"Real Numbers" Real Numbers PPT

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"Real Numbers" Real Numbers PPT

Part One Content: Basic Knowledge Key Points

Knowledge point 1: Concept and classification of real numbers

1. Which of the following statements is correct (B)

A.Irrational numbers include positive irrational numbers, negative irrational numbers and zero

B. Real numbers can be represented by points on the number axis

C. Numbers with a root sign are all irrational numbers

D. Numbers without a root sign are rational numbers

[Variation expansion] Which of the following statements is correct (C)

A. The sum of two irrational numbers must be an irrational number

B. The product of two irrational numbers must be an irrational number

C. The sum of a rational number and an irrational number must be an irrational number

D. The product of a rational number and an irrational number must be an irrational number

Real Number PPT, Part 2: Improvement of Comprehensive Ability

7. The following statements: ①√(- 10 ) ^2 )=-10; ② The points on the number axis have a one-to-one correspondence with the real numbers; ③ The arithmetic square root of a number is still itself, and there are three such numbers; ④ Any Real numbers are either rational numbers or irrational numbers; ⑤ the sum of two irrational numbers is still an irrational number; ⑥ irrational numbers are infinite decimals. The correct statement is (B)

A.2 B.3 C.4 D.5

8. (Textbook Motif Variation) As shown in the figure, the length of side AD of rectangle ABCD is 2, the length of AB is 1, the corresponding point of point A on the number axis is -1, with point A as the center of the circle, the length of diagonal AC is The radius draws an arc, and the intersection axis is at point E. The real number represented by point E is (B)

A.√5+1 B.√5-1

C.√5 D.1-√5

9. Assume [x ) represents the smallest integer greater than x, such as [3 )=4, [-1.2 )=-1, then the correct conclusion among the following is (D)

A.[0 )=0

B.[x )-The minimum value of x is 0

C.[x )-The maximum value of x is 0

D. There exists a real number x, so that [x )-x=0.5 is established

Real Number PPT, Part 3: Expansion, Research and Breakthroughs

15. It is known that the corresponding real numbers of points A and B on the number axis are a and b respectively, where a and b satisfy |a-2|+( b+1 )2=0.

(1) Find the length of line segment AB.

(2) The number corresponding to point C on the number axis is x, and x is the solution to the equation x-1=1/3x+1. Is there a point P on the number axis such that PA+PB=PC? If it exists, find out The number corresponding to point P; if it does not exist, please explain the reason.

(3) Under the conditions of (1) and (2), points A, B, and C start to move on the number axis at the same time. If point A moves to the left at a speed of 1 unit length per second, point B and point C respectively Moving to the right at a speed of 4 units of length and 9 units of length per second, the distance between point B and point C is expressed as BC, and the distance between point A and point B is expressed as AB. Let the movement time be t seconds , try to explore: As time t changes, what quantitative relationship does AB and BC satisfy? Please write the corresponding equation.

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Update Time: 2024-10-19

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