EN17 Introduction to Algebra, Week 1 by Chris Yang https://padlet.com/chrisyang/EN0017Week1 Basic Algebra en-us 2016-09-27 09:44:42 UTC 2023-02-05 14:30:28 UTC hello@padlet.com https://padlet-assets.s3.amazonaws.com/icons/Dartstarget.png Module skeleton chrisyang https://padlet.com/chrisyang/EN0017Week1/wish/126595513 An introduction to the basic concepts and techniques of algebra for students who have not studied mathematics at tertiary level.

Number of Credits | 20
Level | L3
Module Lecturers | Dr Xin Yang and Dr Alistair Reid

On completion of the module a student should be able to
  • Solve linear and quadratic equations
  • Solve simple simultaneous equations
  • Understand the terms function, domain, range, one-to-one function and composition of functions
  • Recognise, sketch and interpret graphs of functions
  • Understand the definition and properties of ex and ln x
  • Understand coordinate geometry and apply it to solving equations
  • Use standard notation of vectors, apply a number of operations to vectors and use them to solve a variety of geometric problems
  • Solve equations numerically

Assessment Breakdown
Examination - Autumn Semester   80%  
Class Test   20%  (4 Nov 2016)

Essential Reading and Resource List
  • Foundation Mathematics – K.A. Stroud (Palgrave Macmillan)
  • Foundation Mathematics – L. Mustoe and M. Barry (Wiley)
]]> 2016-09-27 09:47:26 UTC https://padlet.com/chrisyang/EN0017Week1/wish/126595513 1 Algebraic expressions chrisyang https://padlet.com/chrisyang/EN0017Week1/wish/126599791 Poker Game: Take any poker card, add 15 to it, double the result, add this to the poker card number, divide the result by 3, take away the poker card number, calculate the result.]]> 2016-09-27 10:16:45 UTC https://padlet.com/chrisyang/EN0017Week1/wish/126599791 2. Introduction to clybot C6 chrisyang https://padlet.com/chrisyang/EN0017Week1/wish/126897068 A robot kit for learning maths, programming, electronics, computing, microcontroller.........]]> 2016-09-28 09:46:13 UTC https://padlet.com/chrisyang/EN0017Week1/wish/126897068 3. Algebraic expressions chrisyang https://padlet.com/chrisyang/EN0017Week1/wish/126898549 Example 1: A frequency variable f is assigned by f=100 (Hz). The f will increase by 200 Hz every second, express and calculate the f after 5 seconds.

Answer: f=100, f'=f+200*5=1100(Hz)

clybot C6: listen to the beep over 5 seconds.
]]> 2016-09-28 09:54:27 UTC https://padlet.com/chrisyang/EN0017Week1/wish/126898549 3. Algebraic expressions chrisyang https://padlet.com/chrisyang/EN0017Week1/wish/126916091 Example 2: What if the f doubles each second?

Answer: f=100, f'=f*2*2*2*2*2=3200(Hz)

clybot C6: listen to the difference of the tone.
]]> 2016-09-28 11:43:18 UTC https://padlet.com/chrisyang/EN0017Week1/wish/126916091 3. Algebraic expressions chrisyang https://padlet.com/chrisyang/EN0017Week1/wish/126924955 Example 3: Mitosis is the process in which one cell divides into two cells identical to the parent cell. Calculate the cell number after 5 mitoses of two original cells?]]> 2016-09-28 12:21:32 UTC https://padlet.com/chrisyang/EN0017Week1/wish/126924955 Example 3 chrisyang https://padlet.com/chrisyang/EN0017Week1/wish/126930633 Answer]]> 2016-09-28 12:39:10 UTC https://padlet.com/chrisyang/EN0017Week1/wish/126930633 4. Variables and constants chrisyang https://padlet.com/chrisyang/EN0017Week1/wish/126931604 A constant is a number.
A variable is a value that can change.
Usually, letters from the beginning of the alphabet, i.e. a, b, c, d, … are used to represent constants, and letter from the end of the alphabet, i.e. …v, w, x, y, z are used to represent variables.]]> 2016-09-28 12:42:03 UTC https://padlet.com/chrisyang/EN0017Week1/wish/126931604 4. Variables and constants chrisyang https://padlet.com/chrisyang/EN0017Week1/wish/126932784 Example 4: Which is the constant, which is the variable?

