Disscusion Questions Math 209
MATH 209 — FINAL EXAM
This is an open book quiz – feel free to use all the material at your disposal.
Please remember to show your methodology as well as the answer. How you solve the problems counts almost as much as your correct answer – in other words, even if you get the wrong answer, partial credit is available if you can show that you know how to approach the problem!
These are not difficult – just remember to follow logical rules
AND PLEASE BE CAREFUL — CHECK YOUR ARITHMETIC
WATCH OUT FOR THOSE QUESTIONS THAT NEED ± SOLUTIONS
There are 20 questions.
For questions 1 through 5, perform the indicated operations. If possible, simplify the answer.
1. [2 – 5(6 – 2)²] ÷ (8 – 4•3) parens [2-5(4)^2]/(8-12)
Powers
[2-5(16)]/-4 multiplication (2-80)/-4 parens -78/-4
Cancel the minus
78/4
simplify
39/2
2.
Expand:
27x^6 * 2x^-3 / 6x^3
Simplify:
54x^3 / 6x^3
Cancel x^3:
54/6
Simplify:
9
3.
Common denominators:
3x/x + 3/x
-------------
4x/x + 4/x
Simplify:
(3x+3)/x
-----------
(4x+4)/x
Cancel the x:
(3x+3)/(4x+4)
Factor:
3(x+1)/4(x+1)
Cancel the x+1:
3/4
4.
Factor:
(y-3)(y-1) / (y-3)(y+3)
---------------------------
(y+6)(y+1) / (y+6)(y-3)
Flip the second fraction and multiply:
(y-3)(y-1)(y+6)(y-3)
-------------------------
(y-3)(y+3)(y+6)(y+1)
Cancel like terms:
(y-3)(y-1)
---------------
(y+3)(y+1)
5.
= 1 / 16^3/4
= 1 / 2^3
= 1/8
6. Solve the equation: T = (3a + b)/2 for a.
Multiply by 2:
2T = 3a+b
Subtract b:
3a = 2T-b
Divide by 3: a = (2T-b)/3
7. Factor completely: x³ + 1
Sum of cubes:
(x+1)(x^2-x+1)
For problems 8 – 11, solve each equation, inequality or system of equations. Choose whatever method you like, but remember to show your methodology along with your answer.
8. (x + 2)/3 = (x – 1)/4
Cross multiply:
3(x-1) = 4(x+2)
Distribute:
3x-3 = 4x+8
Subtract 3x:
-3 = x + 8
Subtract 8:
X = -11
9.
Square
This is an open book quiz – feel free to use all the material at your disposal.
Please remember to show your methodology as well as the answer. How you solve the problems counts almost as much as your correct answer – in other words, even if you get the wrong answer, partial credit is available if you can show that you know how to approach the problem!
These are not difficult – just remember to follow logical rules
AND PLEASE BE CAREFUL — CHECK YOUR ARITHMETIC
WATCH OUT FOR THOSE QUESTIONS THAT NEED ± SOLUTIONS
There are 20 questions.
For questions 1 through 5, perform the indicated operations. If possible, simplify the answer.
1. [2 – 5(6 – 2)²] ÷ (8 – 4•3) parens [2-5(4)^2]/(8-12)
Powers
[2-5(16)]/-4 multiplication (2-80)/-4 parens -78/-4
Cancel the minus
78/4
simplify
39/2
2.
Expand:
27x^6 * 2x^-3 / 6x^3
Simplify:
54x^3 / 6x^3
Cancel x^3:
54/6
Simplify:
9
3.
Common denominators:
3x/x + 3/x
-------------
4x/x + 4/x
Simplify:
(3x+3)/x
-----------
(4x+4)/x
Cancel the x:
(3x+3)/(4x+4)
Factor:
3(x+1)/4(x+1)
Cancel the x+1:
3/4
4.
Factor:
(y-3)(y-1) / (y-3)(y+3)
---------------------------
(y+6)(y+1) / (y+6)(y-3)
Flip the second fraction and multiply:
(y-3)(y-1)(y+6)(y-3)
-------------------------
(y-3)(y+3)(y+6)(y+1)
Cancel like terms:
(y-3)(y-1)
---------------
(y+3)(y+1)
5.
= 1 / 16^3/4
= 1 / 2^3
= 1/8
6. Solve the equation: T = (3a + b)/2 for a.
Multiply by 2:
2T = 3a+b
Subtract b:
3a = 2T-b
Divide by 3: a = (2T-b)/3
7. Factor completely: x³ + 1
Sum of cubes:
(x+1)(x^2-x+1)
For problems 8 – 11, solve each equation, inequality or system of equations. Choose whatever method you like, but remember to show your methodology along with your answer.
8. (x + 2)/3 = (x – 1)/4
Cross multiply:
3(x-1) = 4(x+2)
Distribute:
3x-3 = 4x+8
Subtract 3x:
-3 = x + 8
Subtract 8:
X = -11
9.
Square