PHYSICS 11 / 20
Unit 1 ~ Learning Guide Name: ______________________________
Instructions:
Using a pencil, complete the following notes as you work through the related lessons. Show ALL
work as is explained in the lessons. You are required to have this package completed BEFORE
you write your unit test. Do your best and ask questions if you don’t understand anything!
Scientific Notation:
1. Why was scientific notation invented?
2. Do an Internet or book search and find something in your universe that is represented by a
REALLY small number.
a) What is it that is being described?
b) Show the value in scientific notation:
____________________
c) Show the value in regular notation:
____________________
3. Do an Internet or book search and find something in your universe that is represented by a
REALLY large number.
a) What is it that is being described?
b) Show the value in scientific notation:
____________________
c) Show the value in regular notation:
____________________
4. Convert the following to scientific notation in standard form.
a)
34674
________________
b)
.000235
________________
c)
-2300000
________________
d)
-.0000150
________________
e)
0.00750
________________
2022-01-06
Page 1 of 21
PHYSICS 11 / 20
5. Round the following to the number of figures shown and convert to scientific notation in
standard form.
a) 634000
round to 2 sig figs
________________
b) 0.00345
round to 2 sig figs
________________
c) 298.76
round to 1 sig figs
_________________
6. Indicate the number of significant figures in the number given (ans.
a)
b)
c)
d)
e)
f)
g)
h)
120000
32100.0
.00123
0.20040
730.01
0.0300
7.590 x 103
9 x 10-4
_______
_______
_______
_______
_______
_______
_______
_______
7. Ensure you can use your calculator to easily acquire the given results (use EE or EXP button if
available).
a. (5.98 x 1024 kg ) (7.35 x 1022 kg) = _______________
b. (5.98 x 1024 kg ) / (7.35 x 1022 kg) = _______________
Significant Figures:
1. What is the main purpose for learning about significant figures in science and/or technology
courses?
2. Students sometimes get confused between the terms "scientific notation" and "significant
figures." Figure out a way that will ensure you don't get confused between the two. Describe
your method below. (HINT: define notation, define significant).
2022-01-06
Page 2 of 21
PHYSICS 11 / 20
3. Suppose that three people were told to determine the length of a piece of wood and
were given a tape measure whose smallest markings were at 0.1 centimeter intervals.
They report the following values:
Person
Value measured for length
1
11.6 cm
2
11.6283476 cm
3
11.63 cm
Who is documenting this measurement correctly? The correct question is "who
recognizes the questionable digit and documented accordingly?" Justify your answer.
4.
What is your best score on the Sig Fig “Balloon Game” (1.3 - include level and score).
2022-01-06
Page 3 of 21
PHYSICS 11 / 20
5. Evaluate the following and use the correct number of significant figures in your answer (Show
all work)
a. 2.35 cm x 4.6 cm
__________
b) 4/3 (3.14159)(4.7 in)3
__________
c)
(− 1.25m )(3.2m )
3.4m
__________
d)
33560000000 × .00000012km
24.5hr
__________
e) 2301cm + 834.12cm + 9.0cm
__________
6. Summarize the difference between the rules for significant figures when
adding/subtracting and when multiplying/dividing?
2022-01-06
Page 4 of 21
PHYSICS 11 / 20
Equation Solving:
1. Solve for x in the following equations (show all work):
a. 2 = 5 + x
ans. -3
__________
b. 19 = 2x + 7 ans. 6
__________
c.
3 – 5x = 14 ans. -2.2
__________
d. 5 =
x
2
ans. 10
__________
2.
Rearrange the equation, solving for the variable shown (clearly show all steps).
a. Solve for Q1where F =
kQ1Q2
r2
b. Solve for "t" where d = ½at2
2022-01-06
Page 5 of 21
PHYSICS 11 / 20
c. Solve for vo where
 vo + v f
d = 
 2
d. Solve for "a" where
vf2 = vi2 + 2ad
d f − di
e. Solve for df where
v=
f.
