12U Calculus & Vectors
MCV 4U Periods 1
& 2
Extra
Help: 8:30 AM – 8:50 AM, Room 2026
Be
sure to get at least 2 classmates’ e-mails or phone numbers and call them if
you miss class.
Be
sure to see Mr. Lim as soon as problems/frustrations arise.
Being
respectful includes arriving to class on-time and paying
attention/participating during class.
Announcements
Ø Final Check Point: Monday, June 21.
Ø Final Examination: Friday, June 18 from 1:30 PM to 3:30
PM. Location: Cafeteria.
ØAs the weather is getting nicer, it is very important you
stay focused on your studies. Do not fall behind.
What
We Learned, Class Handouts, and Homework
|
Date |
Learning Goals |
Handouts (When
Available) |
Homework |
|
FRI JUN 11 |
-We learn how to find the intersection
of 3 planes. -We learn how to interpret the
geometric significance of our algebraic solution. (if inconsistent system) |
Review Package for examination
distributed. ** For Monday’s Check Point we
will use the co-constructed criteria established. Thanks to Alex and Alicia
for leading the co-construction with the classes J |
|
|
THURS JUN 10 |
-We learn how to find the number
of solutions to the intersection of 3 planes. -We learn how to interpret the
geometric significance of our algebraic solution. (if infinite solutions) |
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WED JUN 9 |
-We learn how to find the number
of solutions to the intersection of 3 planes. -We learn how to interpret the
geometric significance of our algebraic solution. |
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TUES JUN 8 |
-We learn
how to find the number of solutions to the intersection of 2 planes. -We learn
how to interpret the geometric significance of our algebraic solution. |
Textbook
page 517 #6 and #7 |
|
|
MON JUN 7 |
-We learn
how to find the number of solutions to the intersection of a line and a
plane. --We learn
how to interpret the geometric significance of our algebraic solution. |
-Handout |
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|
FRI JUN 4 |
-We learn
how many points of intersection there are for 2 lines in (a) R2
and (b) R3 -We learn
how to interpret the geometric significance of the number of solutions to the
system of equations. |
-Find the
intersection of lines r = (5,-4,1)
+ s(6,4,-2) and r= (2,-3,4) + t(1,2,-3)
and interpretation the geometric significance. -Find the intersection of lines r = (5,1,3) + s(2,1,7) and r= (2,3,9) + t(2,1,7)
and interpretation the geometric significance. |
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|
THURS JUN 3 |
-We learn how many points of intersection there are for 2 lines in (a) R2 and (b) R3 -We learn
how to interpret the geometric significance of the number of solutions to the
system of equations. |
-Page 497
#8b |
|
|
WED JUN 2 |
-We learn
to consolidate our learning of equations of lines and planes, and the
properties of planes. |
-Handout
– all questions J |
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|
TUES JUN 1 |
-We learn
how to develop the scalar equation of the plane (i.e,. Ax + By + Cz + D = 0, with
normal vector (A, B, C). |
-Questions
on chalkboard. |
|
|
MON MAY 31 |
-We learn
how to find the vector equations, parametric equations, and scalar equations
of planes in R3. |
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FRI MAY 28 |
-We learn
how to find the vector equations, parametric equations, and scalar equations
of planes in R3. |
Handout: |
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THURS MAY 27 |
-We learn
how to find vector equations, parametric equations, and scalar equations for
lines in R2. -We learn
how to find vector equations and parametric equations for lines in R3. |
Handout:
2b, 3b, 5b, 6c, 7c, 8b, 9bc, 10b, 11b, 12, 13b, 14b, 21-24 |
|
|
WED MAY 26 |
-We learn
how to find vector equations, parametric equations, and scalar equations for
lines in R2. -We learn
how to find vector equations and parametric equations for lines in R3.
