Mobile Phone Company

Only available on StudyMode
  • Download(s) : 89
  • Published : October 11, 2012
Open Document
Text Preview
DEPARTMENT OF MATHEMATICS NAME: Chen Haiwei Student Id: 42416302 FACULTY OF SCIENCE

MATH123 S212 Mathematics 123 Tutorial Week 3

Tutorial Group:

You must hand in this sheet at your tutorial class. Do not hand in your worked solutions, you should keep these for your own reference.

MATH123 Mathematics 123 S212 2012 Tutorial Week 3
1. Simplify each of the following expressions, to obtain equivalent expressions, and reducing the complexity of denominators wherever possible. Show all your steps. In each case, identify any special values of the variables where the original form may differ in value from the simplified form (including the possibility of being undefined). 1 1 + x + 3y x − 3y 4x2 − 9 x2 − 1 (b) × x+1 4x + 6 x2 − 1 1 (c) ÷ 1+ 2x x (a) 2. Simplify: (a) 3x − 4 x+5 − 3x + 2 2x − 3 (c) (d) 5 3 + x x (x + 1) (x − y) (x + y) − x2 y2 2 2

(d)

25x2 − 4 x+3 × −5 x2 − 9 5x − 2 3 1 2 (e) + − x (x + 2) x2 − 2x x2 − 4 1 1 (f) 2 + 2 x + xy y + xy

a b c + + (b) ab bc ac

3. Factorise each of the following expressions using laws of squares and cubes as necessary: (a) x4 − x2 (b) x6 − y 6 (c) x6 − y 3 (d) x3 y − xy 3 (e) x4 y + xy 4 (f) x2 − y 2 − 7x + 7y

4. Simplify each of the following expressions, showing all your steps. (a) (b) (c) 1 2 3 + 2 − 2 x (x + 2) x − 2x x − 4 y 2xy x − − x − y x + y x2 − y 2 x − 1 / (y − x) y (d) (x + h) − x2 h 1 1 − x+h x (e) h 3 (x + h) − x3 (f) h 2

5. Which pairs of lines in the following list are parallel? Which are perpendicular? (a) 3x + 5y = 2 (b) 5x − 3y = 1 (c) 5x + 3y = 13 (d) 10x − 6y = 9 (e) y = 0.6x + 2

6. (a) The Wonderful Mobile Phone Company charges $70 per month, and calls cost $0.50 per minute. If I use my phone for x minutes in a month, write down an expression for the total cost in terms of x. (b) Repeat the previous part for the Fantastic Mobile Phone Company, which charges $20 per month and $1 per minute. (c) Plot both graphs on the same axes and hence find the call time per month which gives...
tracking img