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BA101 Engineering Mathematics 1
POLYTECHNICS MINISTRY OF HIGHER EDUCATION MALAYSIA DEPARTMENT OF MATHEMATICS, SCIENCE AND COMPUTER
COURSE
:
BA101 ENGINEERING MATHEMATICS 1
INSTRUCTIONAL DURATION
:
15 WEEKS
CREDIT ( S )
:
2
PREREQUISITE(S)
:
NONE
SYNOPSIS ENGINEERING MATHEMATICS 1 exposes students to algebra through theory, practical and tutorial which focuses on standard form, index and logarithm, geometry and measurement as well as coordinate geometry and graph. This course also explains the basic concept of trigonometry and its functions in solving problems.
LEARNING OUTCOMES Upon completion of this course, students should be able to: 1.
show all the relevant steps in solving simultaneous linear equations with two variables and quadratic equations by using various methods based on basic algebraic concept.
2.
perform algebraic operations in standard form and simplify indices and logarithmic expressions by using index and logarithm rules in solving related problems.
3.
apply the fundamental of trigonometric functions, sine and cosine rules, basic trigonometric identities, formula of compound-angle and double-angle in solving simple trigonometric equations.
4.
determine angles, arc length, area of a sector and segment by applying the Pythagoras’ Theorem, the properties of angles with transversal and parallel lines and properties of circles
5.
calculate the length, perimeter, area and volume of specific and similar shapes by using appropriate formulae and concept of similarity.
6.
demonstrate sketching and drawing of linear, quadratic and non-linear graphs accurately to solve simultaneous equations based on intersection points between two lines.
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BA101 Engineering Mathematics 1
SUMMARY
(30 LECTURE : 15 PRACTICAL)
RTA (06:03)
1.0
BASIC ALGEBRA This topic introduces basic algebraic concept and its use in solving linear equations, simultaneous linear equations with two variables and quadratic equations.
2.0
STANDARD FORM, INDEX AND LOGARITHM This topic introduces the standard form, index and logarithm rules and their applications to simplify expression and problem solving. The use of calculator is emphasised.
(06:03)
3.0
TRIGONOMETRY This topic explains the fundamental concept of trigonometric functions particularly the six trigonometric ratios of special angles and simple trigonometric basic identities. The topic also explain about sine and cosine rules. Skills using trigonometric identities, sine and cosine rules, formula of compound-angle and doubleangle to solve simple trigonometric equations will be discussed.
(06:03)
4.0
GEOMETRY AND MEASUREMENT This topic explains the properties of angles with transversal and parallel lines and the properties of angles in a circle. The characteristics of a tangent to a circle are discussed to solve angular problems. The Pythagoras’ Theorem is applied to solve problems related to angle and length. The topic also explains methods of calculating arc length, surface area and volume. The concepts of similarity and how to calculate the length, area and volume for any similar shapes also will be discussed.
(08:04)
5.0
COORDINATE GEOMETRY AND GRAPH This topic includes solving coordinate geometry problems using graphs and formulas. Emphasis will be given to the techniques of drawing straight lines and quadratic graph to ensure accuracy in solving linear and quadratic equations. The topic also emphasis how to sketch cubic and reciprocal graph of functions.
(04:02)
RTA : Recommended Time Allocation
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BA101 Engineering Mathematics 1
SYLLABUS
1.0
2.0
BASIC ALGEBRA 1.1
Understand basic algebra 1.1.1 Simplify algebraic fractions. 1.1.2 Solve algebraic fractions using: a. addition b. subtraction c. multiplication d. division 1.1.3 Perform conversion of formulas.
1.2
Understand quadratic equations 1.2.1 Solve quadratic equations by using factorization. 1.2.2 Solve quadratic equations by using quadratic formula. 1.2.3 Solve quadratic equations by using completing squares.
1.3
Understand simultaneous linear equations with two variables 1.3.1 Solve simultaneous linear equations by using the elimination method. 1.3.2 Solve simultaneous linear equations by using the substitution method.
STANDARD FORM, INDEX AND LOGARITHM 2.1
Know standard form 2.1.1 Convert real number to standard form and vice-versa. 2.1.2 Perform algebraic operations in standard form.
2.2
Know the rules of indices. 2.2.1 State the index rules. 2.2.2 Apply the index rules to find the product of index number. 2.2.3 Apply the index rules to find the quotient of index number. 2.2.4 Simplify expressions related to indices.
2.3
Know the rules of logarithm. 2.3.1 State the logarithm rules. 2.3.2 Express the index number in logarithm form. 2.3.3 Find the value of a logarithm. 2.3.4 Apply the logarithm rules to find the value of logarithms. 2.3.5 Change the base of logarithms. 2.3.6 Simplify logarithm expressions. 2.3.7 Solve equations that contain indices and logarithm expressions.
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3.0
4.0
BA101 Engineering Mathematics 1
TRIGONOMETRY 3.1
Understand the fundamental of trigonometric functions. 3.1.1 Define sine, cosine, tangent, secant, cosecant and cotangent. 3.1.2 Use quadrant to determine the value of trigonometric functions (positive and negative angles). 3.1.3 State the values of the trigonometric ratios of the special angles (30o, 45o and 60o). 3.1.4 Find the values of the trigonometric functions involving special angles. 3.1.5 Use calculator to determine the value of trigonometric functions (including radian).
3.2
Know trigonometric equations and identities. 3.2.1 State trigonometric basic identities. 3.2.2 State the formula of compound-angle and double-angle. 3.2.3 Solve simple trigonometric equations using the appropriate formula involving: a. three trigonometric basic identities b. formula of compound-angle c. formula of double-angle
3.3
Understand sine and cosine rules. 3.3.1 State the sine and cosine rules. 3.3.2 Calculate the area of a triangle using the formula ½ ab sin C. 3.3.3 Solve simple trigonometric problems using sine and cosine rules.
GEOMETRY AND MEASUREMENT 4.1
Understand properties of angles associated with transversal and parallel lines. 4.1.1 Define right angle, acute angle, obtuse angle, adjacent angle, complementary angle and supplementary angle. 4.1.2 Identify transversals, corresponding angles, alternate angles and interior angles. 4.1.3 Find the values of corresponding angles, alternate angles and interior angles associated with parallel lines. 4.1.4 Solve problems involving properties of angles associated with transversals.
4.2
Understand the properties of circles. 4.2.1 State the properties of an angle and chord in a circle. 4.2.2 State the properties of tangent on a circle. 4.2.3 Solve problems on the angles of cyclic quadrilaterals.
4.3
Apply the Pythagoras’ Theorem. 4.3.1 Identify the hypotenuse of right-angled triangles. 4.3.2 Find the length of the missing side of a right-angled triangle using the Pythagoras’ Theorem. 4.3.3 Find the length of side of geometric shapes using Pythagoras’ Theorem.
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5.0
BA101 Engineering Mathematics 1
Solve problems using the Pythagoras’ Theorem.
4.4
Know the arc length, area of a sector and segment of a circle. 4.4.1 Convert an angle from degree to radian and vice-versa. 4.4.2 Calculate the arc length of a circle. 4.4.3 Compute the area of a sector. 4.4.4 Compute the area of a segment.
4.5
Understand the perimeter, area and volume for specific shapes. 4.5.1 State the formula of the perimeter and area for rectangle, parallelogram, triangle and trapezium. 4.5.2 Compute the perimeter and area for rectangle, parallelogram, triangle and trapezium. 4.5.3 State the formula of the surface area and volume for sphere, hemisphere, cylinder, cube, cuboid, prism, pyramid and circular cone. 4.5.4 Compute the surface area and volume for sphere, hemisphere, cylinder, cube, cuboid, prism, pyramid and circular cone.
4.6
Understand the concepts of similarity. 4.6.1 Identify if given shapes are similar. 4.6.2 Calculate the length of unknown side of two similar shapes. 4.6.3 Calculate the area and volume for any similar shapes.
COORDINATE GEOMETRY AND GRAPH 5.1
Know the linear graphs. 5.1.1 Sketch a linear graph when given the gradient and point of interception. 5.1.2 Construct table of values for given linear functions. 5.1.3 Draw a linear graph. 5.1.4 Find the midpoint, distance and gradient between two points. 5.1.5 Solve simultaneous linear equations using linear graphs.
5.2
Know the quadratic graphs. 5.2.1 Construct tables of values for given quadratic functions. 5.2.2 Draw graphs of quadratic functions. 5.2.3 Solve problems involving linear and quadratic equations using graph. 5.2.4 Solve problems involving two quadratic equations using graph.
5.3
Know the basic form of non-linear graphs. 5.3.1 Sketch graphs of cubic functions. 5.3.2 Sketch graphs of reciprocal functions. (y = a/x)
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BA101 Engineering Mathematics 1
ASSESSMENT
TYPES OF ASSESSMENT
The course assessment is carried out in two sections: i. ii.
Continuous Assessment Final Examination
-
(CA) (FE)
The percentage ratio of FE to CA should follow the guideline stated in the Arahan-Arahan Peperiksaan dan Kaedah Penilaian which is approved by the Lembaga Peperiksaan dan Penganugerahan Sijil/Diploma Politeknik.
CONTINUOUS ASSESSMENT (CA): [ The total score of the CA components would be converted to the determined CA percentage ] Continuous assessment is carried out throughout the semester and comprises the followings: a. Quiz (minimum 3) b. Theory Test (minimum 2) c. Lab work (minimum 2) d. Other Assessment Task i. End - of- Chapter (minimum 2) ii. e- Quiz (minimum 2)
20% 30% 20% 20% 10%
[ Assessment Task above (a-c) to be executed during Lecture/Practical/ Tutorial hour)
FINAL EXAMINATION (FE):
Final examination is carried out at the end of the semester.
Note: 1. Refer to Assessment Specification Table for the details. 2.The percentage of Continuous Assessment may vary depending in courses.
