Ba101 Engineering Mathematics 1

RESTRICTED BA101 Engineering Mathematics 1

Version: 080510_1.2_Effective:1June2011 1 / 21 RESTRICTED

POLYTECHNICSMINISTRY 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.



SUMMARY (30 LECTURE : 15 PRACTICAL)

RTA1.0 BASIC ALGEBRA (06:03)

This topic introduces basic algebraic concept and its use insolving linear equations, simultaneous linear equations with twovariables and quadratic equations.

2.0 STANDARD FORM, INDEX AND LOGARITHM (06:03)

This topic introduces the standard form, index and logarithm rulesand their applications to simplify expression and problem solving.The use of calculator is emphasised.

3.0 TRIGONOMETRY (06:03)

This topic explains the fundamental concept of trigonometricfunctions particularly the six trigonometric ratios of special anglesand simple trigonometric basic identities. The topic also explainabout sine and cosine rules. Skills using trigonometric identities,sine and cosine rules, formula of compound-angle and double-angle to solve simple trigonometric equations will be discussed.

4.0 GEOMETRY AND MEASUREMENT (08:04)

This topic explains the properties of angles with transversal andparallel lines and the properties of angles in a circle. Thecharacteristics of a tangent to a circle are discussed to solveangular problems. The Pythagoras’ Theorem is applied to solveproblems related to angle and length. The topic also explainsmethods of calculating arc length, surface area and volume. Theconcepts of similarity and how to calculate the length, area andvolume for any similar shapes also will be discussed.

5.0 COORDINATE GEOMETRY AND GRAPH (04:02)

This topic includes solving coordinate geometry problems usinggraphs and formulas. Emphasis will be given to the techniques ofdrawing straight lines and quadratic graph to ensure accuracy insolving linear and quadratic equations. The topic also emphasishow to sketch cubic and reciprocal graph of functions.

RTA : Recommended Time Allocation



SYLLABUS

1.0 BASIC ALGEBRA

1.1 Understand basic algebra1.1.1 Simplify algebraic fractions.1.1.2 Solve algebraic fractions using:

a. additionb. subtractionc. multiplicationd. division

1.1.3 Perform conversion of formulas.

1.2 Understand quadratic equations1.2.1 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 variables1.3.1 Solve simultaneous linear equations by using the elimination

method.1.3.2 Solve simultaneous linear equations by using the substitution

method.

2.0 STANDARD FORM, INDEX AND LOGARITHM

2.1 Know standard form2.1.1 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.



3.0 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 identitiesb. formula of compound-anglec. 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.

4.0 GEOMETRY AND MEASUREMENT

4.1 Understand properties of angles associated with transversal andparallel 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.



4.3.4 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 circularcone.

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.

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.

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)



ASSESSMENT

TYPES OF ASSESSMENT

The course assessment is carried out in two sections:

i. Continuous Assessment - (CA)ii. Final Examination - (FE)

The percentage ratio of FE to CA should follow the guideline stated in theArahan-Arahan Peperiksaan dan Kaedah Penilaian which is approved bythe Lembaga Peperiksaan dan Penganugerahan Sijil/Diploma Politeknik.

CONTINUOUS ASSESSMENT (CA):[ The total score of the CA components would be converted to thedetermined CA percentage ]

Continuous assessment is carried out throughout the semester andcomprises the followings:

a. Quiz (minimum 3) 20%b. Theory Test (minimum 2) 30%c. Lab work (minimum 2) 20%d. Other Assessment Task

i. End - of- Chapter (minimum 2) 20%ii. e- Quiz (minimum 2) 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.



ASSESSMENT SPECIFICATIONS TABLE (AST)COURSE : BA101 ENGINEERING MATHEMATICS 1

COURSE LEARNING OUTCOME (CLO)

