Download Course Syllabus - Fort Saskatchewan High

MATHEMATICS 30-1
Course Outline
Mrs. Orchard – Semester II, 2016-17
Course Schedule
UNIT
CLASSES
EXAM DATES
(may vary slightly) MARK %
1. Transformations and Functions; Radical Functions (Ch 1&2)
13
February 22
_______
2. Polynomial Functions (Ch 3)
9
March 8
_______
3. Rational Functions; Function Operations (Ch 9 & 10)
11
March 23
_______
4. Exponents and Logarithms (Ch 7 & 8)
12
April 20
_______
5. Trigonometry: unit circle, functions, graphs (Ch 4 & 5)
12
May 9
_______
6. Trigonometric Identities (Ch 6)
12
May 30
_______
7. Permutations and Combinations (Ch 11)
12
June 16
_______
RE-WRITE
DIPLOMA EXAM
Monday, June 26
Note: English Part A June 15, Social Part A June 16
Course Description
Mathematics 30-1 builds on key concepts from Mathematics 20-1. Learning through problem solving is the key
focus. Students develop and refine their own way of solving problems and show their work in a variety of ways.
Students use mathematical vocabulary to explain how they solve problems and continue to acquire the
mathematical processes of communication, making connections, mental mathematics, and visualization, and
the use of technology as a tool.
Students who believe they can learn, take risks and persevere in problem solving will be successful
mathematics students.
The topics in Mathematics 30-1 include:
 Trigonometry: develop trigonometric reasoning
 Relations and Functions: develop algebraic and graphical reasoning through the study of relations
 Permutations, Combinations and Binomial Theorem: develop algebraic and numeric reasoning that
involves combinatorics
Evaluation
There will be a unit exam after each unit. In addition to the 7 unit exams, assignments designed to promote
understanding will occur throughout the course.
Opportunity to improve an exam mark will be offered at specified points throughout the semester. Rewrite
opportunities will be at the teacher’s discretion after you have filled out a re-write form and have displayed
evidence of practice and attention to further your learning. Staying on task and keeping pace with the class is
important. With this in mind, UNIT STUDY NOTES should be presented to me prior to each unit exam in order
for me to consider granting a re-write opportunity.
The mark you achieve in class will be worth 70% of your final Math 30-1 mark, leaving the Diploma exam worth
30% of your final mark.
Exams and assignments
1. If you are absent for an exam, you are required to write the exam upon your return at an
agreed upon time and location.
2. Please be aware that everything counts. All work assigned (assignments, quizzes, exams) may
be used to determine your grade in this course. Once an assignment or quiz is handed back to
the students, any late assignments will not be accepted for the purpose of assessment.
Required Materials
Pre-Calculus 12 textbook, a binder, a pencil, and a graphing calculator. The Key is a booklet that contains an
ample amount of previous Diploma questions and solutions to help you prepare for the Diploma Exam. There
are also a number of useful websites. Please see Mrs. Cooke ASAP if you wish to purchase this booklet.
Classroom Expectations
1. Give your best effort every day; ask questions when you don’t understand. DO NOT FALL BEHIND!
2. Attend class regularly.
3. Conduct yourself in a courteous, respectful manner and comply with all school rules listed in the online
student agenda.
4. If you are late, get a late slip and enter the room in a respectful manner.
5. Use washrooms before class begins.
6. Be sitting at your desk when the bell rings.
7. Bring your required materials to class every day.
8. Please refrain from consuming any food or drink during the entire class, with the exception of water.
9. If the use of a personal device is deemed to be a distraction to the learning environment, it WILL result in
confiscation of the device in question. No exceptions. No arguments.
