unit 2. powers and roots

I.E.S. FERNANDO III EL SANTO / PROYECTO BILINGÜE A.N.L.: MATHS 1

MATHS

UNIT 2: POWERS AND ROOTS.

UNIT 2: POWERS AND ROOTS

OUTLINE

ASPECTOS LINGÜÍSTICOS VOCABULARY

1. POWERS.

A. OPERATIG WITH POWERS:

• WITH THE SAME BASE. • WITH DIFFERENT BASE BUT

THE SAME EXPONENT. B. THE BASE AS NEGATIVE. C. THE BASE AS A FRACTION. D. THE EXPONENT AS

NEGATIVE. E. THE BASE IS 10.

2. ROOTS. A. A SQUARED ROOT. B. ROOT WITH INDEX n.

• PRESENTE CONTINUO • PRESENTE CONTINUO

CON VALOR DE FUTURO.

• VERBOS MODALES : SABER, PODER

(CAN / CAN´T)

• ANSWER • APPROXIMATION • BASE • BELLOW • BOTTOM • EVEN • INDEX • INVERSE • ITSELF • ODD • OPERATION • PERFECT SQUARED • POWER • ROOT • RULE • SQUARED ROOT • TIME • TO CONSIDER • DEEP • MUST • TO THE POWER OF • TO WORK • WHOLE NUMBER • ZERO

PHO�ETICS

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MATHS


1. POWERS

Power is

This is where the small is an exponent. It tells us how many times we must multiply the factor

by itself. is called “BASE” and is called “INDEX” or “EXPONENT”.. A. OPERATING WITH POWERS

• Remember the rules of operation with the same base: 1) Multiplying: . Ex:

2) Dividing: . Ex:

3) The power of a power: . Ex:

4) Power with an index 0 or 1: ;

. Ex:

• If the base is not the same but the exponent is the same:

1) Multiplying: . Ex:

2) Division: . Ex:

B. IF THE BASE IS NEGATIVE. If the base of a power is negative, we must look at the exponent:

• If the exponent is even, the answer is positive. For example:

• If the exponent is odd, the answer is negative. For example:

C. IF THE BASE IS A FRACTION. If the base of a power is a fraction, we must multiply the fraction by itself the number of times that the exponent tells us:

So we have a power in the numerator and a power in the denominator:

Examples:

n times

n times

n times


MATHS


D. IF THE EXPONENT IS NEGATIVE.

When the exponent is negative, we must consider the inverse. We must put the power on the bottom with the positive exponent.

For example:

E. IF THE BASE IS 10

10 to the power of is one bellow zeros. For example: . If the exponent is negative,

the answer is:

2. ROOTS.

A.- SQUARED ROOT.

In this unit we are going to work with squared roots. The definition of squared root is

For example:

Numbers with squared roots are natural numbers called “Perfect squares” All of them are the square of whole numbers. For example: 1, 4, 9, 16, 25,…… Remember that we can obtain the squared root of a number by approximation, like the following:

So If the “Number inside the root” (what’s is its name?) is a fraction, we have to calculate the squared root of the numerator and the squared root of the denominator.

B.- ROOT WITH INDEX

The number inside the root is the root of index of a number to which the power of is equal to.

for example We are not going to go deeper with this.

n times

n times


MATHS


KIND OF EXERCISES:

1. To find Perfect squares 2. To solve by approximation. 3. Expressions with Perfect squares 4. Roots with fractions. 5. To solve roots with two different indexes.

VOCABULARY

Vocabulary Pronunciation Translation

A

Answer. /’ænsər/ respuesta

Approximation /ə‚prɒksə’meɪʃən/ Aproximación

B

Base / beɪs/ Base

Bellow / bɪ’ləʋ/ Bajo

Bottom / ’bɒtəm/ denominador

D

Different adjectivo /'d�frənt/ Diferente

E

Even / ’i:vən/ Par

F

Fraction /frækʃən/ Fracción

I

Index sust. / ’ɪndek/ Índice

Inverse sust / ’ɪnvɜ:rs/ Inversa

Itself /ɪt’self/ Él mismo

N

Negative adjetivo /'negət�v/ Negativo

Number sust. /'n�mbər / Número

O

Odd Adj. / ɒd/ Impar

Operation /‚ɒpə’reɪʃən/ Operación

P

Perfect square / ’pɜ:rfɪkt/ / skweər/ Cuadrado Perfecto

Power / ’paʋər/ Potencia

Positive adjetivo /'pɑ:zət�v / Positivo

R


MATHS


Root / ru:t/ Raiz, Radical

Rule / ru:l/ Regla

S

Square root / skweər/ / ru:t/ Raiz cuadrada

T

Times /taɪmz/ Veces

To consider /kən’sɪdər/ Considerar

Deeper /’di:pən/ Profundizar

Must /mʌst/ Beber, tener que

To the power of /tu:/ /ði:/ / ’paʋər//ɒv/ Elevado a….

To work /wɜ:rk/ trabajar

W

Whole Numbers sustantivo /həʊl/ /'n�mbər / Número entero

Z

Zero /’zɪərəʋ/ Cero

APENDIX: The Power of ten

http://www.google.es/imgres?imgurl=http://www.komenswfl.org/assets/images/power-of-ten.jpg&imgrefurl

Ver el siguiente vídeo en clase.

http://www.youtube.com/watch?v=Kpjyfo_7Klg Activities: Complete as you watch the video what you can see in different distances: Use the following words: angstroms, microns, millimeters, centimeters, meters, light years .Don´t forget the powers. Example: 10º: 1 meter.


MATHS


unit 2. powers and roots

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