1 2 3 4 5 6 L M H L M H L M H L M H L M H L M H

Basic Algebra √ 1 2 1 1 2

Quadratic Equations √ 1 1 2 1 1 1 1 1

Simultaneous Linear Equations With

Two Variables √ 1 1 1 2 1 1 1

Standard Form √ 1 1 1 1 1 1 1

Rules Of Indices √ 1 1 1 2 1 1 1 1

Rules Of Logarithm √ 1 1 2 1 1 1 1 1

Fundamental Of TrigonometricFunctions √ 2 1 1 2 2 1

Trigonometric Equations And Identities √ 1 1 1 1 1 1 1

Sine And Cosine Rules √ 1 1 1 1 1

Properties Of Angles Associated With

Transversal And Parallel Lines √ 2 1 1 1 1

Properties Of Circles √ 1 1 1 1

Pythagoras’ Theorem √ 1 1 1 1 1 1

Arc Length, Area of a Sector and

Segment of a Circle √ 1 1 1 1 1 1

Perimeter, Area And Volume ForSpecific Shapes √ 1 1 1 2 1 1

Concepts Of Similarity √ 1 1 1 1

Linear Graphs √ 1 1 1 1

Quadratic Graphs √ 1 1 1

Basic Form Of Non-Linear Graphs √ 1 1

5 3 2 10 6 5 6 3 2 6 4 2 10 7 5 18 12 6

5 3 2 5 3 2 5 3 2 5 3 2 5 3 2 5 3 2

LEGEND:

Difficulty Level :

L : Low 5 50% of the aspects can be answered correctly by more than 60% of the candidates

M : Medium 3 30% of the aspects can be answered correctly by more than 40% but less than 60% of the candidates

H : High 2 20% of the aspects can be answered correctly by less than 40% of the candidates

GEOMETRY AND

MEASUREMENT

Quiz Theory Test End-of-ChapterLabworkCONTEXT

TOTAL

Final Examination

TRIGONOMETRY

e-Quiz

STANDARD FORM, INDEX AND

LOGARITHM

BASIC ALGEBRA

CONSTRUCT (CLO)

ASSESSMENT TASK

COORDINATE GEOMETRY AND

GRAPH

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

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 problems3. Apply the fundamental of triginometric functions, sine and cosine rules, basic trigonometric identities, formula of compound-angle and double-angle in solving simple trigonometric equations4. 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



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.). McGraw-Hill.

Stroud, K.A. (2007). Engineering Mathematics (6th ed.). Palgrave Macmillan.

Thorning, D.W.S & Sadler. (1999). Understanding Pure Mathematics, OxfordUniversity Press.



DISTRIBUTION OF STUDENT LEARNING TIME


CREDIT : 2

No. ActivitiesCOD

ESLT

1 Lecture [ 2 hour(s) x 15 week(s) ] L 30

- Lecture hours [ √ ]

- Assessment Task

(Theory Test/Quiz) [ √ ]

2 Self Learning: Theory I 15- Preparation before theory class viz. review/download lesson notes. [ √ ]- Preparation after theory class viz. additional references, discussion group,

discussion with lecturers. [ √ ]- Preparation for theory test. [ √ ]

3 Practical [ 1 hour(s) x 15 week(s) ] P 15

- Lab work [ √ ] - Studio work [ ]

Critique- Skill/Practical test [ ] - Workshop [ ] [ ]

- Field work [ ] - Simulation [ ] Oral Presentation [ ]

- Survey/research [ ] - Outdoors [ ]

4 Self Learning: Practical I 15- 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. [ √ ]

5 Tutorial T 0

6 Other Assessment Task O 5

Capstone Project [ ] Portfolio [ ] Essay Question [ ]

(Final Project) Peer Assessment [ ] Observation [ ]

Presentation [ ] Self Assessment [ ] Discussion [ ]

Reflective Journal [ ] End-of-Chapter [ √ ] Project [ ]

Case Study [ ] e-Quiz [ √ ]

Industrial Visit [ ]

Total 80

L Lecture 30

P Practical 15I Self Learning 30

T Tutorial 0O Other Assessment Task 5

SLT (Student Learning Time) 80

Credit = SLT/40 2



TABLE OF LEARNING DOMAINS

COURSE : BA101 ENGINEERING MATHEMATICS

No. Specific OutcomeCognitive Domain Psychomotor Domain Affective Domain

C1 C2 C3 C4 C5 C6 P1 P2 P3 P4 P5 A1 A2 A3 A4 A5

1.0 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. √ √ √


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. √ √ √

2.3.7Solve equations that contain indices and logarithm expressions.