Answer:
]]> 2016-09-28 12:45:39 UTC https://padlet.com/chrisyang/EN0017Week1/wish/126932784 4. Variables and constants chrisyang https://padlet.com/chrisyang/EN0017Week1/wish/126956855 Example 5: Two light sensors are giving the reading of the ambient brightness, S1 and S2, respectively. Write an expression to calculate the average brightness of the two sensors.

Answer: Assume the average brightness is B, the expression would be: B = (S1 + S2) / 2.

clybot C6: 'hear' the brightness, send the average brightness as the frequency to the C6.
]]> 2016-09-28 13:43:21 UTC https://padlet.com/chrisyang/EN0017Week1/wish/126956855 Resource: cancer cell division chrisyang https://padlet.com/chrisyang/EN0017Week1/wish/126971738 2016-09-28 14:16:05 UTC https://padlet.com/chrisyang/EN0017Week1/wish/126971738 1. Algebraic expressions chrisyang https://padlet.com/chrisyang/EN0017Week1/wish/126981541 Group Discussion: Why everybody achieved the same result? Try to explain mathematically on a paper and then upload to Padlet.]]> 2016-09-28 14:37:10 UTC https://padlet.com/chrisyang/EN0017Week1/wish/126981541 5. Rule of Algebra chrisyang https://padlet.com/chrisyang/EN0017Week1/wish/126982064 Group Discussion and Presentation, based on the Note - Summary of Algebra (The Formal Rules of Algebra),
GIVE EXAMPLES!!! Peer marking trial*
Group 1 - 1.The axioms of equals; 2. Commutative rules; 3. Identity elements.
Group 2 - 4. Additive inverse; 5. Multiplicative inverse; 6. Definition of subtraction.
Group 3 - 7. Definition of division; 8. Inverse of inverse; 9- b-a and a-b.
Group 4 - 10. Rule of signs; 11. Rules for 0; 12. Factoring / Multiplying.
Group 5 - 13. Operation on both sides; 14. Change the sign; 15. Change the sing on inequality.
Group 6 - 16. Equations; 17. Change of sense on inequality; 18. Absolute value.
Group 7 - 19. Equivalent fractions; 20. Multiplication of fractions; 21. Division of fractions.
Group 99 - 22. Addition of fractions; 23. Rules of exponents; 24. Negative exponent.
Team X - 25. Exponent 0; 26. Square root; 27. a^2=b.
Volunteer ?- 28. Multiplying radicals; 29. nth root; 30. Rational exponent; 31. Laws of logarithms; 32. Complex unit.
]]> 2016-09-28 14:38:20 UTC https://padlet.com/chrisyang/EN0017Week1/wish/126982064 QR code for this material chrisyang https://padlet.com/chrisyang/EN0017Week1/wish/126994618 2016-09-28 15:06:25 UTC https://padlet.com/chrisyang/EN0017Week1/wish/126994618 The end chrisyang https://padlet.com/chrisyang/EN0017Week1/wish/126995278 2016-09-28 15:07:55 UTC https://padlet.com/chrisyang/EN0017Week1/wish/126995278 6. Terms and coefficients chrisyang https://padlet.com/chrisyang/EN0017Week1/wish/126995418 Algebraic expression notation:
  1 – power (exponent)
  2 – coefficient
  3 – term
  4 – operator
  5 – constant term
  x y c – variables/constants]]> 2016-09-28 15:08:18 UTC https://padlet.com/chrisyang/EN0017Week1/wish/126995418 7. Collecting like terms chrisyang https://padlet.com/chrisyang/EN0017Week1/wish/126996997 Terms which have the same variables are called like terms.