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BA101 Engineering Mathematics 1
ASSESSMENT SPECIFICATIONS TABLE (AST)
COURSE : BA101 ENGINEERING MATHEMATICS 1 COURSE LEARNING OUTCOME (CLO)
1. Show all the relevant steps in solving simultaneous linear equations with two variables and quadratic equations by using various methods based on basic algebraic concept 2. Perform algebraic operations in standard form and simplify indices and logarithmic expressions by using index and logarithm rules in solving related problems 3. Apply the fundamental of triginometric functions, sine and cosine rules, basic trigonometric identities, formula of compound-angle and double-angle in solving simple trigonometric equations 4. Determine angles, arc length, area of a sector and segment by applying the Pythagoras' Theorem, the properties of angles with transversal and parallel lines and properties of circles 5. Calculate the length, perimeter, area and volume of specific and similar shapes by using appropriate formulae and concept of similarity 6. Demonstrate skecthing and drawing of linear, quadratic and non-linear graphs accurately to solve simultaneaous equations based on intersection points between two lines ASSESSMENT TASK CONSTRUCT (CLO)
CONTEXT 1
Quadratic Equations
√ √
Simultaneous Linear Equations With Two Variables
√
Basic Algebra BASIC ALGEBRA
Rules Of Indices Rules Of Logarithm
TRIGONOMETRY
4
5
6
L
M
Theory Test H
L
1
1
1
1
1
2
√ √
1
Pythagoras’ Theorem Arc Length, Area of a Sector and Segment of a Circle
√
Concepts Of Similarity Linear Graphs COORDINATE GEOMETRY AND Quadratic Graphs GRAPH Basic Form Of Non-Linear Graphs
Labwork H
1
1
1
1
2
1
L
M
1
1
End-of-Chapter H
1
1
1
1
1
2
1
2
1
H
1
1
1 1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
M
1
1
1
2
1
1
1
1
1 1
1
1
1 1
1
1
1
1
1 1
√ √ √
L
1
1
√ √
Final Examination H
1
1 1
M
1
1
1
L
2
1
1 1
1
1
5 5
TOTAL
M
1
√ √ √
Perimeter, Area And Volume For Specific Shapes
L
2
1
√
Properties Of Circles
H
1
Trigonometric Equations And Identities
Properties Of Angles Associated With Transversal And Parallel Lines
M
e-Quiz
1
Fundamental Of Trigonometric Functions
Sine And Cosine Rules
GEOMETRY AND MEASUREMENT
3
√ √ √
Standard Form STANDARD FORM, INDEX AND LOGARITHM
2
Quiz
1
1 1
1
2
1
1
1
1
1
1
1
3 3
2 2
10 5
6 3
5 2
6 5
3 3
2 2
6 5
4 3
2 2
10 5
7 3
5 2
1
1
1
18 5
12 3
6 2
LEGEND: Difficulty Level : L : Low M : Medium H : High
5 3 2
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50% of the aspects can be answered correctly by more than 60% of the candidates 30% of the aspects can be answered correctly by more than 40% but less than 60% of the candidates 20% of the aspects can be answered correctly by less than 40% of the candidates
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BA101 Engineering Mathematics 1
REFERENCES Backhouse, J.K., Houldsworth, S.P.T. & Cooper, B.E.D. Pure Mathematics (2nd ed.). Bird, J.O. & May, A.J.C. (1997). Technician Mathematics 1 (3rd ed.). Longman. Robert Moyer. (1998). Trigonometry (3rd ed.). McGraw-Hill. Siti Aishah Sheikh Abdullah, Ch’ng Pei Eng, Teoh Sian Hoon, Muniroh Hamat, Noor’ Aina Abdul Razak. (2006). First Engineering Mathematics. (2nd ed.). McGrawHill. Stroud, K.A. (2007). Engineering Mathematics (6th ed.). Palgrave Macmillan. Thorning, D.W.S & Sadler. (1999). Understanding Pure Mathematics, Oxford University Press.
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BA101 Engineering Mathematics 1
DISTRIBUTION OF STUDENT LEARNING TIME COURSE CREDIT
: :
BA101 ENGINEERING MATHEMATICS 1 2 COD E
SL T
L
30
I
15
P
15
I
15
Tutorial
T
Other Assessment Task
O
0 5
No.
1
Activities
[
Lecture Lecture hours -
3
4
5 6
hour(s) x
15
week(s)
]
[√]
Assessment Task
(Theory Test/Quiz) 2
2
[√]
Self Learning: Theory Preparation before theory class viz. review/ lesson notes. Preparation after theory class viz. additional references, discussion group, discussion with lecturers. Preparation for theory test. [
Practical -
Lab work Skill/Practical test Field work
[√] [ ] [
-
Survey/research
[
1
hour(s) x [
]
- Studio work - Workshop - Simulation
[
]
]
- Outdoors
[
]
15
week(s)
[
]
(Final Project) Presentation Reflective Journal Case Study
[ [ [
] ] ]
Industrial Visit
[
]
[√] [√] ]
] [
[ ] Critique Oral Presentation [ ]
]
Self Learning: Practical Preparation before practical class/field work/survey viz. review notes, checklist/labsheets and/or tools and equipment. Preparation after practical class/field work/survey viz. additional references, discussion session and report writing. Preparation before studio work presentation/critique. Preparation for practical test.
Capstone Project
[√]
Portfolio
[
Peer Assessment Self Assessment End-of-Chapter
[ ] [ ] [√]
]
[√] [√] [√]
[√]
Essay Question
[
]
Observation Discussion Project e-Quiz
[ [ [
] ] ]
[√] 80
Total L
Lecture
30
P I
Practical
15
Self Learning
30
T O
Tutorial Other Assessment Task
0 5
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SLT (Student Learning Time)
80
Credit = SLT/40
2
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BA101 Engineering Mathematics 1
TABLE OF LEARNING DOMAINS COURSE : BA101 ENGINEERING MATHEMATICS
No. 1.0 1.1 1.1.1 1.1.2
Specific Outcome
Cognitive Domain C1
BASIC ALGEBRA Understand Basic Algebra Simplify algebraic fractions. Solve algebraic fractions using: a. addition
C2
C3
√
C4
C5
Psychomotor Domain C6
P1
P2
P3
P4
Affective Domain P5
A1
A2
√
A3
A4
A5
√
√
√
√
b. subtraction c. multiplication 1.1.3 1.2 1.2.1 1.2.2 1.2.3 1.3 1.3.1 1.3.2 2.0 2.1 2.1.1 2.1.2 2.2
d. division Perform conversion of formulas. Understand quadratic equations. Solve quadratic equations by using factorization. Solve quadratic equations by using quadratic formula. Solve quadratic equations by using completing squares. Understand simultaneous linear equations with two variables Solve simultaneous linear equations by using the elimination method. Solve simultaneous linear equations by using the substitution method. STANDARD FORM, INDEX AND LOGARITHM Know standard form Convert real number to standard form and vice-versa. Perform algebraic operations in standard form.
√
√
√
√ √ √
√ √ √
√ √ √
√ √
√ √
√ √
√
√ √
√ √
√
Know the rules of indices.
2.2.1
State the index rules.
2.2.2
Apply the index rules to find the product of index number.
√
√
√
2.2.3
Apply the index rules to find the quotient of index number.
√
√
√
2.2.4
Simplify expressions related to indices.
√
√
2.3
Know the rules of logarithm.
2.3.1
State the logarithm rules.
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√
√
√ √
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No.
BA101 Engineering Mathematics 1
Specific Outcome
C1
Cognitive Domain C2 C3 C4 C5
C6
P1
Psychomotor Domain P2 P3 P4 P5
A1
Affective Domain A2 A3 A4 A5
2.3.2
Express the index number in logarithm form.
2.3.3
Find the value of a logarithm.
2.3.4
Apply the logarithm rules to find the value of logarithms.
√
√
√
2.3.5
Change the base of logarithms.
√
√
√
2.3.6
Simplify logarithm expressions. Solve equations that contain indices and logarithm expressions.
√
√
2.3.7 3.0
TRIGONOMETRY
3.1
Understand the fundamental of trigonometric functions.
3.1.1 3.1.2 3.1.3 3.1.4 3.1.5 3.2
√
√
√
√ √
√
√
√ √
√
Define sine, cosine, tangent, secant, cosecant and cotangent. Use quadrant to determine the value of trigonometric functions (positive and negative angles) State the values of the trigonometric ratios of the special angles. (30o, 45o and 60o)
√
√
√
√
√
√
Find the values of the trigonometric functions involving special angles. Use calculator to determine the value of trigonometric functions (including radian).
√
√
√
√
√
√
√
√
√
Know trigonometric equations and identities.
3.2.1
State trigonometric basic identities
√
√
3.2.2
State the formula of compound-angle and double-angle Solve simple trigonometric equations using the appropriate formula involving: a. three trigonometric basic identities b. formula of compound-angle c. formula of double-angle
√
√
3.2.3
3.3
√
State the sine and cosine rules.
3.3.2
Calculate the area of a triangle using the formula ½ ab sin C.
√
3.3.3
Solve simple trigonometric problems using sine and cosine rules.
√
4.1
√
Understand sine and cosine rules.
3.3.1
4.0
√
√
√ √
√ √
√
GEOMETRY AND MEASUREMENT Understand properties of angles associated with transversal and parallel lines.
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BA101 Engineering Mathematics 1
Cognitive Domain No.
Psychomotor Domain
C1
C2
C3
C4
C5
C6
P1
P2
P3
4.1.1
Define right angle, acute angle, obtuse angle, adjacent angle, complementary angle and supplementary angle.
√
4.1.2
Identify transversals, corresponding angles, alternate angles and interior angles.
√
√
√
√
4.1.3 4.1.4 4.2
Find the values of corresponding angles, alternate angles and interior angles associated with parallel lines. Solve problems involving properties of angles associated with transversals.
√
√
P4
P5
A1
A2
State the properties of an angle and chord in a circle.
√
4.2.2
State the properties of tangent on a circle.
√
4.2.3
Solve problems on the angles of cyclic quadrilaterals.
A5
√ √
√
√ √ √
√
√
√
Apply the Pythagoras’ Theorem. Identify the hypotenuse of right-angled triangles.
√
√
4.3.2
Find the length of the missing side of a right-angled triangle using the Pythagoras’ Theorem.
