2017/18 EN17 Introduction to Algebra, Week 1 by Chris Yang https://padlet.com/chrisyang/EN17W1 Basic Algebra en-us 2017-09-28 09:58:19 UTC 2025-09-24 11:50:55 UTC hello@padlet.com https://padlet-assets.s3.amazonaws.com/icons/Dartstarget.png Module skeleton chrisyang https://padlet.com/chrisyang/EN17W1/wish/191990642 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, Prof Adrian Porch, and Dr Alistair Reid

Assessment Breakdown
Examination - 80%  
Class Test - 20%

Essential Reading and Resource List:
  • Foundation Mathematics – K.A. Stroud (Palgrave Macmillan)
  • Foundation Mathematics – L. Mustoe and M. Barry (Wiley)
]]> 2017-09-28 09:58:19 UTC https://padlet.com/chrisyang/EN17W1/wish/191990642 1 Algebraic expressions chrisyang https://padlet.com/chrisyang/EN17W1/wish/191990643 Poker Game:  Each Discussion Group randomly picks a 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.

Discussion with the Group: how to prove mathematically whatever you picked up, the result will be the same.
]]> 2017-09-28 09:58:19 UTC https://padlet.com/chrisyang/EN17W1/wish/191990643 2.4 Algebraic expressions chrisyang https://padlet.com/chrisyang/EN17W1/wish/191990645 Example 2: 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)


]]> 2017-09-28 09:58:19 UTC https://padlet.com/chrisyang/EN17W1/wish/191990645 2.5 Algebraic expressions chrisyang https://padlet.com/chrisyang/EN17W1/wish/191990646 Example 3: What if the f doubles each second?

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


]]> 2017-09-28 09:58:19 UTC https://padlet.com/chrisyang/EN17W1/wish/191990646 2.2 Algebraic expressions chrisyang https://padlet.com/chrisyang/EN17W1/wish/191990647 Example 1: 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?]]> 2017-09-28 09:58:19 UTC https://padlet.com/chrisyang/EN17W1/wish/191990647 2.3 Algebraic expressions chrisyang https://padlet.com/chrisyang/EN17W1/wish/191990649 Answer to Example 1
1 -> 2 -> 4 ->8 ->16 ->32
1 -> 2 -> 4 ->8 ->16 ->32
Total cell number is 64, or:]]> 2017-09-28 09:58:19 UTC https://padlet.com/chrisyang/EN17W1/wish/191990649 3.1 Variables and constants chrisyang https://padlet.com/chrisyang/EN17W1/wish/191990650 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.]]> 2017-09-28 09:58:19 UTC https://padlet.com/chrisyang/EN17W1/wish/191990650 3.2 Variables and constants chrisyang https://padlet.com/chrisyang/EN17W1/wish/191990651 Example 4: Which is the constant, which is the variable?


]]> 2017-09-28 09:58:19 UTC https://padlet.com/chrisyang/EN17W1/wish/191990651 3.3 Variables and constants chrisyang https://padlet.com/chrisyang/EN17W1/wish/191990652 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 is: 
B = (S1 + S2) / 2.


]]> 2017-09-28 09:58:19 UTC https://padlet.com/chrisyang/EN17W1/wish/191990652 2.1 Algebraic expressions chrisyang https://padlet.com/chrisyang/EN17W1/wish/191990653 The number of cells]]> 2017-09-28 09:58:19 UTC https://padlet.com/chrisyang/EN17W1/wish/191990653 5 Terms and coefficients chrisyang https://padlet.com/chrisyang/EN17W1/wish/191990658 Algebraic expression notation:
  1 – power (exponent)
  2 – coefficient
  3 – term
  4 – operator
  5 – constant term
  x y c – variables/constants]]> 2017-09-28 09:58:19 UTC https://padlet.com/chrisyang/EN17W1/wish/191990658 6 Collecting like terms chrisyang https://padlet.com/chrisyang/EN17W1/wish/191990659 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
]]> 2017-09-28 09:58:19 UTC https://padlet.com/chrisyang/EN17W1/wish/191990659 7 Similar terms, Common factors and factorization chrisyang https://padlet.com/chrisyang/EN17W1/wish/191990661 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

]]> 2017-09-28 09:58:19 UTC https://padlet.com/chrisyang/EN17W1/wish/191990661 8 Expanding brackets chrisyang https://padlet.com/chrisyang/EN17W1/wish/191990662 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
]]> 2017-09-28 09:58:19 UTC https://padlet.com/chrisyang/EN17W1/wish/191990662 4 Group Learning: Rule of Algebra chrisyang https://padlet.com/chrisyang/EN17W1/wish/191990678 Read the material 'The Formal Rules of Algebra'. Peer discussion of potential questions. Prepare a presentation as a group to go through the below elements. Whiling listening to the presentation, peer marking.

  • The title of the rule
  • Mathematical expression of the rule
  • Example for the rule
  • Additional comments / observations of the rule


1.The axioms of equals;
2. Commutative rules;
3. Identity elements.
4. Additive inverse;
5. Multiplicative inverse;
6. Definition of subtraction.
7. Definition of division;
8. Inverse of inverse;
9- b-a and a-b.
10. Rule of signs;
11. Rules for 0;
12. Factoring / Multiplying.
13. Operation on both sides;
14. Change the sign;
15. Change the sing on inequality.
16. Equations;
17. Change of sense on inequality;
18. Absolute value.
19. Equivalent fractions;
20. Multiplication of fractions;
21. Division of fractions.
22. Addition of fractions;
23. Rules of exponents;
24. Negative exponent.
25. Exponent 0;
26. Square root;
27. a^2=b.
28. Multiplying radicals; 
29. nth root; 
30. Rational exponent; 
31. Laws of logarithms; 
32. Complex unit.
]]> 2017-09-28 09:58:19 UTC https://padlet.com/chrisyang/EN17W1/wish/191990678 To visit this padlet for this page chrisyang https://padlet.com/chrisyang/EN17W1/wish/191991075 https://padlet.com/chrisyang/EN17W1]]> 2017-09-28 10:00:29 UTC https://padlet.com/chrisyang/EN17W1/wish/191991075 Visit this padlet to form discussion groups chrisyang https://padlet.com/chrisyang/EN17W1/wish/192045384 https://padlet.com/chrisyang/2017Group]]> 2017-09-28 13:05:12 UTC https://padlet.com/chrisyang/EN17W1/wish/192045384