Like terms can be collected together by addition or subtraction. For example:

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

Exercises: Simplify each of the following by collecting like terms:

(a)   4xy+3xz-6zy-5zx+yx

(b)   -2a+4ab+a-4ba

(c)   3rst-10str+8ts-5rt+2st

(d)   2pq-4pr+qr-2rq+3qp

(e)   5lmn-6ml+7lm+8mnl-4ln
]]> 2016-09-28 15:11:35 UTC https://padlet.com/chrisyang/EN0017Week1/wish/126996997 Group list chrisyang https://padlet.com/chrisyang/EN0017Week1/wish/126997458 2016-09-28 15:12:34 UTC https://padlet.com/chrisyang/EN0017Week1/wish/126997458 8. Similar terms, Common factors and factorization chrisyang https://padlet.com/chrisyang/EN0017Week1/wish/127004096 In the algebraic expression:

ab+bc

Both terms contain the letter b and for this reason these terms, though not like terms, are called similar terms.

Common symbols such as this letter b are referred to as common factors and by using brackets these common factors can be factored out.

Example 6:

ab+bc=b(a+c)

This process is known as factorization.

Exercise: Simplify each of the following by collecting like terms and factorizing:

(a)   4xy+3xz-6zy-5zx+yx

(b)   3rst-10str+8ts-5rt+2st

(c)   2pq-4pr+qr-2rq+3qp

(e)   5lmn-6ml+7lm+8mnl-4ln

]]> 2016-09-28 15:26:58 UTC https://padlet.com/chrisyang/EN0017Week1/wish/127004096 9. Expanding brackets chrisyang https://padlet.com/chrisyang/EN0017Week1/wish/127004724 Removing brackets in algebraic expression is done by:

(a)Multiplying or dividing each term inside the bracket by the term outside the bracket, but 

(b)If the term outside the bracket is negative then each term inside the bracket changes sign.

For example:

3x(y-2z)=3xy-6xz

-2y(2x-4z)=-4yx+8yz

(y+x)/8x-(y-x)/4x=3/8-y/8x

Exercises: Expand the following and then refactorize where possible:

(a)   8x(y-z)+2y(7x+z)

