 2013 46
Extract from the instructions for filling out the forms 46
Option 1 52
Option 2 55
Answers to practice tests 60
Answers to control tests 63.

Free download the e-book in a convenient format, watch and read:
Download the book of Unified State Examination, Mathematics, Thematic training exercises, Level B, C, Lappo L.D., Popov M.A., 2013 - fileskachat.com, fast and free download.

• Unified State Examination, Mathematics, Workshop on the execution of standard test tasks of the Unified State Examination, Educational-methodical manual, Lappo L.D., Popov M.A., 2006
• USE 2019, Mathematics, Profile level, Expert in USE, Lappo L.D., Popov M.A.
• USE 2019, Examination simulator, 20 exam options, Mathematics, Basic and profile levels, Lappo L.D., Popov M.A.

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