|
Handout:
2b, 3b, 5b, 6c, 7c, 8b, 9bc, 10b, 11b, 12, 13b, 14b, 21-24 |
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TUES MAY 25 |
-We
celebrate our learning of Geometric and Algebraic Vectors. |
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FRI MAY 21 |
-We learn
to consolidate our learning of Geometric and Algebraic Vectors. |
Handout: |
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THURS MAY 20 |
-We learn
how to find the horizontal and vertical components given a resultant vector. |
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WED MAY 19 |
-We learn |
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TUES MAY 18 |
-We learn
to extend 2D vectors to 3D vectors, applying the same properties learned in
2D for 3D vectors. |
Handout: #1a; 3(a, c);
4(a, c); 5b; 6b;
7; 8; 9a;
12; 14(b); 15(h);
16; 17b; 19b;
26; 27d; 29b;
30 |
|
|
MON MAY 17 |
-We learn
how to apply dot products to determine scalar projectors and vector
projections. -We learn
to plot points and vectors in 3-space. |
|
-Textbook
pages 398-399 #2, 4, 7 |
|
FRI MAY 14 |
-We learn
to apply our understanding of the dot problem to solve application-type
questions/problems. |
-Complete
the group work assigned. |
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THURS MAY 13 |
-We learn
how to use geometric vectors to determine the dot product. -We learn
how to use algebraic vectors to determine the dot product. -We learn
how to apply the dot product in mechanical work. |
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WED MAY 12 |
-We learn
how to represent unit vectors algebraically. - We
learn how to find the magnitude of a vector. - We
learn how to add vectors, subtract vectors, multiply a vector by a scalar. |
|
Handout –
finish off at home. |
|
TUES MAY 11 |
-We learn
how to resolve vectors into their horizontal and vertical components. |
|
-Page 363
#9 and 10 |
|
MON MAY 10 |
-We learn
to solve real-life applications using vector addition. -We learn
what is meant by “resultant vector” and “equilibrant vector” |
Study for
Check Point (Textbook 6.1 to 6.4) |
|
|
FRI MAY 7 |
-We learn
how to use the properties of commutativity, associativity, and distributivity
to simplify and evaluate expressions with vectors. |
|
Review:
Pages 308-309 # |
|
THURS MAY 6 |
-We learn
how to multiply a vector with a scalar. -We learn
what are collinear vectors. -We learn
what are linear combination of vectors. -We learn
what are unit vectors. |
|
Pages 298-301 #1, 2d, 4(d,e), 5d, 6d, 7 to 16. |
|
WED MAY 5 |
-We learn
how to add vectors. -We learn
how to subtract vectors. -We learn
how to solve application problems using vector addition. |
|
Pages
290-292 #1 to 9; 11 to 14 |
|
TUES MAY 4 |
-We learn
to distinguish between vectors and scalars. -We learn
how to represent geometric vectors using true bearings and quadrant bearings. -We learn
what are parallel, equivalent, and opposite vectors. |
|
-Page 279
#1-9 |
|
MON MAY 3 |
-We
celebrate our understanding of optimization, and derivatives of exponential
and trigonometric functions through a unit test J |
|
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|
FRI APR 30 |
-We continue
to learn to solve non-routine questions/problems in groups of 4, applying the
derivatives of trigonometric functions. |
|
-Study
for the unit test on Monday, May 3 – redo optimization problems from chapter
3 as well as making sure you know everything we learned in class on chapter
5. |
|
THURS APR 29 |
-We
review and consolidate our understanding of derivatives of exponential and
trigonometric functions. |
|
-Pages
263-265 #1 to 18 ALL. |
|
WED APR 28 |
-We learn
to solve non-routine questions/problems in groups of 4, applying the
derivatives of trigonometric functions. |
|
-Page 266
ALL questions. |
|
TUES APR 27 |
-We learn
to develop the rule to find the derivative of the tangent function. -We learn
to use the rule of the derivative of the tangent function. |
|
-Page 260
#1, 2, 3, 4, 5, 6, 8, 10, 11 |
|
MON APR 26 |
-We learn
to develop the rules to find the derivatives of the sine and cosine
functions. -We learn
to use the rules of the derivative of sine and cosine functions. |
|
-Pages
256-257 #1 all; 2 all; 3(b, e); 5 all; 6(b, d) no graphing technology; 7 - 11 |
|
FRI APR 23 |
-We learn
to develop the differentiation rules for logarithmic functions y = logb
x and y = logb g(x). -We learn