10. Review notes and class work every night and complete homework as assigned.
11. Review notes and class work every night and complete homework as assigned.
12. Review notes and class work every night and complete homework as assigned.
13. Review notes and class work every night and complete homework as assigned.
14. Preparation to leave the classroom at the end of the period includes ensuring that your work area is neat.
Unit 1 Transformations and Functions; Radical Functions (Ch 1&2)
1.1 Horizontal and Vertical Translations – pg. 6–15
Assignment: pg. 12–15 #1, 2a, 3, 4b sketch only, 5 - 9, 17, 19, C3
1.2 Stretches and Reflections – pg. 16–31
Assignment: pg 28–31 #2, 5ab, 6, 7ac, 8,9 14acd, 15cd, C4
Assignment: pg. 28–31 #1ad, 3, 4, 5cd, 7bd, 14b, 15ab, 16, C2, C3
1.3 Combining Transformations – pg. 32–43
Assignment: pg. 38–43 #2,3,4,5a (graph paper),6, 7 PC3, 9 PC 3 (graphs), 10, C2, C3
1.4 Inverse of a Relation – pg. 44–55
Assignment: Page 51 #2-4, 5a,c,e, 6, 7a,8a,c, 9a,d, 11, 12a,b,c, 13,15,16,17,21
Chapter Review and Practice Test – pg. 56–58
Assignment: pg. 56–57 #1–17
2.1
Radical Functions and Transformations – pg. 62–77
Assignment: pg. 72–77 #3, 4, 6, 9, 10, 13, 16
2.2
Square Root of a Function – pg. 78–89
Assignment: pg. #2-6, 8, 9, 16
2.3
Solving Radical Equations Graphically – pg. 90–98
Assignment: pg. 96–98 #1, 2, 3 PC2, 4, 5 PC2, 6, 7 PC2, 9, 10, 12, 13, 16
Chapter Review and Practice Test– pg. 99 - 102
Unit 1 Exam Date:______________________________
Need to review/remember:
Unit 2 Polynomial Functions (Ch 3)
3.1
Characteristics of Polynomial Functions – pg. 106–117
Assignment: pg. 114–117 #1–9
3.2
The Remainder Theorem – pg. 118–125
Assignment: pg. 124–125 #2, 4 PC3 for each, 6 ab, 8 ac, 10, 11a, 16
3.3
The Factor Theorem – pg. 126 – 135
Assignment: pg. 133–135 #1-4 PC 2 for each, 5 and 6 PC 5 total, 7-9, 11, 15, 16 i,ii,iii omit d)
3.4
Equations and Graphs of Polynomial Functions – pg. 136–152
Assignment: pg. 147–152 #3-6, 7 bd, 9 bef, 10
Assignment: pg. 147–152 # pg. 150–151 #12-16, 18
Chapter Review and Practice Test – pg. 153–156, pg 160
Assignment: Pg. 153–156 #1, 2(odd), 3, 4cd, 5a, 6, 7, 8(odd), 10–14
Unit 2 Exam Date:______________________________
Need to review/remember:
Unit 3 Rational Functions; Function Operations (Ch 9 & 10)
9.1 Rational Functions using Transformations I – pg. 430–445
Assignment: pg. 442
Rational Functions using Transformations II – pg. 430–445
Assignment: pg. 443–445
9.2 Analyzing Rational Functions – pg. 446–456
Assignment: pg. 451–456
9.3 Graphs and Rational Equations – pg. 457–467
Assignment: pg. 465–467
10.1 Sums and Differences of Functions – pg. 474–487
Assignment: pg. 483–487
10.2 Products and Quotients of Functions – pg. 488–498
Assignment: pg. 496–498
10.3 Composite Functions – pg. 499–509
Assignment: pg. 507–509
Chapter Review – pg. 468–469, pg. 510–511
Assignment: pg. 468–469
Unit 6 Exam Date:______________________________
Need to review/remember:
Unit 4 Exponents and Logarithms (Ch 7 & 8)
7.1 Exponential Functions – pg. 334–345
Assignment: pg. 342–345 #1-8, 10-12, 15
7.2 Transformations of Exponential Functions – pg. 346–357
Assignment: pg. 354–357 #1, 2, 4, 5ab, 6 PC2, 7, 9, 10, 11, 14
7.3 Solving Exponential Equations – pg. 358–365
Assignment: pg. 364–365 #2-5, 7-9
8.1 Logarithms and their functions – pg. 372–382
Assignment: pg. 380–382
8.2 Transformations of Logarithmic Functions – pg. 383–391
Assignment: pg. 389–391
8.3 Laws of Logarithms I – pg. 392–403
