Two-Chances Sheet
Graphing Lines
Name:_______________________
Rules: Graph each by the method indicated. You will get a second chance to graph any problems that
you get wrong after you submit these problems the first time. Each problem is worth 2 points. Late work
is penalized 2 pts per day late.
Attempt 1 DUE
Attempt 2 DUE
1. Use point plotting:
y = 3x – 4
2. Use point plotting:
2x + y = 5
3.
Use point plotting:
y= 1
4. Find the intercepts, then graph
3x – 5y = 15
5. Find the intercepts, then graph
2x + y = – 4
6. Use slope and y-intercept to
graph:
y = – 2x + 5
7. Use slope and y-intercept to
graph:
y = 2
8. Use slope and y-intercept to
graph:
y = 3x
9. Graph using any method:
x=5
10. Graph using any method:
3x – 2y = 0
Two-Chances Sheet
Order of Operations
Name:_______________________
Rules: Evaluate each problem step by step. Highlight or circle your final answer for each.
Use only the boxes on the left. You will get a second chance to work any problems that
you get wrong after you submit these problems the first time. Each problem is worth 2
points. Late work is penalized 2 pts per day late.
Attempt 1 DUE
Attempt 2 DUE
1. 2(3) – 12 ÷ 6(3)
=
=
=
2. [(6 – 3)+ 5]2
=
=
=
3. 82 – 16 ÷ 22(4) – 3
=
=
=
4. -8 + (3 – 7) + 52
=
=
=
5.
−4−2
22 + 9
=
=
6. 6(3 – 5)3 – 2(5 – 9)3
=
=
=
7. -4(-3)2 – (-2)
=
=
=
8. 7 – 2(4 + 32)
=
=
=
9. (3 – 6)3(4 – 8)2
=
=
=
10. -3 – 2(52 – 62)
=
=
=
Two-Chances Sheet
Name:_______________________
Operations with Radicals
Rules: Simplify each problem. Use only the boxes on the left. You will get a second chance to work any
problems that you get wrong after you submit these problems the first time. Each problem is worth 5
points.
Attempt 1
DUE
Attempt 2
DUE
1. √90 2. 280 3.
√ √
4. √32 + √27 + √18
5. √ − √16 − √81 6. 4√56 − 3√5
7. √3 + 5√3 − 2
8. √2 + √7
9. Rationalize the Denominator:
10. Rationalize the Denominator:
√√
√√
Two-Chances Sheet
Name:_______________________
Factoring
Rules: Fully factor each expression. Use only the boxes on the left. You will get a second chance to
work any problems that you get wrong after you submit these problems the first time. Each problem is
worth 5 points.
Attempt 1 DUE
Attempt 2 DUE
5 3 2
5 3
3 2
1. x y z + xy z – xy z
2.
3xy + 18x – 5y – 30
3.
x2 – 18x – 40
4.
-4x2y – 4x3 + 24xy2
5.
35y2 + 11y – 10
6.
4x2 – 17xy + 4y2
7.
9a2 – 24a + 16
8.
81z2 – 121
9.
x3 – 216
10. 16x5 + 54x2y3
Two-Chances Sheet
Name:_______________________
Logarithms
Rules: Follow the directions for each. Round to the thousands place. Use only the boxes on the left.
You will get a second chance to work any problems that you get wrong after you submit these problems
the first time. Each problem is worth 5 points.
Attempt 1
DUE
Attempt 2
DUE
1. Solve for x (show at least one intermediate step):
logx 343 = 3
2. Solve for x (show at least one intermediate step):
log5
=x
3. Solve for x (show at least one intermediate step):
log2 x = 0
4. Solve for x (show at least one intermediate step):
log4 x = − 5. Solve for x (show at least one intermediate step):
logx
= -2
6. Solve for x (show at least one intermediate step):
ln
=x
7. Solve for x: (round to 3 decimal places)
ln x = 0.853
8. Fully Expand:
log √
9. Fully Expand:
log3 10. Write as a single log term:
2 log x + log (x + 1) – 4 log z
Two-Chances Sheet
Name:_______________________
Polynomial Operations
Rules: Simplify each expression. Use only the boxes on the left. You will get a second chance to work
any problems that you get wrong after you submit these problems the first time. Each problem is worth 2
points. Late work is penalized 2 pts per day late.
Attempt 1 DUE
଻௚ర ௛మ
1. ቀ మ ఱ ቁ
଺௚ ௛
ଶ
2. (4‫ି ݔ‬ଶ ‫ ݕ‬ସ )ଷ
3. ቀ
ଷ௫ బ ௬ షమ
௬య௭
ቁ
ିଶ
4. Evaluate -x4 + x3 + x2 – x + 1 for x = -2
5. Add: (a3b + 4a2b – 7ab + 3) + (2a2b – 4ab2 – 8ab)
Attempt 2 DUE
6. Subtract:
(4x5 + 3x4 – 6x3 + 9x – 2) – (3x5 + 8x4 + 7x2 – 10)
7. Multiply:
(3x + 2)(5x – 4)
8. Multiply: (x + 3)(x2 – 2x + 3)
9. Multiply: 5x2(3x – 7)(x – 9)
10. Write each factor in scientific notation, multiply,
then write your answer in standard and scientific
notation:
(0.0000000043)(250,000,000,000)
Two-Chances Sheet
Name:____________________________
Rational Expressions
Rules: Fully simplify each expression, showing your steps. Use only the boxes on the left. You will get
a second chance to work any problems that you get wrong after you submit these problems the first time.
Each problem is worth 5 points.
Attempt 1
DUE
Attempt 2
DUE
଼ି௫
1. Simplify: మ
௫ ିହ௫ିଶସ
2.
Simplify:
3.
Multiply:
4. Divide:
5.
ସሺ௭ାଷሻା ଼
ଷሺ௭ାଷሻା଺
௫ మ ିଵ
௫ మ ାଶ௫
௫ మ ି௫ି଺
ଵିଶ௫
Subtract:
ଷ௫
௫
∙ ௫ାଵ
௫ మ ିଶ௫ିଷ
÷ ଶ௫ మ ା௫ିଵ
௫ିଶ
− ௫ି଻
௫ି଻
௫
6.
Add:
7.
Add:
8.
Subtract:
௫ మ ିଶ௫ି଼
௫
௫ିଵ
+
+
ଶ
௫ మ ିଶ௫ି଼
ଵ
௫
ଶ௬ାଶ
௬ మ ାଶ௬ାଵ
ଵ
− ௬ାଵ