Additional Mathematics Syllabus

ZIMBABWE

MINISTRY OF PRIMARY AND SECONDARY EDUCATION

ADDITIONAL MATHEMATICS SYLLABUS

FORMS 3 - 4

2015 - 2022

Curriculum Development and Technical Services P. O. Box MP 133 Mount Pleasant Harare

Additional Mathematics Syllabus Forms 3 - 4

ACKNOWLEDGEMENTS

The Ministry of Primary and Secondary Education wishes to acknowledge the following for their valued contribution in the production of this syllabus:

• The National Additional Mathematics Syllabus Panel

• Representatives from Universities and Colleges

• Ministry of Higher and Tertiary Education, Science and Technology Development

• Zimbabwe School Examinations Council (ZIMSEC)

• United Nations Children’s Fund (UNICEF )

• United Nations Educational Scientific and ultural Organization (UNESCO)

i Additional Mathematics Syllabus Forms 3 - 4

CONTENTS

ACKNOWLEDGEMENTS...... 3

CONTENTS...... 4

1.0. PREAMBLE...... 1

2.0 PRESENTATION OF SYLLABUS...... 1

3.0 AIMS...... 1

4.0 OBJECTIVES...... 2

5.0 METHODOLOGY...... 2

6.0 TOPICS...... 2

7.0 SCOPE AND SEQUENCE...... 3

8.0 COMPETENCY MATRIX: FORM 3 ...... 8

FORM FOUR (4)...... 15

10.0 COMPETENCY MATRIX: FORM 4...... 20

11.0: ASSESSMENTS...... 23

ii Additional Mathematics Syllabus Forms 3 - 4

1.0. PREAMBLE • can easily master the form 1– 4 Mathematics Syllabus concepts 1.1. Introduction 1.5. Cross Cutting Themes In developing the Additional Mathematics syllabus, cognisance was taken of the need to broaden the form The following are some of the cross cutting themes in 1 – 4 Mathematics and accommodate students with Additional Mathematics: - high ability in the learning area and as well provide a solid base for further studies in mathematics and other • Business and financial literacy career developments. The intention is to provide wider • Disaster and risk management opportunities for mathematically gifted learners who wish • Communication and team building to pursue highly skilled, scientifically and technologically • Problem solving of environmental issues based competences required for the National human • Inclusivity capital development needs in the 21st century. • Enterprise skills • Cultural Diversity 1.2. Rationale • ICT • HIV & AIDS EDUCATION In its socio-economic transformation agenda, Zimbabwe has embarked on an Industrialisation development process, where high mathematical skills are a pre- 2.0 PRESENTATION OF requisite. It is therefore, important to provide a sound SYLLABUS grounding for development and improvement of the learner’s intellectual competencies in logical reasoning, The additional mathematics syllabus is a single docu- spatial visualisation, analytical and abstract thinking. ment covering forms 3 - 4 This will form the basis for creative thinkers, innovators It contains the preamble, aims, objectives, syllabus and inventors. Additional Mathematics optimises the topics, scope and sequence, competency matrix and potential of the mathematically gifted learners through assessment procedures. The syllabus also suggests a exposure to more challenging practical life problems list of resources to be used during learning and teaching that require practical solutions. The thrust is to provide process. wider opportunities for the mathematically gifted learners who desire to undertake technologically and industrially related careers such as actuarial sciences, architecture, 3.0 AIMS engineering and other scientific research activities. Sound knowledge of mathematics enables learners to The syllabus will enable learners to: develop skills such as accuracy, research and analytical competencies essential for life and sustainable develop- 3.1 acquire mathematical skills to solve problems ment. related to industry and technology 3.2 further develop mathematical concepts and 1.3. Summary of Content skills for higher studies 3.3 use mathematical skills in the context of more The Form 3 - 4 Additional Mathematics syllabus will advanced techniques such as research cover the theoretical concepts and their application. This 3.4 apply additional mathematics concepts and two-year secondary course consists of pure mathemat- techniques in other learning areas ics, mechanics, probability and statistics. 3.5 develop an appreciation of the role of mathematics in personal, community and national development (Unhu/Ubuntu/Vumunhu) 1.4 Assumptions 3.6 use I.C.T tools effectively to solve mathematical problems The syllabus assumes that the learner 3.7 apply additional mathematical skills and knowledge in relevant life situations • has a talent in mathematics 3.8 enhance confidence, critical thinking, innova- • has strong algebraic and geometric thinking tiveness, creativity and problem solving skills

