Grade 7 Olympiad 20, Mathematics Olympiad questions for the first year of junior high school

1.It is known that a and b are opposite numbers to each other, c and d are reciprocal to each other, the square of m is equal to two, and p is the number represented by the origin on the number line, then.

p^2005+ cd+ a+b/abcd +m^2=（ 3 ）2.Calculation:

3.Xiao Ming and Sakura race up the stairs, they start from the ground of a tall building (the first floor) and return to the ground after reaching the 28th floor.

When Tom arrives on the 4th floor, Sakura has just arrived on the 3rd floor. If they keep a fixed pace, Xiao Ming reaches the 28th floor and returns to the ground on the way.

On what floor will you meet Sakura? (Note: The stairs between the first and second floors belong to the first floor, and so on).

28-1=27 floors 4-1=3 floors 3-1=2 floors.

3 27 = 9 27-9 * 2 = 9 floors.

9 (3+2) 3rd floor.

18 + 3 + 1 = 22 floors.

1) Calculate 100-99a-99b

A b is the opposite of each other, 99a+99b=0

100-99a-99b=100

2) Determine the symbol of (a-b) (b-a) (a-c).

a-b) is 0

b-a) Negative.

a-c) Positive.

3) Simplify|a|-|a+b|+|c-a|+|c-

b|a-0+c+a+b-c

a+a+b5.Known |a-1|with |b-2|Opposite numbers, try to find them.

1/ab + 1/（a+1）（b+1） +1/（a+2（b+2）+…1 (a+100)(b+100).

Do the math yourself. 6.Calculation:

1）-8x+（6x-5x）-2（3+y+x）

9x-6-2y

7.Simplification first, then evaluation.

4 3x-(3x+2y-3 5)+2(8 3x+3y+2 5), where x=-3, y=2

The old problem, three people went to buy clothes, 100 yuan, the boss instructed the employee to return 50, the employee felt that 50 was not good, so he took 20 himself, and gave 10 yuan to each of the three people, that is, 90 yuan a piece of clothes.

Got 90 3 + 20 = 290 yuan, who else is 10 yuan in his hands?

It should be that the three of them only took out 270 yuan, of which the boss got 250 yuan and the employee got 20 yuan.

The expression is not: (b -a) + a b-3ab )-2 (b -ba).

Simplification: original formula = -(a + b ) + 3 (a b -ab ) = 27 + 3 * (-6) = -45

I'll forget it.,Otherwise, how to simplify.。。。

Solution: If there is a student A, each student should pay X yuan in full, and the total cost is w yuan.

Then: w甲=x+;

w B = if w A< = w B, then: x+<=

By x>0, then: a>=3

When there are 3 students, the consumption of both companies A and B is the same, and when the number of students is greater than 3, company A is more favorable than company B.

After setting up more than x people, Company A has a preferential price compared to Company B.

Company A's total price s1=(x+1)*

Company B's total price s2=(x+2)*

Company A has a better price than Company B.

x>3 people.

-1) Swing.

What is the nth number.

Expressed in an equation.

Categories: Education Academic Examination >> High School Entrance Examination.

Problem description:1My sister took my younger brothers to pick mushrooms, and at first my sister picked 45, and gave all of them to my younger brothers (none of them were picked) On the way home, the eldest brother picked 2, and the younger brother lost 1 and a half, and the second brother doubled compared to the original. The 3rd brother lost 2.

At this time, everyone has an equal number of mushrooms. Q: How many mushrooms did each of the four younger brothers get from their sister?

2.If the positive integer satisfies the square of the equation x minus the square of y is equal to 64. Then the number of such positive certificates has.

A: Group 1, Group B, Group B, Group C, Group C, Group D, Group 4.

4.There are 4 numbers, and the sum of each 3 numbers is 4 numbers.

Thank you, teachers, Kaichai, it's better to have a process (you know that the answer is not interesting).

Thanks for 3 grams of oil

Analysis: 1, let the equal number be x, then the eldest brother is x-2, the younger brother is 2x, the second brother is x 2, and the third brother is x+2

The sum of the four numbers is 45, and the solution is x=10

So 8 were given to the eldest brother, 20 to the younger brother, 5 to the second brother, and 12 to the 3rd brother.

2，x^2-y^2＝（x+y)(x-y)=64

Substituting these four groups of numbers one by one, there are two sets of positive integer solutions, which are x=17, y=15 and x=10, y=6

3, Reel x (1-1 2-......1/1996） y＝（1/2+1/3+1/4+……1996）

Yes: x+y 1

Then the original formula x*(y+1 1997)-(x-1 1997)*y

x+y)/1997＝1/1997

4. Add these four sums, which is equivalent to adding each number three times, then the sum of the four numbers is:

The four numbers are: 28-15 13, 28-22 6, 28-23 5, 28-24 4

First of all, the formula becomes.

Then the root is based on the formula of the decided.

n(an+a1)) 2a1) sub becomes.

Empty Trillion 1 503*504) branch noise +.

According to the formula (1

502*503) is 1 502

The formula becomes. The result is 3