to use the rules to differentiate logarithmic functions y = logb x and y = logb g(x). |
|
-Page
248-249 #1, 2, 3, 4, 5, 6(a-d), 7, 9, 12, 13 (for Monday’s class) -
For fun: read p. 579-581 Logarithmic Differentiation (not in curriculum) |
|
THURS APR 22 |
-We
continue to learn how to use the rules to differentiate exponential functions
of the form y = bx and y = bg(x). |
|
-Page 240
#9 -Read
page 241 -Do page
245 #1, 3(a,b), 6 |
|
WED APR 21 |
-We learn
how to develop the rules for exponential functions of the form y = bx
and y = bg(x). -We learn
how to use the rules to differentiate exponential functions of the form y = bx
and y = bg(x). |
|
-Page 575
#7a, 8, 9a, 10, 11 -Page 240
#1(all) |
|
TUES APR 20 |
-We learn
how to develop the rule to differentiate natural logarithmic functions, y =
ln x and y = ln(g(x)). -We learn
how to use the rules to differentiate natural logarithmic functions, y = ln x
and y = ln(g(x)). |
|
-Page 575
#3, 4, 5a |
|
MON APR 19 |
-We learn
how to apply our understanding of differentiating exponential functions to
more non-routine questions. - We
learn what is a “natural logarithm”. |
|
-Please
incorporate my feedback into your letters (For Optimization Project) – submit
to me ASAP as I want to mail out. -Go over
today’s notes. |
|
FRI APR 16 |
-We learn
how to apply our understanding of differentiating exponential functions to
more non-routine questions. |
|
Complete the
group work questions done in class: pages 233-234 #12-18. |
|
THURS APR 15 |
- We
learn how to develop the derivative of y = ex. - We
learn how to differentiate functions of the form y = eg(x). |
Optimization
Project Marking Scheme (based on Co-Constructed Success Criteria –
weights included) |
Pages
232-233 #2, 3, 4, 5a, 6 to 11 Read
about Leohard Euler: http://schools-wikipedia.org/wp/l/Leonhard_Euler.htm
Postage
Stamps and Paper Money of Euler: http://www.math.dartmouth.edu/~euler/portraits/portraits.html
|
|
WED APR 14 |
- We
learn to explore the properties of exponential functions (review and of
derivatives of exponential functions. |
Study for
Check Point – use success criteria to check you have a complete solution |
|
|
TUES APR 13 |
- We consolidate
our learning of solving classic optimization problems from pure mathematics. - We
also learn how to solve revenue problems using the algorithm for solving
optimization problems. |
|
-Complete
Project – hand in tomorrow - Revenue
problem – page 152 #6 |
|
MON APR 12 |
We
learn how to solve classic optimization problems from pure mathematics. |
Exit Card |
A right
circular can is inscribed in a sphere of radius 15 cm. Find the dimensions of
the cone that has the maximum volume. |
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FRI APR 9 |
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THURS APR 8 |
-We learn
how to solve optimization problems that involve Least Distance. |
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|
WED APR 7 |
(As 1/3
of the class was writing the grade 12 |
Co-Constructed Success
Criteria to Optimization Project (Similar for both classes J) |
Work on
your Optimization Project! |
|
TUES APR 6 |
-We
continue to solve optimization problems involving 2D and 3D. |
Optimization Project (Due April
14) |
|
|
THURS APR 1 |
-We
demonstrate our learning through a unit test. |
|
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WED MAR 31 |
-We learn
to consolidate our learning of the Learning Goals. |
|
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TUES MAR 30 |
-We continue
to learn how to solve optimization problems. |
|
-Be sure
you can solve page 145 #3 to #8 -Go over
unit 2 topics for test – take a pencil and paper and actually REDO the
questions we did in class from scratch |
|
MON MAR 29 |
-We learn
how to define “optimization” -We learn
the algorithm for solving optimization problems. -We learn
how to solve optimization problems. |
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FRI MAR 26 |
-We learn
how to define “optimization” -We learn
the algorithm for solving optimization problems. -We learn
how to solve optimization problems. |
|
Take Home Test Question –
Developing Success Criteria for curve sketching analysis |
|
THUR MAR 25 |
-We learn
how to find the equation of an oblique (slant) asymptote in a rational
function. -We learn
how to sketch the graph of a rational function that has an oblique asymptote.