1 Additional Mathematics Syllabus Forms 3 - 4

for sustainable development. 6.0 TOPICS

4.0 OBJECTIVES The following topics will be covered from Form 3 to 4

The learners should be able to: 6.1 Pure Mathematics 4.1 apply relevant mathematical symbols, definitions, terms and use them appropriately in 6.1.1 Indices and irrational numbers problem solving 6.1.2 Polynomials 4.2 use appropriate skills and techniques that are 6.1.3 Algebraic Identities, equations and inequalities necessary for further studies 6.1.4 Sequences and Series 4.3 formulate problems into mathematical terms 6.1.5 Coordinate geometry in two dimensions 4.4 identify the appropriate mathematical proce- 6.1.6 Functions dure for a given situation 6.1.7 Quadratic functions 4.5 use appropriate techniques to solve selected 6.1.8 Logarithmic and Exponential functions world problems in an ethical manner 6.1.9 Trigonometrical functions 4.6 use appropriate estimation procedures to 6.1.10 Differentiation acceptable degree of accuracy 6.1.11 Integration 4.7 present data through appropriate representa- tions 6.2. Probability and Statistics 4.8 draw inferences through correct manipulation of data 6.2.1 Probability 4.9 use I.C.T tools responsibly in problem solving 6.2.2 Data collection and Presentation 4.10 interpret mathematical data for use in relevant 6.2.3 Measures of central tendency and dispersion situations 6.2.4 Discrete and continuous probability distributions 5.0 METHODOLOGY 6.2.5 Normal distribution 6.2.6 Sampling Methods 6.2.7 Estimation It is recommended that teachers use teaching techniques in which mathematics is seen as a process which arouse 6.3 Mechanics an interest and confidence in tackling problems both in familiar and unfamiliar contexts. The teaching and 6.3.1 Kinematics of motion in a straight line learning of mathematics must be learner centred and 6.3.2 Forces and equilibrium practically oriented. Multi-sensory approach should also 6.3.3 Newton’s Laws of motion be applied during teaching and learning of mathematics. 6.3.4 Energy, Work and Power The following are some of the suggested methods:

• Guided discovery • Collaborative learning • Project based learning • Group work • Interactive e-learning • Problem solving • Simulation • Visual tactile • Educational tours

5.1 Time Allocation

Four periods of 40 minutes each per week should be allocated for the adequate coverage of the syllabus

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7.0 SCOPE AND SEQUENCE

7.1 PURE MATHEMATICS

TOPIC FORM 3 FORM 4 Indices and irrational numbers • Indices: - Rational indices - Rules and notations - Algebraic application - Exponential equations • Irrational numbers: - Surds - Operations

Polynomials • Polynomials: - Definition - Operations • Factor theorem - Factorisation • Remainder theorem

Algebraic identities, Equations • Identities: and Inequalities - Definition - unknown coefficient • Equations: - Linear - Simultaneous - Quadratic • Inequalities: - Linear - Quadratic

Sequences and Series • Sequences: - Notation - Behaviour of a sequence • Series: - Notation - Arithmetic progression - Geometric progression

Coordinate geometry in two • Coordinate Geometry: dimensions - Distance between two points - Gradient - Equation of a straight line - Parallel and perpendicular lines