√ √ √

3.0 TRIGONOMETRY

3.1 Understand the fundamental of trigonometric functions.

3.1.1 Define sine, cosine, tangent, secant, cosecant and cotangent. √ √ √

3.1.2Use quadrant to determine the value of trigonometric functions (positiveand negative angles) √ √ √

3.1.3State 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. √ √ √

3.1.5Use 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 √ √

3.2.3Solve simple trigonometric equations using the appropriate formulainvolving: √ √ √a. three trigonometric basic identitiesb. formula of compound-anglec. 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. √ √ √


4.1Understand properties of angles associated with transversal and parallellines.





4.1.1Define right angle, acute angle, obtuse angle, adjacent angle,complementary angle and supplementary angle. √ √ √

4.1.2Identify transversals, corresponding angles, alternate angles and interiorangles. √ √ √

4.1.3Find the values of corresponding angles, alternate angles and interiorangles associated with parallel lines. √ √ √

4.1.4Solve problems involving properties of angles associated withtransversals. √ √ √

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. √ √ √

4.3.2Find the length of the missing side of a right-angled triangle using thePythagoras’ Theorem. √ √ √

4.3.3 Find the length of side of geometric shapes using Pythagoras’ Theorem. √ √ √

4.3.4 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.

4.5.1State the formula of the perimeter and area for rectangle, parallelogram,triangle and trapezium. √ √

4.5.2Compute the perimeter and area for rectangle, parallelogram, triangleand trapezium. √ √ √

4.5.3State the formula of the surface area and volume for sphere,hemisphere, cylinder, cube, cuboid, prism, pyramid and circular cone. √ √





4.5.4Compute 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. √ √ √


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) √ √ √

TOTAL 21 4 40 0 0 0 21 3 30 4 0 18 26 3 1 15

Legend

Cognitive Domain Psychomotor DomainAffectiveDomain

C1 Knowledge P1 Imitate A1 Receiving PhenomenaC2 Comprehensive P2 Manipulate A2 Responding to PhenomenaC3 Application P3 Precision A3 ValuingC4 Analysis P4 Articulation A4 Organizing ValuesC5 Synthesis P5 Naturalization A5 Internalizing ValuesC6 Evaluation


MATRIX OF SPECIFIC OUTCOMES Vs CLO, GSA AND LEARNING DOMAINS


Note:*Lecturers may use other teaching & learning strategies in order to achieve the learning outcomes.

Generic Student Attributes (GSA) Learning Domain (LD)GSA 1 Communications Skills LD 1 KnowledgeGSA 2 Critical Thinking and Problem Solving Skills LD 2 Technical SkillsGSA 3 Teamwork Skills LD 3 Professionalism & EthicsGSA 4 Moral & Professional Ethics LD 4 Social SkillsGSA 5 Leadership Skills LD 5 Communication SkillsGSA 6 Information Management Skills and Continuous Learning LD 6 Critical ThinkingGSA 7 Entrepreneurship Skills LD 7 Life Long Learning

LD 8 Entrepreneurial Skills


COURSE LEARNING OUTCOME (CLO)

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 variousmethods based on basic algebraic concept.

2. perform algebraic operations in standard form and simplify indices and logarithmic expressions by using index and logarithmrules 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 applyingthe 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 ofsimilarity.

6. demonstrate sketching and drawing of linear, quadratic and non-linear graphs accurately to solve simultaneous equationsbased on intersection points between two lines.

No Specific Outcome

*RecommendedTeaching &

LearningStrategy

CLO GSA & LD

CL

O1

CL

O2

CL

O3

CL

O4

CL

O5

CL

O6

LD

1

LD

2

LD

3G

SA

4

LD

4G

SA

3

LD

5G

SA

1

LD

6G

SA

2

LD

7G

SA

6

LD

8G

SA

7

GS

A5

1.0 BASIC ALGEBRALecture

Question & AnswerPractical, Peer

assisted of OtherStudents

1.1 Understand Basic Algebra

1.1.1 Simplify algebraic fractions. √ √

1.1.2 Solve algebraic fractions using: √ √








No Specific Outcome


LearningStrategy

CLO GSA & LD

CL

O1

CL

O2

CL

O3

CL

O4

CL

O5

CL

O6

LD

1

LD

2

LD

3G

SA

4

LD

4G

SA

3

LD

5G

SA

1

LD

6G

SA

2

LD

7G

SA

6

LD

8G

SA

7

GS

A5

a. addition √

b. subtraction √

c. multiplication √

d. division √

1.1.3 Perform conversion of formulas. √ √

1.2 Understand quadratic equations.

LectureQuestion & AnswerPractical, ProblemSolving in Group,

Computer AssistedLearning

1.2.1 Solve quadratic equations by using factorization. √ √

1.2.2Solve quadratic equations by using quadraticformula. √ √

1.2.3Solve quadratic equations by using completingsquares. √ √

1.3Understand simultaneous linear equations with twovariables

1.3.1Solve simultaneous linear equations by using theelimination method.

