Measuring Rate of Change of Ramps Activity
Name:_
Date:_
We are going to measure the rate of change of several ramps around the school.
1.
Compare the three ramps behind the school by the portablesRamp 1: By back door
Ramp 2: By portable 4/5
Ramp 3: By SS
Interpreting Graphs Introduction
Name:_
Date:_
The trend of a line or curve and the steepness of a line or curve can help you
understand what a graph is showing.
1. Which graph below is telling which story?
a. the height of a person over time
b. the heigh
Investigating Relationships - BALL BOUNCE ACTIVITY
Group Names: _ Date:_
Purpose
To determine the type of relationship between the drop height of a ball and its rebound height.
Hypothesis
I think that as the drop height increases, the rebound height will
Linear and Non- Linear Relations Investigation
Name:_
Date:_
1. Two students are working on an investigation of Linear Relations involving the
pattern below.
a. Sketch the next 3 figures in the pattern. (2 marks)
Figure 1
Figure 2
Figure 5
Figure 3
Figure
Linear Relations and First Differences
Name:_
Date:_
1.
Explain how you know.
2. Which set of data is a linear relation? Explain how you know.
a)
b)
Length (cm)
Volume (cm3)
1
1
2
8
3
27
4
64
Length (m)
Cost ($)
10
4.50
20
7.50
30
10.50
40
13.50
2.
Jane i
Rate of Change Note
Name:_
Date:_
The graph below shows how the distance changes over time during a trip. We can use
the graph to find the rate of change or speed of the car during the trip.
rate of change =
rise = the VERTICAL distance between points
run
Graphing Relations Review
Name:_
Date:_
1.
2.
b.
What time are the lights shut off in the 2nd week? _
c.
Lights shut off before 6:30 a.m. during which week? _
3.
4.
5.
6.
7.
_
8. a.
b.
Time
(s)
Height
(m)
Which graph (s) would have the following table of
Walk This Way Investigation
Name:_
1. Student walks away from home at a steady rate.
2. Student walks towards home at a steady rate.
3. Student walks away from home at a steady rate, then STOPS.
Date:_
4. Student walks away from home at a steady rate, the
Drawing Scatter Plots
Name:_
Date:_
Example
The following table shows the winning times in seconds for the 800-m race at the
Olympic Summer Games from 1960 to 1988.
Year
1960
1964
1968
1972
1976
1980
1984
1988
Mens
Time (s)
106.3
105.1
104.3
104.9
103.5
1
Rate of Change
Name:_
Date:_
1. Determine each rate of change.
a.
b.
c.
Careful with the
units for Nancys
skate.
2. Rate of change can refer to rates other than speed. Find the rate of change in the
situation below. What does the rate of change represent?
Curve of Best Fit
Name:_
1.
Date:_
Draw a curve of best fit.
2. The money a person pays for a life insurance policy is called a premium. The
premium depends on many factors, including how much insurance you want and
your age. The monthly premiums one comp
Drawing Scatter Plots
Name:_
Date:_
The table below shows the world record times in seconds for womens 500 m speed
skating from 1983 to 2001.
Year
Time
(s)
a.
1983
1986
1987
1988
1990
1994
1995
1997
2001
39.7
39.5
39.4
39.1
39.3
39.0
38.7
37.7
37.4
Constr
TEACHERCOPY
Rectangle
Square
w
s
Perimeter = 2L + 2w
Area = Length x Width
Perimeter = 4s
Area = s2
Parallelogram
Triangle
c
a
b
c
b
P = 2b + 2c
Perimeter = a + b + c
A = bh
Area = b x h
Circle
Trapezoid
c
C = d or C = 2r
d
P=a+b+c
+d
A = r2
A = (a + b) h
Graphing Relations Quiz
Name:_
/28 marks
Date:_
a) What does the scatter plot show? (1 mark)
_
_
b) How many points were scored by the boy who
played 12 minutes? _ (1 mark)
How many boys scored 15 or fewer points?
_ (1 mark)
Circle these points. (1 mark)
MFM2P
Unit 3 - Linear Equations Test Review
1. Can you identify all four quadrants of a Cartesian plane (graph)?
Can you correctly label the x and y axis?
Could you plot and label the following points?
A(3,5), B(-3, 2), C(-7, -1), D(5, -4)
y
x
2. Could yo
Type of Line; Type of Line: /g/7,Lo a. Type of Line: -
f'bigrd"! (7 {1 ' C03)? 5"» 7 , $113.5ng?
(60/00 7%". Sam: , my '
Slope: " Slope: .- : Slope:
4A
//
Reminder:
Vertical lines
do not have a
slope. The
slope is
undefined.
Write the equa
MFM2P
Trigonometry
SOHCAHTOA Practice
Sine, Cosine, and Tangent Practice
1. Find the value of the sine, cosine, and tangent ratios for each angle given
below. Give both a fraction and a decimal answer for each one. Round
decimals to 3 places
a) sin P =
b)
A. I; Pi-sf i?
MFMZP Date; M [v 1.»
Methods for Findin Equations of Lines
An equation of a line written in slope y-intercept form:
To find the equation of a line you need two things: i)
METHOD 1 (Given Slope and y-intercept)
Substitute the slope an
MFM2P
Trigonometry
Trig Applications
Applications in Trigonometry
Example 1: Sine Ratio
Find the length of side AB, to the nearest tenth of a
centimetre (one decimal place).
Example 2: Cosine Ratio
Jaimies kite string is 35 m long. It makes an angle of
50
1.
Can you identify all four quadrants of a Cartesian pEane (graph)?
Can you correctly label the x and y axis?
Could you 13101 and iabel the foilowing points?
A(3,5), B(~3, 2), C(7, J); D(5, ~4)
d m
g I}: 3" ti
m {vi/é
§ . . . v . v- . »
M
WotrF-sftccf
2. Sta tethe sl ope a nd '\ ' rnrercep of the fol lowing line s
t
a) t, : -l-r' 7
b)_r,:- 4r +6
c)
nt
nI :
ft1
b=_
l)
d ) - v: -
I
,-r + 2
a
nl:
:
b: _
e) _I'= -r
0 ) ,:5
m:
fi I:
A_
U_
-)
t' - .lt -
b-
b-
3. Ploteachpair of points the grid
st
MFM2P
Notesheet
The Cartesian Plane & 1 Differences
Unit 3 - Linear Relations
LINEAR RELATIONS
y
6
5
4
3
2
1
6
5
4
3
2
1
1
2
3
4
5
6
1
2
3
4
5
6
Label the following:
a) the x axis
b) the y axis
c) the four quadrants
d) the point of origin
e) find and l
st
MFM2P
Worksheet
The Cartesian Plane & 1 Differences
Unit 3 - Linear Relations
1. Plot each point on the Cartesian plane below and state which quadrant it is in.
A(4, 5) Quadrant _
B(-3, 2) Quadrant _
C(-5, -1) Quadrant _
D(3, -4) Quadrant _
E(5, 0) Qua