Assignment: pg. 400–403
Laws of Logarithms II – pg. 392–403
Assignment: pg. 401–403
8.4 Logarithmic and Exponential Equations – pg. 404–415
Assignment: pg. 412–413
Applications of Logarithmic and Exponential Equations – pg. 404–415
Assignment: pg. 413–415
Chapter Review – pg. 366–367, pg. 416–418
Assignment:
Unit 5 Exam Date:______________________________
Need to review/remember:
Unit 5 Trigonometry: unit circle, functions, graphs (Ch 4 & 5)
4.1 Angles and Angle Measure – pg. 166–179
Assignment: pg. 175–179 # 1-8 PC 2 for each, 11 adh, 12 bc, 15, 17 a-f, 18, 27 abc
4.2 The Unit Circle – pg. 180–190
Assignment: pg. 186–190 #1–5(odd), 6, 10, 11, 12a, 13
4.3 Trigonometric Ratios – pg. 191–205
(I) Assignment: pg. 201–205 #1 PC4, 3, 6, 8, 12 PC2
(II) Assignment: pg. 202–205 #2, 7, 9, 10ab, 11ab, 13, 16
4.4 Trigonometric Equations – pg. 206–214
Assignment: pg. 211–214 #1, 2, 4 PC 3, 5 PC 1, 6, 7ac, 8–11, 15, 16, 18
5.1 Graphing Sine and Cosine Functions – pg. 222–237
Assignment: pg.233–237 #4–10, 15, 18, 19
5.2 Transformations of Sinusoidal Functions I – pg. 238–255
Assignment: pg. 250–255 #1 PC3, 2 PC3, 3-5, 6a, 7ab
Assignment: pg. 250–255 #8, 9, 11, 14-16, 22-24, 27 PC2
5.3 The Tangent Function – pg. 256–265
Assignment: pg. pg. 262–265 #1-4, 6, 8, 9, 12
5.4 Equations and Graphs of Trigonometric Functions I– pg. 266–280
Assignment: pg. 275 #1, 3, 4ab, 6z
Assignment: pg. 275–279 #9, 10, 12, 13, 15, 16, 19
Chapter Review (2 days)– pg. 215–217, pg. 282–285
Assignment: pg. 215–217 #1, 2, 5, 7, 9, 11, 13–15, 17, 19–21, 23
pg. 282–285 #3–7, 8, 10–13, 15, 16, 18, 19, 20, 22, 23
Unit 3 Exam Date:______________________________
Need to review/remember:
Unit 6 Trigonometric Identities (Ch 6)
6.1 Reciprocal, Quotient, and Pythagorean Identities – pg. 290–297
Assignment: pg. 296–297 #1, 3 – 6,
10, 11, 13
6.2 Sum, Difference, and Double–Angle Identities – pg. 299–308
Assignment: pg. 306–308
6.3 Proving Identities – pg. 309–315
Assignment: pg. 314–315
6.4 Solving Trigonometric Equations Using Identities – pg. 316 – 321
Assignment: pg. 320–321
Chapter Review – pg. 322–323
Assignment: pg. 322–323
Unit 4 Exam Date:______________________________
Need to review/remember:
Unit 7 Permutations and Combinations (Ch 11)
1. Fundamental Counting Principle
Assignment: Absolute Value Workbook: pg. 375 – 378 #1–14
2. Permutations and Factorial Notation
Assignment: Absolute Value Workbook
pg. 524–527 #1–7,12, 18, 22, 23–25, pg. 526 of text #22
3. Permutations with Repetitions and Restrictions
Assignment: Absolute Value Workbook: pg. 388 – 391 #1–15, pg. 525 of text #8
4. Combinations – pg. 528–536
Assignment: Absolute Value Workbook:
pg. 396 –398 #1–12, pg. 402–404 #1–16, pg. 534 of text #6
5. The Binomial Theorem
Assignment: Absolute Value Workbook:
pg. 410 – 412 #1–13
Chapter Review – pg. 546–547
Assignment: pg. 546–547 #1–12, 14–18
Unit 7 Exam Date:______________________________
Need to review/remember:
Period for sine and cosine: 360o or 2π
Period for tangent: 180o or π
In an equation:
2
360
period =
(for degrees) period =
(for radians)
b
b
Transformations of Trigonometric Functions
y = asin[b(x - c)] + d
amplitude
(vertical stretch by a
factor of 'a')
Amplitude = max - min
2
Think: distance away
from 'centre line', which
is the value of 'd'
horizontal stretch
by a factor of 1/b
value of b HELPS
you find the
period
horizontal
translation
(Phase shift)
vertical
translation
(Vertical
displacement)
-just like before
('b' is NOT the
period!!!!!!)
