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Teaching and learning quality test of the first unit equation of mathematics in the sixth grade of primary school (1)
1. Cheetah is the fastest animal in the world. Its speed can reach 1 10 km per hour, which is 20 km more than twice the fastest speed of a cat. (1) Please write a relation according to this sentence:

Maximum speed of cheetah =2× maximum speed of cat +20km.

(2) Assuming that the fastest speed of a cat is x kilometers per hour, please list an equation:

2X+20= 1 10

(3) (1 10-20) kilometers refers to:

Twice the fastest speed of a cat.

(4) "The fastest speed of a cheetah is 20 kilometers, which is more than twice that of a cat." Please put this sentence in another way:

The fastest speed of a cat is twice that of a cheetah, 20 kilometers less.

(5) The fastest speed of a cheetah at minus 20km is twice that of a cat.

(6) According to the above analysis, two other equations can be listed to find the fastest speed of a cat. One is

2X+20 = 1 10; Another equation is 2X= 1 10-20.

2. Mom spends 135 yuan to buy a suit, and the price of a coat is twice that of trousers.

(1) Please write the relationship between coat and trousers according to this sentence: First, coat price = trousers price ×2.

The other is: 65438+ 0/2 of coat price = trousers price.

(2) If the unit price of trousers is X yuan, the listed equation is 2X+X= 135.

(3) If the unit price of a coat is Y yuan, the equation listed is:

y+ 1/2y= 135

(4) The sentence "The price of coat is twice that of trousers" plays a role in the equation: equivalent substitution.

(5) The sentence "Mom spends 135 yuan buys a suit" plays a role in the equation:

Look for the role of equal relations.

3. Please write the relationship between Xiao Liang's present height and his birth height according to the sentence "Xiao Liang's present height is 3 times less than that at birth, 0.03m": Xiao Liang's present height =3× his birth height -0.03.

If the height at birth is y meters, please list an equation: 3y-0.03= current height.

4. Please write down the relationship between the quantities according to "Class Six (1) planted 25 poplars, 3 rows of pine trees,1* * planted 6 1 tree":

Poplar +3 rows of pine trees =6 1 tree

If there are x pine trees in each row, list an equation:

25+3X=6 1

5. Solving equation 4x-x = 3. 15 is divided into two steps. The first step is 3x = 3. 15. The calculation basis of this step is: merging similar items; In the second step, 3x ÷ 3 = 3. 15 ÷ 3 is obtained. The basis of this step is that the new equation obtained by multiplying (or dividing) both sides of the equation by the same number (except 0) has the same solution as the original equation.

6. Solving practical problems with equations requires two basic skills, one is the ability to solve equations correctly and skillfully, and the other is to correctly understand the meaning of the questions, analyze the relationship between known quantities in the questions, express an unknown number as a known number by letters, find out the equivalent relationship in the questions, and list the equations correctly.