Basic formula: ① Total amount of work = working efficiency × working time.

(2) Work efficiency = total workload ÷ working hours.

(3) Working hours = total workload ÷ working efficiency

Basic idea:

① Assume that the total workload is "1" (independent of the total workload);

(2) Assuming that a convenient number is the total workload (generally the least common multiple of the time they need to complete the total workload), then the work efficiency and working time can be simply expressed by the above three basic relationships.

Key questions:

Determine the correspondence between workload, working hours and work efficiency.

Mathematical knowledge points in the second grade graduation examination of primary school: logical reasoning

Conditional analysis-hypothesis method: assume that one of the possible situations is established, and then judge according to this assumption. If there is a contradiction with the title conditions, it means that the hypothetical situation is not established, then the opposite situation is established. For example, if A is an even number and there are contradictions in the judgment process, then A must be an odd number.

Conditional analysis-list method:

When there are many conditions for setting questions and many assumptions are needed to complete them, lists are needed to assist the analysis. List method is to express all the conditions of the problem with a rectangular table. The rows and columns of the table represent different objects and situations, observe the problems in the table and make judgments by using logical laws.

Conditional analysis-chart method:

When there are only two kinds of relationships between two objects, a connection can be used to represent the relationship between the two objects, with a connection indicating a positive state such as "Yes, Yes" and no connection indicating a negative state. For example, there are two states between A and B: knowing or not knowing. Being connected means knowing, but not knowing.

Logical calculation:

In the process of reasoning, besides conditional analysis, corresponding calculation is needed, and new judgment and screening conditions are provided according to the calculation results for reasoning.

Simple induction and reasoning:

According to the characteristics and data provided by the topic, this paper analyzes the existing laws and methods, and extends them from special situations to general situations, and deduces the relevant relations, thus solving the problems.

The sixth grade graduation examination of primary school mathematics is very difficult. Knowledge point 3: ratio and proportion

Ratio: The division of two numbers is also called the ratio of two numbers. The number before the comparison symbol is called the first item of comparison, and the number after the comparison symbol is called the last item of comparison.

Ratio:

The quotient of the former term divided by the latter term is called the ratio.

The nature of the ratio:

The first term and the second term of the ratio are multiplied or divided by the same number at the same time (except zero), and the ratio remains unchanged.

Proportion:

Two expressions with equal ratios are called proportions. A: b = c: d or

Nature of proportion:

The product of two outer terms is equal to the product of two inner terms (cross multiplication), and ad=bc.

Positive proportion:

If A expands or contracts several times and B also expands or contracts several times (when the quotient of AB is constant), A is directly proportional to B. ..

Inverse ratio:

If A expands or contracts several times and B also contracts or expands several times (when the product of AB is constant), A and B are inversely proportional.

Proportion:

The ratio of the distance on the map to the actual distance is called the scale.

Proportional distribution:

Dividing several numbers into several parts according to a certain proportion is called proportional distribution.

The sixth grade primary school graduation exam mathematics difficult knowledge point 4: geometric area

Basic idea: In the calculation of some areas, if the formula cannot be used directly, it is generally necessary to cut, translate, rotate, fold, decompose, deform and superimpose the graphics to make the irregular graphics into regular ones for calculation; In addition, we need to master and remember some conventional regional rules.

Common methods:

1. Connection auxiliary line method

2. Use two triangles with equal bases and equal heights, with equal areas.

3. Bold assumptions (some points are set at any point in the topic, and you can set any point in a special position when solving problems).

4. Use special laws

(1) isosceles right triangle, it is known that any side can find the area. (The square of hypotenuse divided by 4 equals the area of isosceles right triangle)

② After trapezoid diagonal connection, the waist areas are equal.

③ The area of the circle accounts for 78.5% of the circumscribed circle.

The sixth grade elementary school graduation exam mathematics difficult knowledge point 5: trip problem.

Basic concepts: The travel problem studies the movement of objects, and it studies the relationship among the speed, time and distance of objects.

Basic formula:

Distance = speed × time; Distance ÷ time = speed; Distance/speed = time

Key questions:

Determine the position and direction during the movement.

Meeting problem: speed sum × meeting time = meeting distance (please write other formulas)

Catch-up problem: catch-up time = distance difference ÷ speed difference (write other formulas)

Flow problem: downstream flow range = (ship speed+current speed) × downstream time.

Upstream stroke = (ship speed-water speed) × upstream time

Downstream speed = ship speed+current speed

Current speed = ship speed-water speed

Still water velocity = (downstream velocity+upstream velocity) ÷2

Water velocity = (downstream velocity-upstream velocity) ÷2

Running water problem: the key is to determine the speed of the object, refer to the above formula.

Bridge crossing problem: the key is to determine the moving distance of the object, refer to the above formula.

Main methods: line drawing method.

Basic question:

Given any two quantities of distance (meeting distance and catching distance), time (meeting time and catching time) and speed (speed sum and speed difference), find the third quantity.

Important and difficult knowledge points of mathematics in the sixth grade graduation examination of primary school: indefinite equation

One-dimensional linear indefinite equation: an equation with two unknowns is called binary linear equation, because its solution is incorrect, it is also called binary linear indefinite equation;

Traditional methods:

Observation, experiment and enumeration;

Multivariate indefinite equation:

A ternary linear equation is called ternary linear equation, and its solution is different.

Solution of multivariate indefinite equation;

Determine the value of an unknown number according to the known conditions, or eliminate an unknown number, so as to turn the ternary linear equation into a binary linear indefinite equation and solve it according to the binary linear indefinite equation.

Involving knowledge points:

Column equation, divisibility of numbers, size comparison

Steps to solve indefinite equations:

1, column equation; 2. elimination; 3. Write an expression; 4. Determine the scope; 5. Determine the characteristics; Step 6 determine the answer

Skills summary:

A. Skills of writing expressions: use unknowns with inconspicuous features to represent unknowns with obvious features, and consider using unknowns with small range to represent unknowns with large range.

B, exclusion skills: exclude a wide range of unknowns.