√
√
√
4.3.3
Find the length of side of geometric shapes using Pythagoras’ Theorem.
√
√
√
4.3.4
Solve problems using the Pythagoras’ Theorem.
√
√
√
√
Know the arc length, area of a sector and segment of a circle.
4.4.1
Convert an angle from degree to radian and vice-versa.
4.4.2
Calculate the arc length of a circle.
√
√
√
4.4.3
Compute the area of a sector.
√
√
√
4.4.4
Compute the area of a segment.
√
√
√
4.5
A4
√
4.3.1
4.4
A3
Understand the properties of circles.
4.2.1
4.3
Affective Domain
Specific Outcome
√
√
√
Understand the perimeter, area and volume for specific shapes.
4.5.1
State the formula of the perimeter and area for rectangle, parallelogram, triangle and trapezium.
4.5.2
Compute the perimeter and area for rectangle, parallelogram, triangle and trapezium.
4.5.3
State the formula of the surface area and volume for sphere, hemisphere, cylinder, cube, cuboid, prism, pyramid and circular cone.
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√ √
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No.
Specific Outcome
4.5.4
Compute the surface area and volume for sphere, hemisphere, cylinder, cube, cuboid, prism, pyramid and circular cone.
4.6 4.6.1
C1
C2
Cognitive Domain C3 C4 C5
P1
Psychomotor Domain P2 P3 P4 P5
Affective Domain A2 A3 A4
√
√
Identify if given shapes are similar.
√
√
√
√
A5
√
√
√
4.6.2
Calculate the length of unknown side of two similar shapes.
4.6.3
Calculate the area and volume for any similar shapes.
√
5.0
COORDINATE GEOMETRY AND GRAPH
5.1
Know the linear graphs.
5.1.1
Sketch a linear graph when given the gradient and point of interception.
√
5.1.2
Construct table of values for given linear functions
√
5.1.3
Draw a linear graph.
√
5.1.4
Find the midpoint, distance and gradient between two points.
5.1.5
Solve simultaneous linear equations using linear graphs.
√
√
√
√
√ √
√
√
√ √
√
√
√
Know the quadratic graphs.
5.2.1
Construct tables of values for given quadratic functions.
√
5.2.2 5.2.3
Draw graphs of quadratic functions. Solve problems involving linear and quadratic equations using graph.
√ √
√ √
5.2.4
Solve problems involving two quadratic equations using graph.
√
√
5.3
A1
Understand the concepts of similarity. √
5.2
C6
√
√ √ √ √
Know the basic form of non-linear graphs.
5.3.1
Sketch graphs of cubic functions
√
√
√
5.3.2
Sketch graphs of reciprocal functions. (y=a/x)
√
√
√
TOTAL
21
4
40
0
0
0
21
3
30
4
0
18
26
3
1
Legend Cognitive Domain C1 Knowledge C2 Comprehensive C3 Application C4 Analysis C5 Synthesis C6 Evaluation
Psychomotor Domain P1 Imitate P2 Manipulate P3 Precision P4 Articulation P5 Naturalization
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A1 A2 A3 A4 A5
Affective Domain Receiving Phenomena Responding to Phenomena Valuing Organizing Values Internalizing Values
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MATRIX OF SPECIFIC OUTCOMES Vs CLO, GSA AND LEARNING DOMAINS COURSE : BA101 ENGINEERING MATHEMATICS 1 COURSE LEARNING OUTCOME (CLO) Upon completion of this course, students should be able to:
1.0
BASIC ALGEBRA
1.1
Understand Basic Algebra
1.1.1
Simplify algebraic fractions.
1.1.2
Solve algebraic fractions using:
Lecture Question & Answer Practical, Peer assisted of Other Students
√
√
√
√
LD 3 GSA 4
LD 2
LD 1
CLO 6
CLO 5
GSA & LD CLO 4
CLO3
Specific Outcome
CLO2
No
CLO 1
CLO *Recommended Teaching & Learning Strategy
Note: *Lecturers may use other teaching & learning strategies in order to achieve the learning outcomes. Generic Student Attributes (GSA) GSA 1 Communications Skills GSA 2 Critical Thinking and Problem Solving Skills GSA 3 Teamwork Skills GSA 4 Moral & Professional Ethics GSA 5 Leadership Skills GSA 6 Information Management Skills and Continuous Learning GSA 7 Entrepreneurship Skills
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Learning Domain (LD) LD 1 Knowledge LD 2 Technical Skills LD 3 Professionalism & Ethics LD 4 Social Skills LD 5 Communication Skills LD 6 Critical Thinking LD 7 Life Long Learning LD 8 Entrepreneurial Skills
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GSA 5
6.
LD 8 GSA 7
5.
LD 7 GSA 6
4.
LD 6 GSA 2
3.
LD 5 GSA 1
2.
show all the relevant steps in solving simultaneous linear equations with two variables and quadratic equations by using various methods based on basic algebraic concept. perform algebraic operations in standard form and simplify indices and logarithmic expressions by using index and logarithm rules in solving related problems. apply the fundamental of trigonometric functions, sine and cosine rules, basic trigonometric identities, formula of compoundangle and double-angle in solving simple trigonometric equations. determine angles, arc length, area of a sector and segment by applying the Pythagoras’ Theorem, the properties of angles with transversal and parallel lines and properties of circles calculate the length, perimeter, area and volume of specific and similar shapes by using appropriate formulae and concept of similarity. demonstrate sketching and drawing of linear, quadratic and non-linear graphs accurately to solve simultaneous equations based on intersection points between two lines.
LD 4 GSA 3
1.
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BA101 Engineering Mathematics 1
MATRIX OF SPECIFIC OUTCOMES Vs CLO, GSA AND LEARNING DOMAINS COURSE : BA101 ENGINEERING MATHEMATICS 1
a. addition
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b. subtraction
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c. multiplication
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d. division
√
1.1.3 1.2
Perform conversion of formulas. Understand quadratic equations.
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1.2.1
Solve quadratic equations by using factorization.
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1.2.2 1.2.3 1.3 1.3.1 1.3.2
Solve quadratic equations by using quadratic formula. Solve quadratic equations by using completing squares. Understand simultaneous linear equations with two variables Solve simultaneous linear equations by using the elimination method. Solve simultaneous linear equations by using the substitution method.
2.0
STANDARD FORM, INDEX AND LOGARITHM
2.1
Know standard form
2.1.1
Convert real number to standard form and viceversa.
2.1.2
Perform algebraic operations in standard form.
Lecture Question & Answer Practical, Problem Solving in Group, Computer Assisted Learning
√
√
√
√
Lecture Question & Answer Practical, peer assisted of other students
√ √
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Note: *Lecturers may use other teaching & learning strategies in order to achieve the learning outcomes. Generic Student Attributes (GSA) GSA 1 Communications Skills GSA 2 Critical Thinking and Problem Solving Skills GSA 3 Teamwork Skills GSA 4 Moral & Professional Ethics GSA 5 Leadership Skills GSA 6 Information Management Skills and Continuous Learning GSA 7 Entrepreneurship Skills
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GSA 5
LD 8 GSA 7
LD 7 GSA 6
LD 6 GSA 2
LD 5 GSA 1
LD 4 GSA 3
LD 3 GSA 4
LD 2
LD 1
CLO 6
CLO 5
GSA & LD CLO 4
CLO3
Specific Outcome
CLO2
No
CLO 1
CLO *Recommended Teaching & Learning Strategy
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MATRIX OF SPECIFIC OUTCOMES Vs CLO, GSA AND LEARNING DOMAINS COURSE : BA101 ENGINEERING MATHEMATICS 1
2.2 2.2.1 2.2.2 2.2.3 2.2.4
State the index rules. Apply the index rules to find the product of index number. Apply the index rules to find the quotient of index number.
2.3.1
State the logarithm rules.
2.3.2
Express the index number in logarithm form.
2.3.3
Find the value of a logarithm. Apply the logarithm rules to find the value of logarithms. Change the base of logarithms.
2.3.6 2.3.7
Lecture Question & Answer Practical, Writing reflections on learning (3-4 minutes)
TRIGONOMETRY
3.1
Understand the fundamental of trigonometric functions.
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Note: *Lecturers may use other teaching & learning strategies in order to achieve the learning outcomes. Generic Student Attributes (GSA) GSA 1 Communications Skills GSA 2 Critical Thinking and Problem Solving Skills GSA 3 Teamwork Skills GSA 4 Moral & Professional Ethics GSA 5 Leadership Skills GSA 6 Information Management Skills and Continuous Learning GSA 7 Entrepreneurship Skills
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GSA 5
LD 8 GSA 7
LD 7 GSA 6
LD 6 GSA 2
LD 5 GSA 1
LD 4 GSA 3
LD 3 GSA 4
LD 2
CLO 6
CLO 5
CLO 4
LD 1 √
√
√ Lecture Question & Answer Practical, Problem solving in group, Rounds (giving turn to students to talk)
Simplify logarithm expressions. Solve equations that contain indices and logarithm expressions.
3.0
√
√
Simplify expressions related to indices. Know the rules of logarithm.
2.3.5
GSA & LD
Know the rules of indices.
2.3
2.3.4
CLO3
Specific Outcome
CLO2
No
CLO 1
CLO *Recommended Teaching & Learning Strategy
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MATRIX OF SPECIFIC OUTCOMES Vs CLO, GSA AND LEARNING DOMAINS COURSE : BA101 ENGINEERING MATHEMATICS 1
3.1.1
Define sine, cosine, tangent, secant, cosecant and cotangent.
3.1.2
Use quadrant to determine the value of trigonometric functions (positive and negative angles)
3.1.3
State the values of the trigonometric ratios of the o o o special angles. (30 , 45 and 60 )
3.1.4 3.1.5 3.2
Lecture Question & Answer Practical, Group discussion
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Find the values of the trigonometric functions involving special angles.
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Use calculator to determine the value of trigonometric functions (including radian).
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Know trigonometric equations and identities.