-just like before,
PLUS, it cuts the
graph in half
horizontally...good
to know!
**Reflection: -a, +a
Interval Notation:
(description)
Open Interval: (a, b) is interpreted as a < x < b where the
endpoints are NOT included.
(diagram)
(1, 5)
(While this notation resembles an ordered pair, in this context it refers
to the interval upon which you are working.)
Closed Interval: [a, b] is interpreted as a < x < b where the
endpoints are included.
Half–Open Interval: (a, b] is interpreted as a < x < b where a
is not included, but b is included.
Half–Open Interval: [a, b) is interpreted as a < x < b where a
is included, but b is not included.
[1, 5]
(1, 5]
[1, 5)
Non–ending Interval: (𝑎, ∞) is interpreted as x > a where a is
not included and infinity is always expressed as being "open"
(not included).
(1, ∞)
Non–ending Interval: (−∞, 𝑏] is interpreted as x < b where b
is included and again, infinity is always expressed as being
"open" (not included).
(−∞, 5]
Mathematics 30-1 Formula Sheet
For ax 2  bx  c  0,
x
Trigonometry

b  b 2  4ac
2a
Relations and Functions
Graphic Calculator Window Format
x :  xmin , xmax , xsc1 
y :  ymin , ymax , ysc1 
Laws of Logarithms
log b  M  N   log b M  log b N
M
log b 
N

  log b M  log b N

log b  M n   n log b M
log b c 
sin x
cos x
cot x 
cos x
sin x
csc x 
1
sin x
sec x 
1
cos x
cot x 
1
tan x
sin 2 x  cos 2 x  1
1  tan 2 x  sec 2 x
1  cot 2 x  csc 2 x
sin  A  B   sin A cos B  cos A sin B
log a c
log a b
cos  A  B   cos A cos B  sin A sin B
cos  A  B   cos A cos B  sin A sin B
t
p
General Function
y  af b  x  h    k
Permutations, Combinations, and the
Binomial Theorem
n!  n  n 1 n  2 ...3  2 1,
where n  N and 0! = 1
tan  A  B  
tan A  tan B
1  tan A tan B
tan  A  B  
tan A  tan B
1  tan A tan B
sin  2 A   2sin A cos A
cos  2 A   cos 2 A  sin 2 A
cos  2 A   2cos 2 A  1
cos  2 A   1  2sin 2 A
n!
n Pr 
 n  r !
n!
n Cr 
 n  r  !r !
tan x 
sin  A  B   sin A cos B  cos A sin B
Growth/Decay Formula
y  ab
a
r
n
n Cr   
r
In the expansion of  x  y  ,
n
the general term is tk 1  n Ck x n  k y k
tan  2 A  
2 tan A
1  tan 2 A
y  a sin b  x  c    d
y  a cos b  x  c    d