KP(IPG)8282/600/20 Jld.2(77)
SUMMARY OF COURSE INFORMATION 1. 2.
Name of Course /Module
Pre-Calculus Pra Kalkulus
Course Code
MTE1064
3.
Name(s) of academic staff
Zainab Bee binti Hamid
4.
Rasionale for the course/module in the programme
This course is offered so that students are able to master the basic concepts in the field of calculus and apply them in problem solving.
5.
Semester and Year offered
Semester 2
6.
Total Student Learning Time (SLT)
Face-to-Face
L = Lecture T = Tutorial P = Practical A = Assessment Assessment
L
T
P
Total Guided and Independent Learning
Non Face-to-Face
A
L
T
P
A 170
30
7.
Credit Value
4
8.
Prerequisite (if any)
None
Berkuat kuasa Jun 2013 (Kemas kini November 2016)
30
3.5
60
30
16.5
9.
Course Learning Outcomes (CLO)
At the end of the course students are able to : 1.
Determine the basic properties of function, domain and range by sketching the graphs of various functions (C3, P2, PLO1, PLO2, PLO3, CTPS2)
2.
Derive composite and inverse functions. (C3, PLO1, PLO 3, CTPS2)
3.
Determine the limit of continous function. (C4, PLO1, PLO3, CTPS3)
4.
Apply differentiation techniques in problem solving. (C4, PLO3, CTPS3)
5.
Apply integration techniques in problem solving. (C4, PLO3, CTPS3) LEARNING TAXONOMIES COGNITIVE DOMAIN
CLO
10. Transferable Skills 11. Teaching-Learning and Assessment Strategy
g n i r e b m e m e R
g n i d n a t s r e d n U
g n i y l p p A
C 1
C 2
C 3
1
x
2
x
g n i s y l a n A
g n i t a u l a v E
C 4
C 5
PSYCHOMOTOR DOMAIN
g n i t a e r C
n o i t p e c r e P
t e S
e s n o p s e R d e d i u G
C 6
P 1
P 2
P 3
e m s i n a h c e M
e s n o p s e r t r e v o r o s e l p m o C
P 4
P 5
AFFECTIVE DOMAIN
n o i t a t p a d A
n o i t a n i g i r O
g n e i v i e c e R
g n i s n o p s e R
g n i u l a V
n o o i t a z i n a g r O
P 6
P 7
A 1
A 2
A 3
A 4
s e ) u n l o a i v t a z g i n r i e z t i l c a a n r r a e h t n C I (
A 5
x
3
x
4
x
x
5
x
x
Critical thinking and prolem solving skills (CTPS3) Teaching-learning strategies: Lecture, tutorial,- demonstration, group activities, discussion
Assessment strategies: Student’s assessment of this course is determined via two (2) methods: final examination (50%) and coursework (50%) Programme Learning Outcome (PLO)
PLO1 – Knowledge
Teaching and Learning Strategies
Lecture discussion
PLO2- Practical skills
demonstration, group activities,
PLO3 – Scientific skills, thinking skills and problem solving skills
Lecture group activities, discussion
Berkuat kuasa Jun 2013 (Kemas kini November 2016)
Types of Assessment
Written test Quiz Written test Quiz Written test Quiz Problem solving project
12. Synopsis
This course focuses on the key concepts of the calculus: functions, graph of functions, composite functions, inverse functions, limits, continuity and the application of differentiation and integration in solving problems. Kursus ini memfokus kepada konsep asas dalam kalkulus: fungsi, graf fungsi, fungsi gubahan, fungsi songsang, had, keselanjaran dan pengaplikasian teknik-teknik pembezaan dan pengamiran dalam menyelesaikan masalah.
13. Mode of Delivery 14. Assessment Methods and Types
Lecture and Tutorial Coursework Final Examination Types of assessment Written
: :
50 % 50% Methods of assessment
Percentage
Final Examination
50
Quiz 1 (30 min) to access CLO 1 –Topic 1
10
Quiz 2 (30 min) to access CLO 2 and CLO3 –Topic 2 and Coursework topic 3
10
Problem Solving Project (CLO 4 and CLO5) – Topic 3 or topic 4
Berkuat kuasa Jun 2013 (Kemas kini November 2016)
30
e c a f o t e c a F
Content Outline of the Course and the T otal Student 17. Learning Time (SLT) for each topic
e r u t c e L
e c a f n - o o i t t - c e a c r a e f t n n I o N
n o i t c a r e t n I
l a i r o t u T
l a c i t c a r P
t n e e l a i m r u r s t o s c t e e u s L T s A
T L S l a t o T
l a c i t c a r P
t n e m s s e s s A
1. Functions Introduction to functions - definition of functions - relation and function - domain and range of function - representation of function
Graphs of functions linear quadratic cubic square root rational absolute value trigonometry exponent and logarithm (note: each graph of function has to be sketched and drawn accurately with or without the use of ICT)
- - - - - -
5
5
10
5
25
5
10
5
25
Composite and Inverse Function composite function inverse function
-
2. Limit and continuity Introduction to the concept of limit - definition of limit - properties of limit
Theorem and calculation of limit - limit theorem - calculation of the limit of polynomial function Types of limit one sided limit two sided limit
Asymptotes - Vertical asymptotes - Horizontal asymptotes - Curve sketching
Continuity - Continuity test of a function at a point - Continuity test of a function at an interval [a,b]
Berkuat kuasa Jun 2013 (Kemas kini November 2016)
5
3. Differentiation Meaning of differentiation - differentiation as the slope of a tangent
Differentiation from first principles Differentiation techniques algebraic functions trigonometric functions exponential functions logarithmic functions
Rules of differentiation product rule quotient rule chain rule
Application of differentiation tangent and normal problem involving maximum and minimum values
Rate of change Small change and approximation
- small change - approximation
Second degree differentiation maximum and minimum points
-
Berkuat kuasa Jun 2013 (Kemas kini November 2016)
10
10
20
10
50
4.