3.2.1
State trigonometric basic identities
3.2.2
State the formula of compound-angle and doubleangle
3.2.3
Solve simple trigonometric equations using the appropriate formula involving: a. three trigonometric basic identities
√ Lecture Question & Answer Practical, Students producing mind maps in class,
√ √
√ √ √
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b. formula of compound-angle
√
c. formula of double-angle
√
Note: *Lecturers may use other teaching & learning strategies in order to achieve the learning outcomes. Generic Student Attributes (GSA) GSA 1 Communications Skills GSA 2 Critical Thinking and Problem Solving Skills GSA 3 Teamwork Skills GSA 4 Moral & Professional Ethics GSA 5 Leadership Skills GSA 6 Information Management Skills and Continuous Learning GSA 7 Entrepreneurship Skills
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GSA 5
LD 8 GSA 7
LD 7 GSA 6
LD 6 GSA 2
LD 5 GSA 1
LD 4 GSA 3
LD 3 GSA 4
LD 2
LD 1
CLO 6
CLO 5
GSA & LD CLO 4
CLO3
Specific Outcome
CLO2
No
CLO 1
CLO *Recommended Teaching & Learning Strategy
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MATRIX OF SPECIFIC OUTCOMES Vs CLO, GSA AND LEARNING DOMAINS COURSE : BA101 ENGINEERING MATHEMATICS 1
3.3
State the sine and cosine rules.
3.3.2
Calculate the area of a triangle using the formula ½ ab sin C.
3.3.3
Solve simple trigonometric problems using sine and cosine rules.
4.1 4.1.1 4.1.2 4.1.3 4.1.4 4.2 4.2.1 4.2.2
GEOMETRY AND MEASUREMENT Understand properties of angles associated with transversal and parallel lines. Define right angle, acute angle, obtuse angle, adjacent angle, complementary angle and supplementary angle. Identify transversals, corresponding angles, alternate angles and interior angles.
Lecture Question & Answer Practical, Buzz group (short discussion in two)
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Lecture Question & Answer Practical, Writing reflections on learning (3-4 minutes)
Find the values of corresponding angles, alternate angles and interior angles associated with parallel lines. Solve problems involving properties of angles associated with transversals. Understand the properties of circles. State the properties of an angle and chord in a circle. State the properties of tangent on a circle.
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Lecture Question & Answer
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Note: *Lecturers may use other teaching & learning strategies in order to achieve the learning outcomes. Generic Student Attributes (GSA) GSA 1 Communications Skills GSA 2 Critical Thinking and Problem Solving Skills GSA 3 Teamwork Skills GSA 4 Moral & Professional Ethics GSA 5 Leadership Skills GSA 6 Information Management Skills and Continuous Learning GSA 7 Entrepreneurship Skills
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GSA 5
LD 8 GSA 7
LD 7 GSA 6
LD 6 GSA 2
LD 5 GSA 1
LD 4 GSA 3
LD 3 GSA 4
LD 2
LD 1
CLO 6
CLO 5
CLO 4
GSA & LD
Understand sine and cosine rules.
3.3.1
4.0
CLO3
Specific Outcome
CLO2
No
CLO 1
CLO *Recommended Teaching & Learning Strategy
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MATRIX OF SPECIFIC OUTCOMES Vs CLO, GSA AND LEARNING DOMAINS COURSE : BA101 ENGINEERING MATHEMATICS 1
4.2.3 4.3 4.3.1 4.3.2 4.3.3 4.3.4 4.4 4.4.1
Identify the hypotenuse of right-angled triangles.
Know the arc length, area of a sector and segment of a circle. Convert an angle from degree to radian and viceversa.
4.4.3
Compute the area of a sector.
4.4.4
Compute the area of a segment.
4.5.2
Lecture Question & Answer Practical, Student class presentations
Find the length of the missing side of a right-angled triangle using the Pythagoras’ Theorem. Find the length of side of geometric shapes using Pythagoras’ Theorem. Solve problems using the Pythagoras’ Theorem.
Calculate the arc length of a circle.
4.5.1
√
Understand the perimeter, area and volume for specific shapes. State the formula of the perimeter and area for rectangle, parallelogram, triangle and trapezium. Compute the perimeter and area for rectangle, parallelogram, triangle and trapezium.
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Lecture Question & Answer Practical, Rounds (giving turns to individual students to talk)
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Lecture Question & Answer Practical, Students producing mind maps
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Note: *Lecturers may use other teaching & learning strategies in order to achieve the learning outcomes. Generic Student Attributes (GSA) GSA 1 Communications Skills GSA 2 Critical Thinking and Problem Solving Skills GSA 3 Teamwork Skills GSA 4 Moral & Professional Ethics GSA 5 Leadership Skills GSA 6 Information Management Skills and Continuous Learning GSA 7 Entrepreneurship Skills
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GSA 5
LD 8 GSA 7
LD 7 GSA 6
LD 6 GSA 2
LD 5 GSA 1
LD 4 GSA 3
LD 3 GSA 4
LD 2
LD 1
CLO 6
√
Apply the Pythagoras’ Theorem.
4.4.2
4.5
CLO 5
Practical, Buzz group (short discussion in two)
GSA & LD CLO 4
Solve problems on the angles of cyclic quadrilaterals.
CLO3
Specific Outcome
CLO2
No
CLO 1
CLO *Recommended Teaching & Learning Strategy
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BA101 Engineering Mathematics 1
MATRIX OF SPECIFIC OUTCOMES Vs CLO, GSA AND LEARNING DOMAINS COURSE : BA101 ENGINEERING MATHEMATICS 1
4.5.3 4.5.4 4.6 4.6.1 4.6.2 4.6.3
State the formula of the surface area and volume for sphere, hemisphere, cylinder, cube, cuboid, prism, pyramid and circular cone. Compute the surface area and volume for sphere, hemisphere, cylinder, cube, cuboid, prism, pyramid and circular cone. Understand the concepts of similarity. Identify if given shapes are similar. Calculate the length of unknown side of two similar shapes. Calculate the area and volume for any similar shapes.
5.0
COORDINATE GEOMETRY AND GRAPH
5.1
Know the linear graphs.
5.1.1
Sketch a linear graph when given the gradient and point of interception.
5.1.2
Construct table of values for given linear functions
5.1.3
Draw a linear graph.
5.1.4 5.1.5 5.2 5.2.1
Find the midpoint, distance and gradient between two points. Solve simultaneous linear equations using linear graphs. Know the quadratic graphs. Construct tables of values for given quadratic
in class
√
Lecture Question & Answer Practical, Student class presentations
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Note: *Lecturers may use other teaching & learning strategies in order to achieve the learning outcomes. Generic Student Attributes (GSA) GSA 1 Communications Skills GSA 2 Critical Thinking and Problem Solving Skills GSA 3 Teamwork Skills GSA 4 Moral & Professional Ethics GSA 5 Leadership Skills GSA 6 Information Management Skills and Continuous Learning GSA 7 Entrepreneurship Skills
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GSA 5
LD 8 GSA 7
LD 7 GSA 6
LD 6 GSA 2
LD 5 GSA 1
LD 4 GSA 3
√
√ Lecture Question & Answer
LD 3 GSA 4
LD 2
√
√ Lecture Question & Answer Practical, Peer assisted of other students
LD 1
CLO 6
CLO 5
GSA & LD CLO 4
CLO3
Specific Outcome
CLO2
No
CLO 1
CLO *Recommended Teaching & Learning Strategy
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BA101 Engineering Mathematics 1
MATRIX OF SPECIFIC OUTCOMES Vs CLO, GSA AND LEARNING DOMAINS COURSE : BA101 ENGINEERING MATHEMATICS 1
functions. 5.2.2 5.2.3 5.2.4 5.3
Draw graphs of quadratic functions. Solve problems involving linear and quadratic equations using graph. Solve problems involving two quadratic equations using graph.
Sketch graphs of cubic functions.
5.3.2
Sketch graphs of reciprocal functions. (y = a/x)
√
√
√
√
√ √
√
√
Note: *Lecturers may use other teaching & learning strategies in order to achieve the learning outcomes. Generic Student Attributes (GSA) GSA 1 Communications Skills GSA 2 Critical Thinking and Problem Solving Skills GSA 3 Teamwork Skills GSA 4 Moral & Professional Ethics GSA 5 Leadership Skills GSA 6 Information Management Skills and Continuous Learning GSA 7 Entrepreneurship Skills
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GSA 5
LD 8 GSA 7
LD 7 GSA 6
LD 6 GSA 2
LD 5 GSA 1
LD 4 GSA 3
√
√ Lecture Question & Answer Practical , Student class presentations
LD 3 GSA 4
LD 2
LD 1
CLO 6
CLO 5
CLO 4
GSA & LD
Practical, problem solving in group, Student class presentations, creating solutions
Know the basic form of non-linear graphs.
5.3.1
CLO3
Specific Outcome
CLO2
No
CLO 1
CLO *Recommended Teaching & Learning Strategy
BA101 Engineering Mathematics 1
POLYTECHNICS MINISTRY OF HIGHER EDUCATION MALAYSIA DEPARTMENT OF MATHEMATICS, SCIENCE AND COMPUTER
COURSE
:
BA101 ENGINEERING MATHEMATICS 1
INSTRUCTIONAL DURATION
:
15 WEEKS
CREDIT ( S )
:
2
PREREQUISITE(S)
:
NONE
SYNOPSIS ENGINEERING MATHEMATICS 1 exposes students to algebra through theory, practical and tutorial which focuses on standard form, index and logarithm, geometry and measurement as well as coordinate geometry and graph. This course also explains the basic concept of trigonometry and its functions in solving problems.
LEARNING OUTCOMES Upon completion of this course, students should be able to: 1.
show all the relevant steps in solving simultaneous linear equations with two variables and quadratic equations by using various methods based on basic algebraic concept.
2.
perform algebraic operations in standard form and simplify indices and logarithmic expressions by using index and logarithm rules in solving related problems.
3.
apply the fundamental of trigonometric functions, sine and cosine rules, basic trigonometric identities, formula of compound-angle and double-angle in solving simple trigonometric equations.