(b)   (3a-b)(b-3a)+b^2

(c)    -3{w-7[x-8(3-z)]}

(d)    (2a-3)/4b+(3a+2)/6b
]]> 2016-09-28 15:28:23 UTC https://padlet.com/chrisyang/EN0017Week1/wish/127004724 Group 1 https://padlet.com/chrisyang/EN0017Week1/wish/127198364 [[(X+15) × 2 + x] /3] -×
-> [(2x + 30 + x)/3] - x
-> [(3x + 30)/3] - ×
-> × +10 - x 
-> 10]]> 2016-09-29 10:30:59 UTC https://padlet.com/chrisyang/EN0017Week1/wish/127198364 1. https://padlet.com/chrisyang/EN0017Week1/wish/127198374 Group 2]]> 2016-09-29 10:31:02 UTC https://padlet.com/chrisyang/EN0017Week1/wish/127198374 Group 6 https://padlet.com/chrisyang/EN0017Week1/wish/127198536 2016-09-29 10:31:55 UTC https://padlet.com/chrisyang/EN0017Week1/wish/127198536 Group 2 https://padlet.com/chrisyang/EN0017Week1/wish/127198637 ((X+15).2)/3 - x/3 -->> 10]]> 2016-09-29 10:32:28 UTC https://padlet.com/chrisyang/EN0017Week1/wish/127198637 https://padlet.com/chrisyang/EN0017Week1/wish/127198848 2016-09-29 10:33:41 UTC https://padlet.com/chrisyang/EN0017Week1/wish/127198848 Group 5 https://padlet.com/chrisyang/EN0017Week1/wish/127198920 2016-09-29 10:34:06 UTC https://padlet.com/chrisyang/EN0017Week1/wish/127198920 carpenter_h https://padlet.com/chrisyang/EN0017Week1/wish/127199051 Group 3]]> 2016-09-29 10:34:46 UTC https://padlet.com/chrisyang/EN0017Week1/wish/127199051 Team X https://padlet.com/chrisyang/EN0017Week1/wish/127199134 2016-09-29 10:35:10 UTC https://padlet.com/chrisyang/EN0017Week1/wish/127199134 Group 7 https://padlet.com/chrisyang/EN0017Week1/wish/127199439 2016-09-29 10:36:33 UTC https://padlet.com/chrisyang/EN0017Week1/wish/127199439 Group  https://padlet.com/chrisyang/EN0017Week1/wish/127199719 2016-09-29 10:38:05 UTC https://padlet.com/chrisyang/EN0017Week1/wish/127199719 https://padlet.com/chrisyang/EN0017Week1/wish/127199793 2016-09-29 10:38:26 UTC https://padlet.com/chrisyang/EN0017Week1/wish/127199793 https://padlet.com/chrisyang/EN0017Week1/wish/127200226 2016-09-29 10:40:49 UTC https://padlet.com/chrisyang/EN0017Week1/wish/127200226 Group99 https://padlet.com/chrisyang/EN0017Week1/wish/127201997 2016-09-29 10:50:54 UTC https://padlet.com/chrisyang/EN0017Week1/wish/127201997 Feedback https://padlet.com/chrisyang/EN0017Week1/wish/127218391 2016-09-29 12:20:24 UTC https://padlet.com/chrisyang/EN0017Week1/wish/127218391 5. Rule of Algebra chrisyang https://padlet.com/chrisyang/EN0017Week1/wish/127471773 Presentation flowchart:
  • The title of the rule
  • Mathematical expression of the rule
  • Example for the rule
  • Additional comments / observations of the rule
]]> 2016-09-30 09:35:10 UTC https://padlet.com/chrisyang/EN0017Week1/wish/127471773 Student Rep chrisyang https://padlet.com/chrisyang/EN0017Week1/wish/127490357 2016-09-30 11:46:35 UTC https://padlet.com/chrisyang/EN0017Week1/wish/127490357 5. Group 1 chrisyang https://padlet.com/chrisyang/EN0017Week1/wish/127594178 2016-09-30 17:06:01 UTC https://padlet.com/chrisyang/EN0017Week1/wish/127594178 5. Group 2 chrisyang https://padlet.com/chrisyang/EN0017Week1/wish/127594739 2016-09-30 17:08:01 UTC https://padlet.com/chrisyang/EN0017Week1/wish/127594739 5. Group 3 chrisyang https://padlet.com/chrisyang/EN0017Week1/wish/127594951 2016-09-30 17:08:42 UTC https://padlet.com/chrisyang/EN0017Week1/wish/127594951 5. Group 4 chrisyang https://padlet.com/chrisyang/EN0017Week1/wish/127595301 2016-09-30 17:09:50 UTC https://padlet.com/chrisyang/EN0017Week1/wish/127595301 5. Group 5 chrisyang https://padlet.com/chrisyang/EN0017Week1/wish/127595578 2016-09-30 17:10:35 UTC https://padlet.com/chrisyang/EN0017Week1/wish/127595578 5. Group 6 chrisyang https://padlet.com/chrisyang/EN0017Week1/wish/127595745 2016-09-30 17:11:06 UTC https://padlet.com/chrisyang/EN0017Week1/wish/127595745 5. Group 7 chrisyang https://padlet.com/chrisyang/EN0017Week1/wish/127595920 2016-09-30 17:11:41 UTC https://padlet.com/chrisyang/EN0017Week1/wish/127595920 5. Group 99 chrisyang https://padlet.com/chrisyang/EN0017Week1/wish/127596107 2016-09-30 17:12:19 UTC https://padlet.com/chrisyang/EN0017Week1/wish/127596107 5. Team X chrisyang https://padlet.com/chrisyang/EN0017Week1/wish/127596297 2016-09-30 17:12:56 UTC https://padlet.com/chrisyang/EN0017Week1/wish/127596297