|
|
-Perform
a curve sketching analysis for y = (-x2 + x + 1)/(x – 1). |
|
WED MAR 24 |
-We learn
how to sketch polynomial and rational functions using calculus methods: (a)
intercepts; (b) asymptotes and their behaviour; (c) local extrema and
intervals of increase and decrease; (d) points of inflection and concavity. |
|
-Page 213
#4(e) ß perform
a complete curve sketch analysis as done in class (focus on presentation of
solution! -Also,
page 213 #6, 7 |
|
TUES MAR 23 |
-We learn
how to sketch polynomial and rational functions using calculus methods: (a)
intercepts; (b) asymptotes and their behaviour; (c) local extrema and
intervals of increase and decrease; (d) points of inflection and concavity. |
|
-Sketch
the graph of the function f(x) = (x-4)/(x2 – x- 2). You can check your
work to the textbook, page 209 example 2. |
|
MON MAR 22 |
-We learn
how to find the intervals where the function is concave up and concave down. -We learn
how to find the points of inflection. |
|
-Page 206
#8 (find P.O.I. & intervals of concavity); 9-11 -Read
pages 182-192 to refresh vertical, horizontal, and oblique asymptotes. |
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FRI MAR 12 |
-We learn
how to find the intervals of increase and decrease of a function. -We learn
how to use the First Derivative Test to find the local maximum and local
minimum of a function. |
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THURS MAR 11 |
-We learn
what is meant by “Related Rates”. -We solve
Related Rates problems using the GURDSS method. |
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Workhsheet
– page 3 do all questions; first 2 pages choose any 3 questions. |
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WED MAR 10 |
Both
classes co-constructed similar success criteria J Here’s what
period 2 came up with in groups and then as a whole class: |
Group Work: Writing
Learning Goal; Co-Construct Success Criteria; Self/Peer Assessment |
Page 564 #12 Find dy/dx:
3x2y + y2 – y3 – 7 = 0 Study for
tomorrow’s Check Point! |
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TUE MAR 9 |
We learn how
to use implicit differentiation to find the derivative of relations. |
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Page 564
#2-10 |
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MON MAR 8 |
We learn
how to find the maximum and minimum values of a function in a given
interval. |
|
Finish
off 2-sided Velocity and Acceleration worksheet Page 135
#1, 2, 3(a, e), 4-5, 7-9 |
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FRI MAR 5 |
We learn
to apply derivatives to velocity and acceleration problems. |
Feedback:
Learning Goals, Success Criteria, Self/Peer Assessment |
Page 127
#4 Pages
128-9 #8, 10, 11 For s(t)
= 10 + 65 – t2, is the object moving towards or away from the
origin at t = 3 seconds? |
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THURS MAR 4 |
We demonstrate
and celebrate our learning and accomplishments by writing the first unit test
J |
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Page 127
#2f, h, i, j Velocity
& acceleration question from chalkboard |
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WED MAR 3 |
-We learn
how to calculate the 2nd and higher order derivatives. |
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TUES MAR 2 |
We learn
to consolidate our learning for the first unit test (Introduction to Calculus
and Derivatives) |
Pages
56-58 #2(c) first principles; 4, 7, 8, 9, 11, 16, 17(all), 18(all) Page 110-112 #3e, 5(c,d,f), 6, 7(b,c), 11b, 12, 23,
29 |
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MON MAR 1 |
We learn
how to use the Chain Rule to find the derivative (con’t – today, Leibniz Notation) |
Co-Constructed Success
Criteria (Period 2) |
Page 106
#13(all); Page 113 #28(all)+simplify |
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FRI FEB 26 |
|
Long
worksheet #2(all); #3(all); #7(all); #12(all); #13(all) |
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THURS FEB 25 |
|
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- Textbook
pages 105-106 #2(b); 4(all); 7; 8(all) |
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WED FEB 24 |
|
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- Prove
the Quotient Rule. - Long
Worksheet – do circled questions |
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TUES FEB 23 |
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- Product
Rule Worksheet [on long paper]: #1(a, c, e, g, i, k, m, o, q); #4(b); #5(a,
c); #6(a, c); #9; #10(all) |
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MON FEB 22 |
|
- Prove
the Product Rule - Extra
Questions Worksheet -
Textbook page 83-84 #17(b); 23 |
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FRI FEB 19 |
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Pages
82-83 #3 all; 4 all; 5 all; 6b; 8(b, d); 9(d, e); 10(d, e) ß find
equation of normal line to 9(d, e) 14, 15, 16,
18, 19, 21, 25a(iii) [It looks
like a lot but each question is very short J) |
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THURS FEB 18 |
|
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- Page 75 #15 - Page 74 #13 - Page 82-83
#2(d,f); 3e; 4a; 7all; 8c; 9c; 10c; 11 – 13, 20 - Be sure
you can develop the constant function rule! |
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WED FEB 17 |
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Page
73-75 #1, 2, 3, 11, 18, 19 |
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TUES FEB 16 |
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-
Complete Mr. T’s Limits and continuity worksheet, if not done. - Study
for Check Point #2. |
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MON FEB 15 |
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FRI FEB 12 |
- We learn
how to evaluate infinite limits. - We also
learn the types of discontinuity. |
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-
Infinite limits worksheet: #1(f, r); #2(f, h, i) - p. 52
#8, 11, 13 -
Sketch y=f(x), state where function is discontinuous and types of
discontinuities:
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THURS FEB 11 |
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Textbook:
p. 46 #8 all; #10 all; #9 all (please do #9 last). |
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WED FEB 10 |
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TUES FEB 9 |
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MON FEB 8 |
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FRI FEB 5 |
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THURS FEB 4 |
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WED FEB 3 |
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TUES FEB 2 |
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