4.
determine angles, arc length, area of a sector and segment by applying the Pythagoras’ Theorem, the properties of angles with transversal and parallel lines and properties of circles
5.
calculate the length, perimeter, area and volume of specific and similar shapes by using appropriate formulae and concept of similarity.
6.
demonstrate sketching and drawing of linear, quadratic and non-linear graphs accurately to solve simultaneous equations based on intersection points between two lines.
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BA101 Engineering Mathematics 1
SUMMARY
(30 LECTURE : 15 PRACTICAL)
RTA (06:03)
1.0
BASIC ALGEBRA This topic introduces basic algebraic concept and its use in solving linear equations, simultaneous linear equations with two variables and quadratic equations.
2.0
STANDARD FORM, INDEX AND LOGARITHM This topic introduces the standard form, index and logarithm rules and their applications to simplify expression and problem solving. The use of calculator is emphasised.
(06:03)
3.0
TRIGONOMETRY This topic explains the fundamental concept of trigonometric functions particularly the six trigonometric ratios of special angles and simple trigonometric basic identities. The topic also explain about sine and cosine rules. Skills using trigonometric identities, sine and cosine rules, formula of compound-angle and doubleangle to solve simple trigonometric equations will be discussed.
(06:03)
4.0
GEOMETRY AND MEASUREMENT This topic explains the properties of angles with transversal and parallel lines and the properties of angles in a circle. The characteristics of a tangent to a circle are discussed to solve angular problems. The Pythagoras’ Theorem is applied to solve problems related to angle and length. The topic also explains methods of calculating arc length, surface area and volume. The concepts of similarity and how to calculate the length, area and volume for any similar shapes also will be discussed.
(08:04)
5.0
COORDINATE GEOMETRY AND GRAPH This topic includes solving coordinate geometry problems using graphs and formulas. Emphasis will be given to the techniques of drawing straight lines and quadratic graph to ensure accuracy in solving linear and quadratic equations. The topic also emphasis how to sketch cubic and reciprocal graph of functions.
(04:02)
RTA : Recommended Time Allocation
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BA101 Engineering Mathematics 1
SYLLABUS
1.0
2.0
BASIC ALGEBRA 1.1
Understand basic algebra 1.1.1 Simplify algebraic fractions. 1.1.2 Solve algebraic fractions using: a. addition b. subtraction c. multiplication d. division 1.1.3 Perform conversion of formulas.
1.2
Understand quadratic equations 1.2.1 Solve quadratic equations by using factorization. 1.2.2 Solve quadratic equations by using quadratic formula. 1.2.3 Solve quadratic equations by using completing squares.
1.3
Understand simultaneous linear equations with two variables 1.3.1 Solve simultaneous linear equations by using the elimination method. 1.3.2 Solve simultaneous linear equations by using the substitution method.
STANDARD FORM, INDEX AND LOGARITHM 2.1
Know standard form 2.1.1 Convert real number to standard form and vice-versa. 2.1.2 Perform algebraic operations in standard form.
2.2
Know the rules of indices. 2.2.1 State the index rules. 2.2.2 Apply the index rules to find the product of index number. 2.2.3 Apply the index rules to find the quotient of index number. 2.2.4 Simplify expressions related to indices.
2.3
Know the rules of logarithm. 2.3.1 State the logarithm rules. 2.3.2 Express the index number in logarithm form. 2.3.3 Find the value of a logarithm. 2.3.4 Apply the logarithm rules to find the value of logarithms. 2.3.5 Change the base of logarithms. 2.3.6 Simplify logarithm expressions. 2.3.7 Solve equations that contain indices and logarithm expressions.
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3.0
4.0
BA101 Engineering Mathematics 1
TRIGONOMETRY 3.1
Understand the fundamental of trigonometric functions. 3.1.1 Define sine, cosine, tangent, secant, cosecant and cotangent. 3.1.2 Use quadrant to determine the value of trigonometric functions (positive and negative angles). 3.1.3 State the values of the trigonometric ratios of the special angles (30o, 45o and 60o). 3.1.4 Find the values of the trigonometric functions involving special angles. 3.1.5 Use calculator to determine the value of trigonometric functions (including radian).
3.2
Know trigonometric equations and identities. 3.2.1 State trigonometric basic identities. 3.2.2 State the formula of compound-angle and double-angle. 3.2.3 Solve simple trigonometric equations using the appropriate formula involving: a. three trigonometric basic identities b. formula of compound-angle c. formula of double-angle
3.3
Understand sine and cosine rules. 3.3.1 State the sine and cosine rules. 3.3.2 Calculate the area of a triangle using the formula ½ ab sin C. 3.3.3 Solve simple trigonometric problems using sine and cosine rules.
GEOMETRY AND MEASUREMENT 4.1
Understand properties of angles associated with transversal and parallel lines. 4.1.1 Define right angle, acute angle, obtuse angle, adjacent angle, complementary angle and supplementary angle. 4.1.2 Identify transversals, corresponding angles, alternate angles and interior angles. 4.1.3 Find the values of corresponding angles, alternate angles and interior angles associated with parallel lines. 4.1.4 Solve problems involving properties of angles associated with transversals.
4.2
Understand the properties of circles. 4.2.1 State the properties of an angle and chord in a circle. 4.2.2 State the properties of tangent on a circle. 4.2.3 Solve problems on the angles of cyclic quadrilaterals.
4.3
Apply the Pythagoras’ Theorem. 4.3.1 Identify the hypotenuse of right-angled triangles. 4.3.2 Find the length of the missing side of a right-angled triangle using the Pythagoras’ Theorem. 4.3.3 Find the length of side of geometric shapes using Pythagoras’ Theorem.
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5.0
BA101 Engineering Mathematics 1
Solve problems using the Pythagoras’ Theorem.
4.4
Know the arc length, area of a sector and segment of a circle. 4.4.1 Convert an angle from degree to radian and vice-versa. 4.4.2 Calculate the arc length of a circle. 4.4.3 Compute the area of a sector. 4.4.4 Compute the area of a segment.
4.5
Understand the perimeter, area and volume for specific shapes. 4.5.1 State the formula of the perimeter and area for rectangle, parallelogram, triangle and trapezium. 4.5.2 Compute the perimeter and area for rectangle, parallelogram, triangle and trapezium. 4.5.3 State the formula of the surface area and volume for sphere, hemisphere, cylinder, cube, cuboid, prism, pyramid and circular cone. 4.5.4 Compute the surface area and volume for sphere, hemisphere, cylinder, cube, cuboid, prism, pyramid and circular cone.
4.6
Understand the concepts of similarity. 4.6.1 Identify if given shapes are similar. 4.6.2 Calculate the length of unknown side of two similar shapes. 4.6.3 Calculate the area and volume for any similar shapes.
COORDINATE GEOMETRY AND GRAPH 5.1
Know the linear graphs. 5.1.1 Sketch a linear graph when given the gradient and point of interception. 5.1.2 Construct table of values for given linear functions. 5.1.3 Draw a linear graph. 5.1.4 Find the midpoint, distance and gradient between two points. 5.1.5 Solve simultaneous linear equations using linear graphs.
5.2
Know the quadratic graphs. 5.2.1 Construct tables of values for given quadratic functions. 5.2.2 Draw graphs of quadratic functions. 5.2.3 Solve problems involving linear and quadratic equations using graph. 5.2.4 Solve problems involving two quadratic equations using graph.
5.3
Know the basic form of non-linear graphs. 5.3.1 Sketch graphs of cubic functions. 5.3.2 Sketch graphs of reciprocal functions. (y = a/x)
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BA101 Engineering Mathematics 1
ASSESSMENT
TYPES OF ASSESSMENT
The course assessment is carried out in two sections: i. ii.
Continuous Assessment Final Examination
-
(CA) (FE)
The percentage ratio of FE to CA should follow the guideline stated in the Arahan-Arahan Peperiksaan dan Kaedah Penilaian which is approved by the Lembaga Peperiksaan dan Penganugerahan Sijil/Diploma Politeknik.
CONTINUOUS ASSESSMENT (CA): [ The total score of the CA components would be converted to the determined CA percentage ] Continuous assessment is carried out throughout the semester and comprises the followings: a. Quiz (minimum 3) b. Theory Test (minimum 2) c. Lab work (minimum 2) d. Other Assessment Task i. End - of- Chapter (minimum 2) ii. e- Quiz (minimum 2)
20% 30% 20% 20% 10%
[ Assessment Task above (a-c) to be executed during Lecture/Practical/ Tutorial hour)
FINAL EXAMINATION (FE):
Final examination is carried out at the end of the semester.
Note: 1. Refer to Assessment Specification Table for the details. 2.The percentage of Continuous Assessment may vary depending in courses.