E p = mgh
Solve for m where
g. Solve for m where E k =
2022-01-06

t

t f − ti
1
mv 2
2
Page 6 of 21
PHYSICS 11 / 20
h. Solve for ti where v =
d f − di
t f − ti
1 2
at
2
i.
Solve for vo where d = v o t +
j.
Solve for vi where vf2 = vi2 + 2ad
 vo + v f
 2
k. Solve for vf where d = 
l.
Solve for v where E k =
2022-01-06

t

1
mv 2
2
Page 7 of 21
PHYSICS 11 / 20
Trigonometry:
1. Solve the following triangles using SOHCAHTOA and Pythagoras. Show all work.
a) In the figure below, the 4.0 meter ladder is making a 60. degree angle with the ground. How
high does the ladder reach? How far is the base of the ladder from the wall?
h = ____________
b = ____________
b) In the figure below, the 4.0 meter ladder reaches only 1.5 meters up the wall. How far is the
base of the ladder from the wall? What is the angle the ladder makes with the ground?
b = ____________
 = ____________
2022-01-06
Page 8 of 21
PHYSICS 11 / 20
c) Solve for x, y, and A.
x = ____________
y = ____________
A = ____________
d) Solve for R and ɵ.
R = ____________
 = ____________
e) Solve for BC and the total height.
BC = ____________
Total Height = ____________
2022-01-06
Page 9 of 21
PHYSICS 11 / 20
Units of Measure:
1. Unit conversions (show all work – lay out in brackets and cancel units, as in lesson examples)
a.
2.67 hours into seconds
b.
80. km/hr to m/s
c.
34 km into meters
d.
1.0 day into seconds
e.
12 hours into seconds
f.
100. km/hr into m/s
g.
40 km/hr into m/s
h.
12 m/s into km/hr
i.
200 g into kg
j.
10 kg into grams
2022-01-06
Page 10 of 21
PHYSICS 11 / 20
2. We can only add and subtract numbers in Physics if they have the same units. For example I can
add 5.0m to 12m to get 17m but I cannot add 5.0m to 10m/s. You cannot add a velocity (10m/s)
to a distance (5m) and get anything meaningful. Use dimensional analysis (see video in
lessons) to ensure that the kinematic equations shown below adhere to this rule. (Note: it does
not matter at this stage if you understand the physics behind the equations). The units for each
variable are given. The first one is done for you.
Variable
d
vi
vf
a
t
a.
Units
m
m/s
m/s
m/s2
s
vf = vi + at
vf
=
vi
+
at
Step 1: replace each variable with units only [m/s] = [m/s] + [m/s2][s]
Step 2: cancel and simplify where possible [m/s] = [m/s] + [m/s2][s]
Step 3: compare resulting terms (same?)
[m/s] = [m/s] + [m/s]
Conclusion: Since each term has the units of m/s, the equation is likely valid.
b.
v = dt
conclusion: valid / invalid (circle one)
c.
d = vt
conclusion: valid / invalid (circle one)
d.
d = vit + ½at2
(remember that the ½ doesn’t have a unit so isn’t considered)
conclusion: valid / invalid (circle one)
2022-01-06
Page 11 of 21
PHYSICS 11 / 20
Graphs Review:
1. Describe how you can recognise a positive vs. a negative vs a zero slope on a graph. Sketch
and explain.
2. Using the definition of intercept, explain what an x and y-intercept on a graph are?
Intercept = _____________________________________________________________
y-intercept = ____________________________________________________________
x-intercept = ____________________________________________________________
3. Describe each letter in the equation y=mx+b.
4. What type of graph does y=mx+b represent? How do you recognize a graph that can be
represented by it?