Integration Concept of anti-differentiation reverse of differentiation -
Standard integral for
- -
constant, 1
x
n
,
ax
n
,
x x
, expression in the form of [f(x)] f ’(x) e
Integration of trigonometric function 2
sine x, cosine x, sec x
Techniques of integration
-
by substitution
-
by parts
by partial fractions
10
10
20
10
50
Definite integration general characteristics of definite integral integration as summation power rule substitution method integration by parts partial fractions
Volume of revolution generated when area of region is rotated along x-axis along y-axis Application of Integration - problem solving
Coursework
1
9
10
7.5
7.5
Practical Revision Examination Total
Berkuat kuasa Jun 2013 (Kemas kini November 2016)
2.5 30
30
-
3.5
2.5 60
30
-
16.5 170.0
TOTAL FACE-TO-FACE AND NON FACETO-FACE LEARNING TIME
Face-to-face
Non face-to-face
Lecture
30
60
Tutorial
30
30
Quiz 1 (30 min)
0.5
1.5
Quiz 2 (30 min)
0.5
1.5
Problem Solving Project
-
6
2.5
7.5
63.5
106.5
Final Examination
Total
18. Main References
Total SLT
170
Credit Hours
4
Coburn,J. W., & Herdlick J. D. (2012). Precalculus: graphs and models. New York: McGraw. Hill. th
Goldstein, L. J., Lay, D. C., & Schneider, D. I. (2014). Calculus and its applications (13 ed). New York: Pearson. Steward, J. (2015). Calculus. Early transcendentals. Eighth edition. Boston, MA: Cengage Learning. Additional References
Ayres, F, Jr. & Mendelson, E. (2013). Schaum's Outlines: Calculus. McGraw Hill. Demana, F. D., Waits, B. K., Foley, G. D., & Kennedy, D. (2006). Precalculus: Graphical, Numerical, Algebraic . Boston: Pearson. Larson, R., & Hodgkins, A. V. (2008). College algebra and calculus an applied approach . Boston: Houghton Mifflin Torrence, B., & Torrence, E. (2009). The student's introduction to Mathematica a handbook for precalculus, calculus, and linear algebra. (2nd ed). New York: Cambridge University Press. Wrede, R., & Spiegel, M. R. (2010). Schaum's outline of advanced calculus . New York: McGraw.
19.
Other additional Information
None
Berkuat kuasa Jun 2013 (Kemas kini November 2016)
COURSE LEARNING OUTCOMES MATRIX – PROGRAMME LEARNING OUTCOMES MTE1064 Pre-Calculus (4 CREDITS) PROGRAMME LEARNING Teaching and OUTCOME Learning COURSE LEARNING OUTCOMES Assessment PLO PLO PLO PLO PLO PLO 1 2 3 4 5 6
1.
2.
Determine the basic properties of function, domain and range by sketching the graphs of various functions (C3, P2, PLO1, PLO2, PLO3, CTPS1) Derive composite and inverse functions (C3, PLO1, PLO3, CTPS1) Determine the limit of continous function. (C4, PLO1, PLO3, CTPS3)
4.
Apply differentiation techniques in problem solving. (C3, PLO3, CTPS1)
5.
Apply integration techniques in problem solving. (C3, PLO3, CTPS1)
TOTAL
Written test Quiz 1
x
Lecture and tutorial
x
x
Lecture and tutorial
Written test Quiz 2
x
x
Lecture and tutorial
Written test Quiz 2
x
Lecture and tutorial
x
Lecture and tutorial
Written test Problem solving project Written test Problem solving project Written test
x
3.
Strategies
x
x
x
x
Lecture and tutorial
Quiz
Problem solving project
Review Panel: No.
Name
Siti Khadzimah Binti Sallip 1
2
Salmiah Md Salleh
Akademic Qualifications
Sarjana Pendidikan(Pengajian Matematik), UKM (2001) Sarjana Musa Sains Serta Pendidikan (Matematik & Sains Komputer), UTM (1988) Diploma Sains serta Pendidikan (Matematik & Fizik), UTM (1986) Sarjana Pendidikan Matematik & ICT, UM (2009) Sarjana Muda Sains dengan Pendidikan (Matematik) , UM (2005)
Panel for Translation: No.
Name
Akademic Qualifications
1
Ong Lock Tong
2
Nur Izzati Lojinin
M. Ed – Psychometry (1998), Universiti Sains Malaysia B Sc (Hons) – Matematik (1991), Universiti Sains Malaysia Msc – Literacy in Mathematics (2009), Universiti Putra Malaysia B.Sc. (Hons) – Mathematics (1992), UMIST, Manchester.
Berkuat kuasa Jun 2013 (Kemas kini November 2016)