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BA101 Engineering Mathematics 1
ASSESSMENT SPECIFICATIONS TABLE (AST)
COURSE : BA101 ENGINEERING MATHEMATICS 1 COURSE LEARNING OUTCOME (CLO)
1. Show all the relevant steps in solving simultaneous linear equations with two variables and quadratic equations by using various methods based on basic algebraic concept 2. Perform algebraic operations in standard form and simplify indices and logarithmic expressions by using index and logarithm rules in solving related problems 3. Apply the fundamental of triginometric functions, sine and cosine rules, basic trigonometric identities, formula of compound-angle and double-angle in solving simple trigonometric equations 4. Determine angles, arc length, area of a sector and segment by applying the Pythagoras' Theorem, the properties of angles with transversal and parallel lines and properties of circles 5. Calculate the length, perimeter, area and volume of specific and similar shapes by using appropriate formulae and concept of similarity 6. Demonstrate skecthing and drawing of linear, quadratic and non-linear graphs accurately to solve simultaneaous equations based on intersection points between two lines ASSESSMENT TASK CONSTRUCT (CLO)
CONTEXT 1
Quadratic Equations
√ √
Simultaneous Linear Equations With Two Variables
√
Basic Algebra BASIC ALGEBRA
Rules Of Indices Rules Of Logarithm
TRIGONOMETRY
4
5
6
L
M
Theory Test H
L
1
1
1
1
1
2
√ √
1
Pythagoras’ Theorem Arc Length, Area of a Sector and Segment of a Circle
√
Concepts Of Similarity Linear Graphs COORDINATE GEOMETRY AND Quadratic Graphs GRAPH Basic Form Of Non-Linear Graphs
Labwork H
1
1
1
1
2
1
L
M
1
1
End-of-Chapter H
1
1
1
1
1
2
1
2
1
H
1
1
1 1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
M
1
1
1
2
1
1
1
1
1 1
1
1
1 1
1
1
1
1
1 1
√ √ √
L
1
1
√ √
Final Examination H
1
1 1
M
1
1
1
L
2
1
1 1
1
1
5 5
TOTAL
M
1
√ √ √
Perimeter, Area And Volume For Specific Shapes
L
2
1
√
Properties Of Circles
H
1
Trigonometric Equations And Identities
Properties Of Angles Associated With Transversal And Parallel Lines
M
e-Quiz
1
Fundamental Of Trigonometric Functions
Sine And Cosine Rules
GEOMETRY AND MEASUREMENT
3
√ √ √
Standard Form STANDARD FORM, INDEX AND LOGARITHM
2
Quiz
1
1 1
1
2
1
1
1
1
1
1
1
3 3
2 2
10 5
6 3
5 2
6 5
3 3
2 2
6 5
4 3
2 2
10 5
7 3
5 2
1
1
1
18 5
12 3
6 2
LEGEND: Difficulty Level : L : Low M : Medium H : High
5 3 2
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50% of the aspects can be answered correctly by more than 60% of the candidates 30% of the aspects can be answered correctly by more than 40% but less than 60% of the candidates 20% of the aspects can be answered correctly by less than 40% of the candidates
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REFERENCES Backhouse, J.K., Houldsworth, S.P.T. & Cooper, B.E.D. Pure Mathematics (2nd ed.). Bird, J.O. & May, A.J.C. (1997). Technician Mathematics 1 (3rd ed.). Longman. Robert Moyer. (1998). Trigonometry (3rd ed.). McGraw-Hill. Siti Aishah Sheikh Abdullah, Ch’ng Pei Eng, Teoh Sian Hoon, Muniroh Hamat, Noor’ Aina Abdul Razak. (2006). First Engineering Mathematics. (2nd ed.). McGrawHill. Stroud, K.A. (2007). Engineering Mathematics (6th ed.). Palgrave Macmillan. Thorning, D.W.S & Sadler. (1999). Understanding Pure Mathematics, Oxford University Press.
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DISTRIBUTION OF STUDENT LEARNING TIME COURSE CREDIT
: :
BA101 ENGINEERING MATHEMATICS 1 2 COD E
SL T
L
30
I
15
P
15
I
15
Tutorial
T
Other Assessment Task
O
0 5
No.
1
Activities
[
Lecture Lecture hours -
3
4
5 6
hour(s) x
15
week(s)
]
[√]
Assessment Task
(Theory Test/Quiz) 2
2
[√]
Self Learning: Theory Preparation before theory class viz. review/ lesson notes. Preparation after theory class viz. additional references, discussion group, discussion with lecturers. Preparation for theory test. [
Practical -
Lab work Skill/Practical test Field work
[√] [ ] [
-
Survey/research
[
1
hour(s) x [
]
- Studio work - Workshop - Simulation
[
]
]
- Outdoors
[
]
15
week(s)
[
]
(Final Project) Presentation Reflective Journal Case Study
[ [ [
] ] ]
Industrial Visit
[
]
[√] [√] ]
] [
[ ] Critique Oral Presentation [ ]
]
Self Learning: Practical Preparation before practical class/field work/survey viz. review notes, checklist/labsheets and/or tools and equipment. Preparation after practical class/field work/survey viz. additional references, discussion session and report writing. Preparation before studio work presentation/critique. Preparation for practical test.
Capstone Project
[√]
Portfolio
[
Peer Assessment Self Assessment End-of-Chapter
[ ] [ ] [√]
]
[√] [√] [√]
[√]
Essay Question
[
]
Observation Discussion Project e-Quiz
[ [ [
] ] ]
[√] 80
Total L
Lecture
30
P I
Practical
15
Self Learning
30
T O
Tutorial Other Assessment Task
0 5
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SLT (Student Learning Time)
80
Credit = SLT/40
2
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TABLE OF LEARNING DOMAINS COURSE : BA101 ENGINEERING MATHEMATICS
No. 1.0 1.1 1.1.1 1.1.2
Specific Outcome
Cognitive Domain C1
BASIC ALGEBRA Understand Basic Algebra Simplify algebraic fractions. Solve algebraic fractions using: a. addition
C2
C3
√
C4
C5
Psychomotor Domain C6
P1
P2
P3
P4
Affective Domain P5
A1
A2
√
A3
A4
A5
√
√
√
√
b. subtraction c. multiplication 1.1.3 1.2 1.2.1 1.2.2 1.2.3 1.3 1.3.1 1.3.2 2.0 2.1 2.1.1 2.1.2 2.2
d. division Perform conversion of formulas. Understand quadratic equations. Solve quadratic equations by using factorization. Solve quadratic equations by using quadratic formula. Solve quadratic equations by using completing squares. Understand simultaneous linear equations with two variables Solve simultaneous linear equations by using the elimination method. Solve simultaneous linear equations by using the substitution method. STANDARD FORM, INDEX AND LOGARITHM Know standard form Convert real number to standard form and vice-versa. Perform algebraic operations in standard form.
√
√
√
√ √ √
√ √ √
√ √ √
√ √
√ √
√ √
√
√ √
√ √
√
Know the rules of indices.
2.2.1
State the index rules.
2.2.2
Apply the index rules to find the product of index number.
√
√
√
2.2.3
Apply the index rules to find the quotient of index number.
√
√
√
2.2.4
Simplify expressions related to indices.
√
√
2.3
Know the rules of logarithm.
2.3.1
State the logarithm rules.
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√
√
√ √
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No.
BA101 Engineering Mathematics 1
Specific Outcome
C1
Cognitive Domain C2 C3 C4 C5
C6
P1
Psychomotor Domain P2 P3 P4 P5
A1
Affective Domain A2 A3 A4 A5
2.3.2
Express the index number in logarithm form.
2.3.3
Find the value of a logarithm.
2.3.4
Apply the logarithm rules to find the value of logarithms.
√
√
√
2.3.5
Change the base of logarithms.
√
√
√
2.3.6
Simplify logarithm expressions. Solve equations that contain indices and logarithm expressions.
√
√
2.3.7 3.0
TRIGONOMETRY
3.1
Understand the fundamental of trigonometric functions.
3.1.1 3.1.2 3.1.3 3.1.4 3.1.5 3.2
√
√
√
√ √
√
√
√ √
√
Define sine, cosine, tangent, secant, cosecant and cotangent. Use quadrant to determine the value of trigonometric functions (positive and negative angles) State the values of the trigonometric ratios of the special angles. (30o, 45o and 60o)
√
√
√
√
√
√
Find the values of the trigonometric functions involving special angles. Use calculator to determine the value of trigonometric functions (including radian).
√
√
√
√
√
√
√
√
√
Know trigonometric equations and identities.
3.2.1
State trigonometric basic identities
√
√
3.2.2
State the formula of compound-angle and double-angle Solve simple trigonometric equations using the appropriate formula involving: a. three trigonometric basic identities b. formula of compound-angle c. formula of double-angle
√
√
3.2.3
3.3
√
State the sine and cosine rules.
3.3.2
Calculate the area of a triangle using the formula ½ ab sin C.
√
3.3.3
Solve simple trigonometric problems using sine and cosine rules.
√
4.1
√
Understand sine and cosine rules.
3.3.1
4.0
√
√
√ √
√ √
√
GEOMETRY AND MEASUREMENT Understand properties of angles associated with transversal and parallel lines.
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Cognitive Domain No.
Psychomotor Domain
C1
C2
C3
C4
C5
C6
P1
P2
P3
4.1.1
Define right angle, acute angle, obtuse angle, adjacent angle, complementary angle and supplementary angle.
√
4.1.2
Identify transversals, corresponding angles, alternate angles and interior angles.
√
√
√
√
4.1.3 4.1.4 4.2
Find the values of corresponding angles, alternate angles and interior angles associated with parallel lines. Solve problems involving properties of angles associated with transversals.
√
√
P4
P5
A1
A2
State the properties of an angle and chord in a circle.
√
4.2.2
State the properties of tangent on a circle.
√
4.2.3
Solve problems on the angles of cyclic quadrilaterals.
A5
√ √
√
√ √ √
√
√
√
Apply the Pythagoras’ Theorem. Identify the hypotenuse of right-angled triangles.
√
√
4.3.2
Find the length of the missing side of a right-angled triangle using the Pythagoras’ Theorem.
√
√
√
4.3.3
Find the length of side of geometric shapes using Pythagoras’ Theorem.
√
√
√
4.3.4
Solve problems using the Pythagoras’ Theorem.
√
√
√
√
Know the arc length, area of a sector and segment of a circle.
4.4.1
Convert an angle from degree to radian and vice-versa.
4.4.2
Calculate the arc length of a circle.
√
√
√
4.4.3
Compute the area of a sector.
√
√
√
4.4.4
Compute the area of a segment.
√
√
√
4.5
A4
√
4.3.1
4.4
A3
Understand the properties of circles.
4.2.1
4.3
Affective Domain
Specific Outcome
√
√
√
Understand the perimeter, area and volume for specific shapes.
4.5.1
State the formula of the perimeter and area for rectangle, parallelogram, triangle and trapezium.
4.5.2
Compute the perimeter and area for rectangle, parallelogram, triangle and trapezium.
4.5.3
State the formula of the surface area and volume for sphere, hemisphere, cylinder, cube, cuboid, prism, pyramid and circular cone.
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√ √
√
√
√ √
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No.
Specific Outcome
4.5.4
Compute the surface area and volume for sphere, hemisphere, cylinder, cube, cuboid, prism, pyramid and circular cone.
4.6 4.6.1
C1
C2
Cognitive Domain C3 C4 C5
P1
Psychomotor Domain P2 P3 P4 P5
Affective Domain A2 A3 A4
√
√
Identify if given shapes are similar.
