Download Lekcja 2 B

SJO PW - Język angielski ogólnotechniczny, Poziom B2
Opracowanie: Teresa Olechowska
Lekcja 2 B
______________________________________________________________________________________________
MATHEMATICS
INTRODUCTION (in the class):
POWERS, ROOTS, MATRICES
TASK 1
Think and try to match the answers to the following questions:
1. What does it mean, when we say x squared?
2. What does it mean when you see the following:
16
3.
4.
5.
6.
a.
b.
c.
d.
e.
What is a matrix?
What do matrices consist of?
How can matrices be added?
How can matrices be multiplied?
By adding corresponding elements - only if they have the same order.
It means the squared root of sixteen and it equals 4.
Elements (numbers/letters), rows and columns.
Then the 2 is called the power or index.
If the number of elements in the columns of one matrix equals the number of elements in the rows of
the other matrix.
f. It is an array of numbers or letters in the shape of a rectangle.
INPUT –HOMEWORK
Table of higher powers –just to help you in finding the results 
A partial table of xn.
Bases are on the left, exponents are across the top:
xn 0 1
2
3
4
5
6
7
8
9
10
11
12 ... n
0 ? 0
0
0
0
0
0
0
0
0
0
0
0
1 1 1
1
1
1
1
1
1
1
1
1
1
1
2 1 2
4
8
16
32
64
3 1 3
9
27
81
243 729 2187 6561
4 1 4 16
64
256 1024 4096
5 1 5 25 125
128 256 512 1024 2048 4096
0
1
2n
625 3125
6 1 6 36 216 1296 7776
7 1 7 49 343 2401
8 1 8 64 512 4096
9 1 9 81 729 6561
10 1 10 100 1000 10000
11 1 11 121 1331
12 1 12 144 1728
13 1 13 169 2197
14 1 14 196 2744
15 1 15 225 3375
16 1 16 256 4096
...
x 1 x
x2
x3
http://en.wikibooks.org/wiki/Primary_Mathematics/Powers,_roots,_and_exponents
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SJO PW - Język angielski ogólnotechniczny, Poziom B2
Opracowanie: Teresa Olechowska
Lekcja 2 B
______________________________________________________________________________________________
TASK 2
Knowing that:
a x a² = a³ (a times a squared is equal to a cubed)
a³ x a² = a (a cubed times a squared is equal to a to the power of five, or a to the fifth power )
a. practice reading out the following:
1. a² + b²
2. x² + y³
3. p
4. xⁿ
b. Can you solve the following equations:
1. 4a² + 2a² = ?
2. 4a² - 2a² = ?
3. 4a² x 2a² = ?
4. 4a² ÷ 2a² = ?
TASK 3
Complete the following statements about procedure:
1. When multiplying two numbers which have been raised to certain powers e.g. n³ (n… … … … … ..)
and n (n … … … … … … … … fifth), we add the … … … … … … … .. .
2. When we wish to … … … … … … … … … a power … … … … … … … … a power, the … … … … … … ..
must be … … … … … … … … . In the above case the answer is n¹.
To learn more you can visit the YouTube site:
http://www.youtube.com/watch?v=qOn-NW_lsvE&feature=related
TASK 4
Why "Root" ... ?
When you see "root" think:
"I know the tree, but what is the root that produced it?"
Example: in √9 = 3 the "tree" is 9, and the root is 3.
http://www.mathsisfun.com/numbers/nth-root.html
Knowing that:
is called the radical sign;
64 means the square root of 64;
27 means the cube root of 27;
x means the fifth root of x.
If we want to find the root in the following example, we must divide the index by the root:
Practice reading out the following, and then express them in more simple terms:
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SJO PW - Język angielski ogólnotechniczny, Poziom B2
Lekcja 2 B
Opracowanie: Teresa Olechowska
______________________________________________________________________________________________
√x²;
√4x;
√a²b²
∜mn
1.
2.
3.
4.
5.
b³
6.
a³
7. √16b²
If you want to learn and practice more, check the YouTube sites:
http://www.youtube.com/watch?v=PlZZ6ZZJBg4
TASK 5
Words which retain their original Greek or Latin forms make their plurals according to the rules of Greek
and Latin.
-us > -i
-is > -es
-um
-ix
-a
-on
-ices
-ex
Supply the proper plurals of the words in the brackets.
1.
2.
3.
4.
5.
The new (syllabus)… … … … … … will be drawn up according to different (criterion)… … … … … .
These (index) … … … … … … … must be multiplied.
(Matrix)… … … … … can be added if they have the same order.
He agreed that these were strange (phenomenon) … … … … … … … .. .
Television and newspapers are the mass (medium) … … … … … … … .
TASK 6
Have a look at the following pictures:
ROW
x
COLUMN
=
RESULT
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SJO PW - Język angielski ogólnotechniczny, Poziom B2
Lekcja 2 B
Opracowanie: Teresa Olechowska
______________________________________________________________________________________________
http://en.wikipedia.org/wiki/Matrix_multiplication
1. Now add two matrices:
a 4
1
7
5
2
8
3
6
9
+
b 3
5
6
1
4
9
7
2
8
=
2. And multiply the following two matrices:
a
2 0 3
- 1 3 1
x
b 3 1
2 1
1 0
=
If you want to learn more - visit:
http://www.mathwarehouse.com/algebra/matrix/multiply-matrix.php
http://www.youtube.com/watch?v=sYlOjyPyX3g
CLASSWORK CHECKING
TASK 7
Discuss the following questions:
1. Can numbers or other mathematical concepts be said to exist?
2. Are numbers ‘discovered’or ‘invented’(Leopold Kronecker said that “God made the integers. All
else is the work of men”)?
3. Taking negative numbers into consideration –has anyone seen ‘minus one cow’?
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SJO PW - Język angielski ogólnotechniczny, Poziom B2
Opracowanie: Teresa Olechowska
Lekcja 2 B
______________________________________________________________________________________________
1.
2.
3.
4.
5.
6.
7.
BIBLIOGRAPHY
A Mathematical Dictionary, Jason, R.E., Pergamon Press, 1979
Alex’s Adventures in Numberland, Bellos, Alex, Bloomsbury, 2010
Computer Adventures in Lingua Land, Olechowska, Teresa, Rouba, Wojciech, WSiP, 1992
English for Basic Maths, Blackie, David, Nelson, 1978
Lingua Land Kappa Land, Olechowska, Teresa, WPW, 1986
Mathematics and the Imagination, Kasner, Edward, Newman, James, Penguin Books, reprinted 1979
MINI anglojęzyczne –EAP & ESP, Olechowska, Teresa, wydanie własne, 2012
http://dictionary.reference.com
http://www.purplemath.com/modules/radicals.htm
http://www.mathsisfun.com/numbers/nth-root.html
http://en.wikibooks.org/wiki/Primary_Mathematics/Powers,_roots,_and_exponents
http://www.youtube.com/watch?v=qOn-NW_lsvE&feature=related
http://www.youtube.com/watch?v=PlZZ6ZZJBg4
http://en.wikipedia.org/wiki/Matrix_multiplication
http://www.mathwarehouse.com/algebra/matrix/multiply-matrix.php
http://www.youtube.com/watch?v=sYlOjyPyX3g
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