5. Label each of the following as linear or non-linear in the box below each graph.
2022-01-06
Page 12 of 21
PHYSICS 11 / 20
6. Determine the equation of each line shown:
Slope = _______
Slope = _______
y-int = _______
y-int = _______
Equation:
Equation:
______________
______________
Slope = _______
Slope = _______
y-int = _______
y-int = _______
Equation:
Equation:
______________
______________
Slope = _______
Slope = _______
y-int = _______
y-int = _______
Equation:
Equation:
______________
______________
Slope = _______
Slope = _______
y-int = _______
y-int = _______
Equation:
Equation:
______________
______________
7. Using the PhET Simulation in your lessons called Graphing Lines to explore then try the “Line
Game” (1.7). Make sure you try levels 1 - 3? What was your highest score in level 3?
2022-01-06
Page 13 of 21
PHYSICS 11 / 20
8. Given the equations, identify the slope and y-intercept then sketch the graph. Make sure you
label the axis correctly (given the variables in your equation).
2022-01-06
Slope = _______
Slope = _______
y-int = _______
y-int = _______
Equation:
Equation:
d = 3t + 2
v = -3t + 2
Slope = _______
Slope = _______
y-int = _______
y-int = _______
Equation:
Equation:
a = - 2t
d = -2t + 4
Slope = _______
Slope = _______
y-int = _______
y-int = _______
Equation:
Equation:
v = 3t - 2
a = -2t + 2
Slope = _______
Slope = _______
y-int = _______
y-int = _______
Equation:
Equation:
a = 4t - 1
d = ½t + 2
Page 14 of 21
PHYSICS 11 / 20
Graphing Data:
1. The data below shows a group of people plotted by their height and age. Below each person
identify their dot on the graph.
2. Consider the graph showing the population of a town called Newtown to answer the questions.
a)
b)
c)
d)
e)
f)
What year did the data on Newtown begin? ___________
What was the population when the data collection began? ___________
What was the population when the data collection stopped? ___________
When was the maximum population in Newton? ___________
What are the units of slope in this graph? ___________
What range of years has the greatest rate of increase in population in the above graph?
Calculate the rate of increase (showing all work and units):
g) What range of years has the slowest rate of increase in population in the above graph?
Calculate the rate of increase (showing all work and units):
h) What range of years has a decrease in population in the above graph? Calculate the rate of
decrease (showing all work and units):
2022-01-06
Page 15 of 21
PHYSICS 11 / 20
3. Consider the graph showing the height of plants over time, based on sunshine per day.
a) What does the y-intercept represent? ______________________
b) What are the units of slope in this graph? ___________
c) Over the first 6 days, which plant:
a. Grew really fast but then growth slowed? ___________
b. Growth rate increased?__________
c. Growth rate stayed about the same ______________ and ______________.
d) If someone told you that they chased away a cat that was digging in one of the plants on
one of the days, make your guess of which day and which plants. How do you know?
e) If you heard that there was a particularly cold day:
a. Which day would you guess? Why?
b. One plant was nearest the warm house. Which one? Why?
c. One plant was more impacted than the others by the cold. Which one? Why?
f)
What range of time (between days) has the fastest growth for a given plant? Identify the
plant, the day, then alculate the rate of growth (showing all work and units):
g) What range of time (between hours) has the most dramatic drop in height in the above
graph? Calculate the rate of decrease (showing all work and units):
2022-01-06
Page 16 of 21
PHYSICS 11 / 20
4. Suppose that the water level of a river is 34 meters and that it is receding at a rate of 0.50
meters per day.
a) Write an equation for the water level, L, after d days. ________________________
b) What does the slope in this relationship represent? ________________________
c) Determine the number of days it would take to reach 26 meters (show all work):
d) Sketch a graph of this situation for 10 days (include titles and units for everything)
5. A plumber charges $25 for a service call plus $50 per hour of service.
a) Write an equation in slope-intercept form for the cost, C, after h hours of service
________________________
b) What does the slope in this relationship represent? ________________________
c) Determine the number of hours it would take to reach a cost of $500 (show all work):
d) Sketch a graph of this situation for 10 hours (include titles and units for everything)
2022-01-06
Page 17 of 21
PHYSICS 11 / 20
6. For each experiment below: think about independent vs dependent variables, then specify
appropriate titles (including units for axis titles).
a) A student wanted to test how the mass of a paper airplane affected the distance it would
fly. Paper clips were added before each test flight. As each paper clip was added, the plane
was tested to determine how far it would fly in meters.