√
√
√
√
A5
√
√
√
4.6.2
Calculate the length of unknown side of two similar shapes.
4.6.3
Calculate the area and volume for any similar shapes.
√
5.0
COORDINATE GEOMETRY AND GRAPH
5.1
Know the linear graphs.
5.1.1
Sketch a linear graph when given the gradient and point of interception.
√
5.1.2
Construct table of values for given linear functions
√
5.1.3
Draw a linear graph.
√
5.1.4
Find the midpoint, distance and gradient between two points.
5.1.5
Solve simultaneous linear equations using linear graphs.
√
√
√
√
√ √
√
√
√ √
√
√
√
Know the quadratic graphs.
5.2.1
Construct tables of values for given quadratic functions.
√
5.2.2 5.2.3
Draw graphs of quadratic functions. Solve problems involving linear and quadratic equations using graph.
√ √
√ √
5.2.4
Solve problems involving two quadratic equations using graph.
√
√
5.3
A1
Understand the concepts of similarity. √
5.2
C6
√
√ √ √ √
Know the basic form of non-linear graphs.
5.3.1
Sketch graphs of cubic functions
√
√
√
5.3.2
Sketch graphs of reciprocal functions. (y=a/x)
√
√
√
TOTAL
21
4
40
0
0
0
21
3
30
4
0
18
26
3
1
Legend Cognitive Domain C1 Knowledge C2 Comprehensive C3 Application C4 Analysis C5 Synthesis C6 Evaluation
Psychomotor Domain P1 Imitate P2 Manipulate P3 Precision P4 Articulation P5 Naturalization
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A1 A2 A3 A4 A5
Affective Domain Receiving Phenomena Responding to Phenomena Valuing Organizing Values Internalizing Values
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MATRIX OF SPECIFIC OUTCOMES Vs CLO, GSA AND LEARNING DOMAINS COURSE : BA101 ENGINEERING MATHEMATICS 1 COURSE LEARNING OUTCOME (CLO) Upon completion of this course, students should be able to:
1.0
BASIC ALGEBRA
1.1
Understand Basic Algebra
1.1.1
Simplify algebraic fractions.
1.1.2
Solve algebraic fractions using:
Lecture Question & Answer Practical, Peer assisted of Other Students
√
√
√
√
LD 3 GSA 4
LD 2
LD 1
CLO 6
CLO 5
GSA & LD CLO 4
CLO3
Specific Outcome
CLO2
No
CLO 1
CLO *Recommended Teaching & Learning Strategy
Note: *Lecturers may use other teaching & learning strategies in order to achieve the learning outcomes. Generic Student Attributes (GSA) GSA 1 Communications Skills GSA 2 Critical Thinking and Problem Solving Skills GSA 3 Teamwork Skills GSA 4 Moral & Professional Ethics GSA 5 Leadership Skills GSA 6 Information Management Skills and Continuous Learning GSA 7 Entrepreneurship Skills
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Learning Domain (LD) LD 1 Knowledge LD 2 Technical Skills LD 3 Professionalism & Ethics LD 4 Social Skills LD 5 Communication Skills LD 6 Critical Thinking LD 7 Life Long Learning LD 8 Entrepreneurial Skills
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GSA 5
6.
LD 8 GSA 7
5.
LD 7 GSA 6
4.
LD 6 GSA 2
3.
LD 5 GSA 1
2.
show all the relevant steps in solving simultaneous linear equations with two variables and quadratic equations by using various methods based on basic algebraic concept. perform algebraic operations in standard form and simplify indices and logarithmic expressions by using index and logarithm rules in solving related problems. apply the fundamental of trigonometric functions, sine and cosine rules, basic trigonometric identities, formula of compoundangle and double-angle in solving simple trigonometric equations. determine angles, arc length, area of a sector and segment by applying the Pythagoras’ Theorem, the properties of angles with transversal and parallel lines and properties of circles calculate the length, perimeter, area and volume of specific and similar shapes by using appropriate formulae and concept of similarity. demonstrate sketching and drawing of linear, quadratic and non-linear graphs accurately to solve simultaneous equations based on intersection points between two lines.
LD 4 GSA 3
1.
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BA101 Engineering Mathematics 1
MATRIX OF SPECIFIC OUTCOMES Vs CLO, GSA AND LEARNING DOMAINS COURSE : BA101 ENGINEERING MATHEMATICS 1
a. addition
√
b. subtraction
√
c. multiplication
√
d. division
√
1.1.3 1.2
Perform conversion of formulas. Understand quadratic equations.
√
√
1.2.1
Solve quadratic equations by using factorization.
√
√
√
√
√
√
1.2.2 1.2.3 1.3 1.3.1 1.3.2
Solve quadratic equations by using quadratic formula. Solve quadratic equations by using completing squares. Understand simultaneous linear equations with two variables Solve simultaneous linear equations by using the elimination method. Solve simultaneous linear equations by using the substitution method.
2.0
STANDARD FORM, INDEX AND LOGARITHM
2.1
Know standard form
2.1.1
Convert real number to standard form and viceversa.
2.1.2
Perform algebraic operations in standard form.
Lecture Question & Answer Practical, Problem Solving in Group, Computer Assisted Learning
√
√
√
√
Lecture Question & Answer Practical, peer assisted of other students
√ √
√ √
Note: *Lecturers may use other teaching & learning strategies in order to achieve the learning outcomes. Generic Student Attributes (GSA) GSA 1 Communications Skills GSA 2 Critical Thinking and Problem Solving Skills GSA 3 Teamwork Skills GSA 4 Moral & Professional Ethics GSA 5 Leadership Skills GSA 6 Information Management Skills and Continuous Learning GSA 7 Entrepreneurship Skills
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Learning Domain (LD) LD 1 Knowledge LD 2 Technical Skills LD 3 Professionalism & Ethics LD 4 Social Skills LD 5 Communication Skills LD 6 Critical Thinking LD 7 Life Long Learning LD 8 Entrepreneurial Skills
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GSA 5
LD 8 GSA 7
LD 7 GSA 6
LD 6 GSA 2
LD 5 GSA 1
LD 4 GSA 3
LD 3 GSA 4
LD 2
LD 1
CLO 6
CLO 5
GSA & LD CLO 4
CLO3
Specific Outcome
CLO2
No
CLO 1
CLO *Recommended Teaching & Learning Strategy
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MATRIX OF SPECIFIC OUTCOMES Vs CLO, GSA AND LEARNING DOMAINS COURSE : BA101 ENGINEERING MATHEMATICS 1
2.2 2.2.1 2.2.2 2.2.3 2.2.4
State the index rules. Apply the index rules to find the product of index number. Apply the index rules to find the quotient of index number.
2.3.1
State the logarithm rules.
2.3.2
Express the index number in logarithm form.
2.3.3
Find the value of a logarithm. Apply the logarithm rules to find the value of logarithms. Change the base of logarithms.
2.3.6 2.3.7
Lecture Question & Answer Practical, Writing reflections on learning (3-4 minutes)
TRIGONOMETRY
3.1
Understand the fundamental of trigonometric functions.
√ √
√
√
√
√
√
√
√
√
√
√
√
√
√
√
Note: *Lecturers may use other teaching & learning strategies in order to achieve the learning outcomes. Generic Student Attributes (GSA) GSA 1 Communications Skills GSA 2 Critical Thinking and Problem Solving Skills GSA 3 Teamwork Skills GSA 4 Moral & Professional Ethics GSA 5 Leadership Skills GSA 6 Information Management Skills and Continuous Learning GSA 7 Entrepreneurship Skills
Version: 080510_1.2_Effective:1June2011
Learning Domain (LD) LD 1 Knowledge LD 2 Technical Skills LD 3 Professionalism & Ethics LD 4 Social Skills LD 5 Communication Skills LD 6 Critical Thinking LD 7 Life Long Learning LD 8 Entrepreneurial Skills
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GSA 5
LD 8 GSA 7
LD 7 GSA 6
LD 6 GSA 2
LD 5 GSA 1
LD 4 GSA 3
LD 3 GSA 4
LD 2
CLO 6
CLO 5
CLO 4
LD 1 √
√
√ Lecture Question & Answer Practical, Problem solving in group, Rounds (giving turn to students to talk)
Simplify logarithm expressions. Solve equations that contain indices and logarithm expressions.
3.0
√
√
Simplify expressions related to indices. Know the rules of logarithm.
2.3.5
GSA & LD
Know the rules of indices.
2.3
2.3.4
CLO3
Specific Outcome
CLO2
No
CLO 1
CLO *Recommended Teaching & Learning Strategy
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MATRIX OF SPECIFIC OUTCOMES Vs CLO, GSA AND LEARNING DOMAINS COURSE : BA101 ENGINEERING MATHEMATICS 1
3.1.1
Define sine, cosine, tangent, secant, cosecant and cotangent.
3.1.2
Use quadrant to determine the value of trigonometric functions (positive and negative angles)
3.1.3
State the values of the trigonometric ratios of the o o o special angles. (30 , 45 and 60 )
3.1.4 3.1.5 3.2
Lecture Question & Answer Practical, Group discussion
√
√
√
√
√
√
Find the values of the trigonometric functions involving special angles.
√
√
Use calculator to determine the value of trigonometric functions (including radian).
√
√
Know trigonometric equations and identities.
