"Exponent" Exponential function and logarithmic function PPT (radical formula in the first lesson)

Description

"Exponent" Exponential function and logarithmic function PPT (radical formula in the first lesson)

Part One: Learning Objectives

1. Understand the concepts of nth square roots and radical expressions, and master the properties of radical expressions. (emphasis)

2. Be able to use the properties of radical expressions to perform operations on radical expressions. (key points, difficult points, easy to make mistakes)

core competencies

Use the properties of radical expressions to perform operations on radical expressions and cultivate mathematical operation literacy.

Index PPT, part 2: independent preview to explore new knowledge

A preliminary exploration of new knowledge

1. Radicals and related concepts

(1) Definition of nth root of a

If _____, then x is called the nth root of a, where n>1, and n∈N*.

(2) Expression of the nth root of a

Parity of n Symbol of the nth root of a Value range of a

n is an odd number na R

n is an even number ±na [0, +∞)

(3) Radical formula

The formula na is called a radical formula, here n is called _____, and a is called _____.

2. Properties of radicals (n>1, and n∈N*)

(1) When n is an odd number, nan=_____.

(2) When n is an even number, nan=_____=_____, a≥0, _____, a<0.

(3)n0=_____.

(4) Negative numbers do not have _____ square roots.

Thinking: (na) Is the range of the real number a in n any real number?

Tip: Not necessarily, when n is an odd number greater than 1, a∈R;

When n is an even number greater than 1, a≥0.

First try

The operation result of 1.481 is ()

A． 3

B． -3

C． ±3

D. ±3

2. m is a real number, then the following formula may not be meaningful ()

A.4m2

B.5m

C.6m

D.5－m

3． The correct number of the following statements is ()

①The fourth square root of 16 is 2; ②The operation result of 416 is ±2; ③When n is an odd number greater than 1, na is meaningful for any a∈R; ④When n is an even number greater than 1, na is only valid when It is meaningful only when a≥0.

A． 1B. 2

C． 3D． 4

Index PPT, the third part: cooperative exploration to improve literacy

Conceptual issues with nth root

【Example 1】(1)The cube root of 27 is ________.

(2) It is known that x6=2 019, then x=___________.

(3) If 4x+3 is meaningful, then the value range of real number x is ________.

(1)3　(2)±62 019　(3)＋3，＋∞)　(1)The cube root of 27 is 3.

(2) Because x6=2 019, so x=±62 019.

(3) To make 4x+3 meaningful, x+3≥0 is required, that is, x≥-3.

Therefore, the value range of real number x is [-3, +∞). ]

regular method

Determination of the number and sign of nth root

The parity of 1n determines the number of nth roots;

When 2n is an odd number, the sign of a determines the sign of the nth root.

Class summary

1. Note the difference between nan and (na)n. When solving the former, you need to determine whether n is an odd or even number, and you must also pay attention to the sign of the real number a, while the latter (na)n=a is an identity. As long as (na)n is meaningful, its value is always equal to a.

2. To determine whether a number has an n-th square root, we must first consider whether the radicand is a positive or negative number, and we must also distinguish between the two situations where n is an odd number or an even number.

Index PPT, the fourth part: reaching the standard and solidifying the double foundation in the hall

1. Thinking and analysis

(1) There is only one odd square root of a real number a. ()

(2) When n∈N*, (n-2)n=-2.()

(3)π－42＝π－4.()

2. It is known that m10=2, then m equals ()

A.102B． -102

C.210 D． ±102

3.π－42＋3π－33＝________.

4． Given -1

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Update Time: 2024-10-07

This template belongs to Mathematics courseware People's Education High School Mathematics Edition A Compulsory Course 1 industry PPT template

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