Graph Title: ___________________________________________________
X-axis Title: ___________________________________________________
Y-axis Title: ___________________________________________________
b) A technician wanted to see if a spring could be used on his car. He added various weights
to the spring and measured how much the spring compressed. He used weights from his
home gym (plates in kg) and a ruler (in cm).
Graph Title: ___________________________________________________
X-axis Title: ___________________________________________________
Y-axis Title: ___________________________________________________
c) A scientist studying new winter tires wants to determine their stopping ability. She takes
has an assistant drive a car at various speeds 20km/hr, 30km/hr, 40km/hr….etc and
measures theirs stopping distance in meters.
Graph Title: ___________________________________________________
X-axis Title: ___________________________________________________
Y-axis Title: ___________________________________________________
7. Draw a good “best fit line” through each set of data (representing the data). If a there’s a
situation where a best fit line doesn’t represent the data well, just write “no trend.”
2022-01-06
Page 18 of 21
PHYSICS 11 / 20
8. Use the data below to determine whether it’s true that “the older you are, the more money you
earn” using plotted data. Ensure both axes include: 1) a breaker to show that they don’t start
at zero 2) scales that increase in equal increments 3) good titles and units.
a) What’s the general trend shown by your best fit line?
b) Does it generally support the hypothesis?
c) About how much more does a person earn per year (in general)? Show all work.
d) Is there an area of the graph that doesn’t seem to follow this trend? Can you explain why?
9. Graph the above data using a spreadsheet program and include the results as your last page.
2022-01-06
Page 19 of 21
PHYSICS 11 / 20
Science and Conspiracy Theories:
Refer back to the beginning of the unit and consider the role of science before we push forward.
1. Briefly describe the scientific method (in your own words). How does this help us have confidence
in scientific findings?
2. Provide some ideas (in your own words) on how you can recognize pseudoscience & conspiracy
theories when it's being presented as science?
3. Briefly describe 3 reasons that might cause a person/company/country to start spreading a
conspiracy theory as truth.
Person:
Company (industry):
Country:
2022-01-06
Page 20 of 21
PHYSICS 11 / 20
Answers:
Scientific Notation:
4) 3.4674x104, 2.35x10-4, -2.3x106, -1.50x10-5, 7.50x10-3 5) 6.3x105, 3.5x10-3, 3x102 6) 2,6,3,5,5,3,4,1
7) 4.40 x 1047, 81.4
Significant Figures:
1) communication (expand) 3) Person3 5) 11cm2, 430in3, -1.2m, 160km/hr, 3144cm
Equation Solving:
1) -3, 6, -2.2, 10 (all work shown)
Fr 2
2) a) Q1 =
b) t =
kQ2
f) m =
Ep
gh
g) m =
j) 𝑣𝑣𝑖𝑖 = �𝑣𝑣𝑓𝑓 2 − 2𝑎𝑎𝑎𝑎
k) v f =
2d − v o t
t
2d
a
2Ek
v2
l) v =
c) v o =
h) t i =
2d − v f t
t
2
d) a =
vt f + d i − d f
v
or
v f − vi
2
2d
di − d f
v
e) d f = vt f − vt i + di
+ tf
1
d − at 2
2
i) v0 =
t
2Ek
m
Trigonometry:
1) a) h=3.5 m, b=2.0 m
b) b=3.7 m, 𝜃𝜃 =22 c) x=8.0, y=11, A=45° d) R=8.0, Ɵ=23° e) 26.7m, 28.2m
Units of Measure:
1)a)9610s B) 22 m/s C) 34000 m d) 86000 s e) 4.3x104 f) 27.7 m/s g) 11 m/s h) 43 km/h i) 0.2 kg
j) 10000 g
Graphing Data:
2) 1900, 500, 2500, 1980 3 f) 52mm/day 4 a) L=34-0.5d, 16days
2022-01-06
Page 21 of 21