3.2.1
State trigonometric basic identities
3.2.2
State the formula of compound-angle and doubleangle
3.2.3
Solve simple trigonometric equations using the appropriate formula involving: a. three trigonometric basic identities
√ Lecture Question & Answer Practical, Students producing mind maps in class,
√ √
√ √ √
√
b. formula of compound-angle
√
c. formula of double-angle
√
Note: *Lecturers may use other teaching & learning strategies in order to achieve the learning outcomes. Generic Student Attributes (GSA) GSA 1 Communications Skills GSA 2 Critical Thinking and Problem Solving Skills GSA 3 Teamwork Skills GSA 4 Moral & Professional Ethics GSA 5 Leadership Skills GSA 6 Information Management Skills and Continuous Learning GSA 7 Entrepreneurship Skills
Version: 080510_1.2_Effective:1June2011
Learning Domain (LD) LD 1 Knowledge LD 2 Technical Skills LD 3 Professionalism & Ethics LD 4 Social Skills LD 5 Communication Skills LD 6 Critical Thinking LD 7 Life Long Learning LD 8 Entrepreneurial Skills
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GSA 5
LD 8 GSA 7
LD 7 GSA 6
LD 6 GSA 2
LD 5 GSA 1
LD 4 GSA 3
LD 3 GSA 4
LD 2
LD 1
CLO 6
CLO 5
GSA & LD CLO 4
CLO3
Specific Outcome
CLO2
No
CLO 1
CLO *Recommended Teaching & Learning Strategy
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BA101 Engineering Mathematics 1
MATRIX OF SPECIFIC OUTCOMES Vs CLO, GSA AND LEARNING DOMAINS COURSE : BA101 ENGINEERING MATHEMATICS 1
3.3
State the sine and cosine rules.
3.3.2
Calculate the area of a triangle using the formula ½ ab sin C.
3.3.3
Solve simple trigonometric problems using sine and cosine rules.
4.1 4.1.1 4.1.2 4.1.3 4.1.4 4.2 4.2.1 4.2.2
GEOMETRY AND MEASUREMENT Understand properties of angles associated with transversal and parallel lines. Define right angle, acute angle, obtuse angle, adjacent angle, complementary angle and supplementary angle. Identify transversals, corresponding angles, alternate angles and interior angles.
Lecture Question & Answer Practical, Buzz group (short discussion in two)
√
√
√
√
√
Lecture Question & Answer Practical, Writing reflections on learning (3-4 minutes)
Find the values of corresponding angles, alternate angles and interior angles associated with parallel lines. Solve problems involving properties of angles associated with transversals. Understand the properties of circles. State the properties of an angle and chord in a circle. State the properties of tangent on a circle.
√
√
√
√
√ √
√ √
Lecture Question & Answer
√
√
√
√
√
Note: *Lecturers may use other teaching & learning strategies in order to achieve the learning outcomes. Generic Student Attributes (GSA) GSA 1 Communications Skills GSA 2 Critical Thinking and Problem Solving Skills GSA 3 Teamwork Skills GSA 4 Moral & Professional Ethics GSA 5 Leadership Skills GSA 6 Information Management Skills and Continuous Learning GSA 7 Entrepreneurship Skills
Version: 080510_1.2_Effective:1June2011
Learning Domain (LD) LD 1 Knowledge LD 2 Technical Skills LD 3 Professionalism & Ethics LD 4 Social Skills LD 5 Communication Skills LD 6 Critical Thinking LD 7 Life Long Learning LD 8 Entrepreneurial Skills
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GSA 5
LD 8 GSA 7
LD 7 GSA 6
LD 6 GSA 2
LD 5 GSA 1
LD 4 GSA 3
LD 3 GSA 4
LD 2
LD 1
CLO 6
CLO 5
CLO 4
GSA & LD
Understand sine and cosine rules.
3.3.1
4.0
CLO3
Specific Outcome
CLO2
No
CLO 1
CLO *Recommended Teaching & Learning Strategy
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MATRIX OF SPECIFIC OUTCOMES Vs CLO, GSA AND LEARNING DOMAINS COURSE : BA101 ENGINEERING MATHEMATICS 1
4.2.3 4.3 4.3.1 4.3.2 4.3.3 4.3.4 4.4 4.4.1
Identify the hypotenuse of right-angled triangles.
Know the arc length, area of a sector and segment of a circle. Convert an angle from degree to radian and viceversa.
4.4.3
Compute the area of a sector.
4.4.4
Compute the area of a segment.
4.5.2
Lecture Question & Answer Practical, Student class presentations
Find the length of the missing side of a right-angled triangle using the Pythagoras’ Theorem. Find the length of side of geometric shapes using Pythagoras’ Theorem. Solve problems using the Pythagoras’ Theorem.
Calculate the arc length of a circle.
4.5.1
√
Understand the perimeter, area and volume for specific shapes. State the formula of the perimeter and area for rectangle, parallelogram, triangle and trapezium. Compute the perimeter and area for rectangle, parallelogram, triangle and trapezium.
√
√
√
√
√
√
√
Lecture Question & Answer Practical, Rounds (giving turns to individual students to talk)
√
√
√
√
√
√
√
√
√
Lecture Question & Answer Practical, Students producing mind maps
√ √
√ √
Note: *Lecturers may use other teaching & learning strategies in order to achieve the learning outcomes. Generic Student Attributes (GSA) GSA 1 Communications Skills GSA 2 Critical Thinking and Problem Solving Skills GSA 3 Teamwork Skills GSA 4 Moral & Professional Ethics GSA 5 Leadership Skills GSA 6 Information Management Skills and Continuous Learning GSA 7 Entrepreneurship Skills
Version: 080510_1.2_Effective:1June2011
Learning Domain (LD) LD 1 Knowledge LD 2 Technical Skills LD 3 Professionalism & Ethics LD 4 Social Skills LD 5 Communication Skills LD 6 Critical Thinking LD 7 Life Long Learning LD 8 Entrepreneurial Skills
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GSA 5
LD 8 GSA 7
LD 7 GSA 6
LD 6 GSA 2
LD 5 GSA 1
LD 4 GSA 3
LD 3 GSA 4
LD 2
LD 1
CLO 6
√
Apply the Pythagoras’ Theorem.
4.4.2
4.5
CLO 5
Practical, Buzz group (short discussion in two)
GSA & LD CLO 4
Solve problems on the angles of cyclic quadrilaterals.
CLO3
Specific Outcome
CLO2
No
CLO 1
CLO *Recommended Teaching & Learning Strategy
RESTRICTED
BA101 Engineering Mathematics 1
MATRIX OF SPECIFIC OUTCOMES Vs CLO, GSA AND LEARNING DOMAINS COURSE : BA101 ENGINEERING MATHEMATICS 1
4.5.3 4.5.4 4.6 4.6.1 4.6.2 4.6.3
State the formula of the surface area and volume for sphere, hemisphere, cylinder, cube, cuboid, prism, pyramid and circular cone. Compute the surface area and volume for sphere, hemisphere, cylinder, cube, cuboid, prism, pyramid and circular cone. Understand the concepts of similarity. Identify if given shapes are similar. Calculate the length of unknown side of two similar shapes. Calculate the area and volume for any similar shapes.
5.0
COORDINATE GEOMETRY AND GRAPH
5.1
Know the linear graphs.
5.1.1
Sketch a linear graph when given the gradient and point of interception.
5.1.2
Construct table of values for given linear functions
5.1.3
Draw a linear graph.
5.1.4 5.1.5 5.2 5.2.1
Find the midpoint, distance and gradient between two points. Solve simultaneous linear equations using linear graphs. Know the quadratic graphs. Construct tables of values for given quadratic
in class
√
Lecture Question & Answer Practical, Student class presentations
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√
√
√
√
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√
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Note: *Lecturers may use other teaching & learning strategies in order to achieve the learning outcomes. Generic Student Attributes (GSA) GSA 1 Communications Skills GSA 2 Critical Thinking and Problem Solving Skills GSA 3 Teamwork Skills GSA 4 Moral & Professional Ethics GSA 5 Leadership Skills GSA 6 Information Management Skills and Continuous Learning GSA 7 Entrepreneurship Skills
Version: 080510_1.2_Effective:1June2011
Learning Domain (LD) LD 1 Knowledge LD 2 Technical Skills LD 3 Professionalism & Ethics LD 4 Social Skills LD 5 Communication Skills LD 6 Critical Thinking LD 7 Life Long Learning LD 8 Entrepreneurial Skills
20 / 21
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GSA 5
LD 8 GSA 7
LD 7 GSA 6
LD 6 GSA 2
LD 5 GSA 1
LD 4 GSA 3
√
√ Lecture Question & Answer
LD 3 GSA 4
LD 2
√
√ Lecture Question & Answer Practical, Peer assisted of other students
LD 1
CLO 6
CLO 5
GSA & LD CLO 4
CLO3
Specific Outcome
CLO2
No
CLO 1
CLO *Recommended Teaching & Learning Strategy
RESTRICTED
BA101 Engineering Mathematics 1
MATRIX OF SPECIFIC OUTCOMES Vs CLO, GSA AND LEARNING DOMAINS COURSE : BA101 ENGINEERING MATHEMATICS 1
functions. 5.2.2 5.2.3 5.2.4 5.3
Draw graphs of quadratic functions. Solve problems involving linear and quadratic equations using graph. Solve problems involving two quadratic equations using graph.
Sketch graphs of cubic functions.
5.3.2
Sketch graphs of reciprocal functions. (y = a/x)
√
√
√
√
√ √
√
√
Note: *Lecturers may use other teaching & learning strategies in order to achieve the learning outcomes. Generic Student Attributes (GSA) GSA 1 Communications Skills GSA 2 Critical Thinking and Problem Solving Skills GSA 3 Teamwork Skills GSA 4 Moral & Professional Ethics GSA 5 Leadership Skills GSA 6 Information Management Skills and Continuous Learning GSA 7 Entrepreneurship Skills
Version: 080510_1.2_Effective:1June2011
Learning Domain (LD) LD 1 Knowledge LD 2 Technical Skills LD 3 Professionalism & Ethics LD 4 Social Skills LD 5 Communication Skills LD 6 Critical Thinking LD 7 Life Long Learning LD 8 Entrepreneurial Skills
21 / 21
RESTRICTED
GSA 5
LD 8 GSA 7
LD 7 GSA 6
LD 6 GSA 2
LD 5 GSA 1
LD 4 GSA 3
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√ Lecture Question & Answer Practical , Student class presentations
LD 3 GSA 4
LD 2
LD 1
CLO 6
CLO 5
CLO 4
GSA & LD
Practical, problem solving in group, Student class presentations, creating solutions
Know the basic form of non-linear graphs.
5.3.1
CLO3
Specific Outcome
CLO2
No
CLO 1
CLO *Recommended Teaching & Learning Strategy
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