Math123 Week 3 Essay
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 …show more content…
(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 the same total cost for these two companies. (d) Write a short paragraph of consumer advice regarding which company’s plan to choose in various situations. √ √ √ 7. (a) Find the average slope of the graph y = x between the point (a, a) and the point (a + h, a + h) on the curve. (The average slope between two points is given by the slope of the straight line joining those
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 …show more content…
(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 the same total cost for these two companies. (d) Write a short paragraph of consumer advice regarding which company’s plan to choose in various situations. √ √ √ 7. (a) Find the average slope of the graph y = x between the point (a, a) and the point (a + h, a + h) on the curve. (The average slope between two points is given by the slope of the straight line joining those