√ √

1.3.2Solve simultaneous linear equations by using thesubstitution method.

√ √


LectureQuestion & Answer

Practical, peer assistedof other students

2.1 Know standard form

2.1.1Convert real number to standard form and vice-versa. √

√

2.1.2 Perform algebraic operations in standard form. √ √








No Specific Outcome


LearningStrategy

CLO GSA & LD

CL

O1

CL

O2

CL

O3

CL

O4

CL

O5

CL

O6

LD

1

LD

2

LD

3G

SA

4

LD

4G

SA

3

LD

5G

SA

1

LD

6G

SA

2

LD

7G

SA

6

LD

8G

SA

7

GS

A5

2.2 Know the rules of indices.

LectureQuestion & AnswerPractical, Writing

reflections on learning(3-4 minutes)

2.2.1 State the index rules. √ √

2.2.2Apply the index rules to find the product of indexnumber. √

√

2.2.3Apply the index rules to find the quotient of indexnumber. √

√

2.2.4 Simplify expressions related to indices. √ √

2.3 Know the rules of logarithm.

LectureQuestion & AnswerPractical, Problemsolving in group,

Rounds (giving turn tostudents to talk)

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. √ √

2.3.4Apply the logarithm rules to find the value oflogarithms. √ √

2.3.5 Change the base of logarithms. √ √

2.3.6 Simplify logarithm expressions. √ √

2.3.7Solve equations that contain indices and logarithmexpressions. √

3.0 TRIGONOMETRY

3.1Understand the fundamental of trigonometricfunctions.








No Specific Outcome


LearningStrategy

CLO GSA & LD

CL

O1

CL

O2

CL

O3

CL

O4

CL

O5

CL

O6

LD

1

LD

2

LD

3G

SA

4

LD

4G

SA

3

LD

5G

SA

1

LD

6G

SA

2

LD

7G

SA

6

LD

8G

SA

7

GS

A5

3.1.1Define sine, cosine, tangent, secant, cosecant andcotangent.


Practical, Groupdiscussion

√ √

3.1.2Use quadrant to determine the value of trigonometricfunctions (positive and negative angles)

√ √

3.1.3State the values of the trigonometric ratios of thespecial angles. (30

o, 45

oand 60

o)

√ √

3.1.4Find the values of the trigonometric functionsinvolving special angles.

√ √

3.1.5Use calculator to determine the value oftrigonometric functions (including radian).

√ √

3.2 Know trigonometric equations and identities.

LectureQuestion & AnswerPractical, Students

producing mind mapsin class,

3.2.1 State trigonometric basic identities√

√

3.2.2State the formula of compound-angle and double-angle √ √

3.2.3Solve simple trigonometric equations using theappropriate formula involving: √ √

a. three trigonometric basic identities √

b. formula of compound-angle √

c. formula of double-angle √








No Specific Outcome


LearningStrategy

CLO GSA & LD

CL

O1

CL

O2

CL

O3

CL

O4

CL

O5

CL

O6

LD

1

LD

2

LD

3G

SA

4

LD

4G

SA

3

LD

5G

SA

1

LD

6G

SA

2

LD

7G

SA

6

LD

8G

SA

7

GS

A5

3.3 Understand sine and cosine rules.


Practical, Buzz group(short discussion in

two)

3.3.1 State the sine and cosine rules. √ √

3.3.2Calculate the area of a triangle using the formula ½ab sin C. √ √

3.3.3Solve simple trigonometric problems using sine andcosine rules.

√ √


LectureQuestion & AnswerPractical, Writing

reflections on learning(3-4 minutes)

4.1Understand properties of angles associated withtransversal and parallel lines.

4.1.1Define right angle, acute angle, obtuse angle,adjacent angle, complementary angle andsupplementary angle.

