Download Assignment 2 - math173DF

Name: __________________
Student #: ______________
MATH 173 DF
Assignment #2
Due: Friday, Oct 31st, 2008
For each question below, provide full solutions and show all your work. Solutions
without justification may receive zero marks. Express all your answers to the
correct number of significant digits and be sure to include a concluding sentence
for all word problems.
1. The second of two numbers is 4 more than the first. The sum of the numbers
if 56. Find the numbers.
[3 marks]
2. From 12.5L of coolant containing 13.4% antifreeze, 5.50L are removed. If
5.50L of pure antifreeze are then added, how much antifreeze will be
contained in the final mixture.
[3 marks]
3. A company has $86 500 invested in bonds and earns $6751 in interest
annually. Part of the money is invested at 7.4%, and the remainder at 8.1%,
both simple interest. How much is invested at each rate?
[3 marks]
Name: __________________
Student #: ______________
4. Two numbers are represented by x and y. Write algebraic expressions to
represent these phrases:
[1 mark each]
a) the sum of the two numbers:
____________________
b) five more than the first number:
____________________
c) 8 less than the second number:
____________________
d) the sum of double the first number and triple the second number:
____________________
5. Write a phrase to represent the following algebraic expression [1 mark each]
a) x + 1 = 2(x-1)
___________________________________________
___________________________________________
b) 4x = 3x – 2
___________________________________________
___________________________________________
6. Simplify as much as possible. Express each answer with positive exponents.
[1 mark each]
a) (x2y)  (x5y6)
b) (x5y6) ÷ (x2y) + (xy)
c) (x5y6) 3
Name: __________________
Student #: ______________
7. Write out the rows of Pascal’s triangle:
[2 marks]
0th Row:
1st Row:
2nd Row:
3rd Row:
4th Row:
8. Expand:
a) (3x + 1)( 5x – 3)
[2 marks each]
b) (2x + 4)(2x – 4)
c) (2a - b)4
9. Factor:
a) n2 + n – 56
c) 27x2 + 36x – 15
[2 marks each]
b)
16x2
– 36
d) (2x – 1)2 – (3x + 1)2
Name: __________________
Student #: ______________
10. A student was asked to factor the following trinomial on a test:
This is the solution she provided:
4 y2  7 y  2
4 y2  7 y  2  4 y2  8 y  y  2
 (4 y 2  8 y )  ( y  2)
 4 y ( y  2)  ( y  2)
 (4 y  1)( y  2)
Check to see if the solution is correct by expanding. If it isn’t correct, identify all of
the mistakes and rewrite the solution correctly.
[6 marks]
 Final Check: Have you done the following?
□ Attempted to answer all the questions
□ Checked all your answers
□ Written all answers with the correct number of significant digits
□ Defined all variables with “Let” statements wherever necessary
□ Written a concluding sentence to all word problems.