√ √

4.1.2Identify transversals, corresponding angles,alternate angles and interior angles. √ √

4.1.3Find the values of corresponding angles, alternateangles and interior angles associated with parallellines. √

√

4.1.4Solve problems involving properties of anglesassociated with transversals. √ √

4.2 Understand the properties of circles.


4.2.1State the properties of an angle and chord in acircle. √ √

4.2.2 State the properties of tangent on a circle. √ √








No Specific Outcome


LearningStrategy

CLO GSA & LD

CL

O1

CL

O2

CL

O3

CL

O4

CL

O5

CL

O6

LD

1

LD

2

LD

3G

SA

4

LD

4G

SA

3

LD

5G

SA

1

LD

6G

SA

2

LD

7G

SA

6

LD

8G

SA

7

GS

A5

4.2.3Solve problems on the angles of cyclicquadrilaterals.

Practical, Buzz group(short discussion in

two)√ √

4.3Apply the Pythagoras’ Theorem.

LectureQuestion & AnswerPractical, Student

class presentations

4.3.1 Identify the hypotenuse of right-angled triangles. √ √

4.3.2Find the length of the missing side of a right-angledtriangle using the Pythagoras’ Theorem.

√ √

4.3.3Find the length of side of geometric shapes usingPythagoras’ Theorem.

√ √

4.3.4Solve problems using the Pythagoras’ Theorem.

√ √

4.4Know the arc length, area of a sector and segmentof a circle.

LectureQuestion & AnswerPractical, Rounds

(giving turns toindividual students to

talk)

4.4.1Convert 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. √ √

4.5Understand the perimeter, area and volume forspecific shapes.

LectureQuestion & AnswerPractical, Students

producing mind maps

4.5.1State the formula of the perimeter and area forrectangle, parallelogram, triangle and trapezium. √ √

4.5.2Compute the perimeter and area for rectangle,parallelogram, triangle and trapezium.

√ √








No Specific Outcome


LearningStrategy

CLO GSA & LD

CL

O1

CL

O2

CL

O3

CL

O4

CL

O5

CL

O6

LD

1

LD

2

LD

3G

SA

4

LD

4G

SA

3

LD

5G

SA

1

LD

6G

SA

2

LD

7G

SA

6

LD

8G

SA

7

GS

A5

4.5.3State the formula of the surface area and volume forsphere, hemisphere, cylinder, cube, cuboid, prism,pyramid and circular cone.

in class√ √

4.5.4Compute the surface area and volume for sphere,hemisphere, cylinder, cube, cuboid, prism, pyramidand circular cone.

√ √

4.6 Understand the concepts of similarity. LectureQuestion & Answer

Practical, Peerassisted of other

students

4.6.1 Identify if given shapes are similar. √ √

4.6.2Calculate the length of unknown side of two similarshapes. √ √

4.6.3Calculate the area and volume for any similarshapes. √ √


LectureQuestion & AnswerPractical, Student

class presentations

5.1 Know the linear graphs.

5.1.1Sketch a linear graph when given the gradient andpoint of interception.

√ √

5.1.2 Construct table of values for given linear functions √ √

5.1.3 Draw a linear graph. √ √

5.1.4Find the midpoint, distance and gradient betweentwo points.

√ √

5.1.5Solve simultaneous linear equations using lineargraphs.

√ √

5.2 Know the quadratic graphs. LectureQuestion & Answer5.2.1 Construct tables of values for given quadratic √ √








No Specific Outcome


LearningStrategy

CLO GSA & LD

CL

O1

CL

O2

CL

O3

CL

O4

CL

O5

CL

O6

LD

1

LD

2

LD

3G

SA

4

LD

4G

SA

3

LD

5G

SA

1

LD

6G

SA

2

LD

7G

SA

6

LD

8G

SA

7

GS

A5

functions. Practical, problemsolving in group,

Student classpresentations, creating

solutions

5.2.2 Draw graphs of quadratic functions. √ √

5.2.3Solve problems involving linear and quadraticequations using graph.

√√

5.2.4Solve problems involving two quadratic equationsusing graph. √

√

5.3 Know the basic form of non-linear graphs.Lecture

Question & AnswerPractical , Studentclass presentations

5.3.1 Sketch graphs of cubic functions. √

5.3.2 Sketch graphs of reciprocal functions. (y = a/x) √ √ √

Ba101 Engineering Mathematics 1

Documents

generic student attributes

perform algebraic operations

solve algebraic fractions

lecture question

student class presentations

recommended teaching

student learning time

practical class field work survey