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7.1 PURE MATHEMATICS

TOPIC FORM 3 FORM 4 Functions • Functions: - Definitions - Domain - Range - One to one mapping - Inverse functions - Composite function • Graphs: - Graphical illustration

Quadratic Functions • Quadratic expression • Quadratic equation • Quadratic function • Maximum / minimum value • Nature of roots

Logarithmic and Exponential • Logarithms: functions - Definition - Laws - Sketch graphs - Sketch inverse • Logarithmic equations • Exponential equations

Trigonometrical functions • Trigonometry: - Ratios - Simple identities - Simple Equations • Trigonometric Functions

Differentiation • Differentiation: - Gradient of a curve - Derivative notation - Rules of derivatives - Derivative of simple functions • Stationery Points - Maximum - Minimum • Application - Tangent and normal - Rates of change

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7.1 PURE MATHEMATICS

TOPIC FORM 3 FORM 4 Integration • Integration • Reverse process of differentiation • Notation • Integration of simple functions • Application - Area under the curve

7.1 PROBABILITY AND STATISTICS

TOPIC FORM 3 FORM 4 Probability • Set Language and notation - Trial - Samples spaces - Outcomes/events - Venn diagrams • Approaches to probability - Objective probability - Experimental - Classic - Subjective probability • Addition and product Rules - Independent events -Mutually exclusive events - Outcome Tables - Tree Diagram Conditional probability

Data collection and Presentation • Key Statistical terms • Statistics data • Frequency • Tally system • Population • Samples • Data - Sources - Classification - Types - Merits and demerit • Data collection methods • Forms of data presentation

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7.2 PROBABILITY AND STATISTICS

TOPIC FORM 3 FORM 4 Measures of central tendency • The mean, median and mode and dispersion • Measures of dispersion - Variance - Standard deviation - Coefficient of variation - Range Interquartile range

Discrete and continuous • Discrete random variables probability distributions - Probability distribution of a discrete variable - Binomial probability distribution • Continuous random variables - Probability distribution of a continuous variable • Mean and variance of a random variable

Normal distribution • Properties of normal distribution curve • The standard normal variable, Z • Probabilities • Using standard normal tables (including reverse to find Z when is known  (z) Finding σ or μ or both

Sampling Methods • Sampling techniques - Random and non-random sampling • Central limit theorem • Distribution of sample mean (when population of X is normal)

Estimation • Point estimation - Mean and variance • Interval estimation - Confidence interval (for mean of the population and mean of a normal population with known variance and arge sample

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7.3 MECHANICS

TOPIC FORM 3 FORM 4 Kinematics of motion in a straight • Distance and speed line - x – t graphs - Gradient as Velocity • Vector and scalar quantity • Velocity and acceleration - v – t graphs - Gradient as acceleration • Equations of motion

Forces and Equilibrium • Force - Types of forces - Representation of force by vectors - Resultants and components - Composition and Resolutions - Equilibrium of a particle - Friction

Newton’s Laws of motion • Newton’s laws of motion • Application

Energy, Work and Power • Energy • Work • Power • Principle of energy conservation

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8.0 COMPETENCY MATRIX: FORM 3

TOPIC 1: INDICES AND IRRATIONAL NUMBERS

SUB TOPIC LEARNING OBJEC- CONTENT (Atti- SUGGESTED SUGGESTED RE- TIVES tudes, Knowldege NOTES AND ACTIV- SOURCES and Skills) ITIES Indices • define an index • Indices: • Discussing indices • ICT tools • use the laws of - indices • Applying the rules • Braille materials indices in algebraic - Rules and notations of indices in algebraic and equipment application - Algebraic applica- expression • Talking books or • solve equations tion • Finding values of software involving indices • Exponential unknown in problems • Relevant texts equations involving indices

Irrational Numbers • Simplify given surds • Irrational numbers: • Reducing surds to • ICT tools • Carryout basic - Surds simplest form • Brail materials operations involving • Operations • Performing • Talking books or surds - addition operations software - subtraction involving surds • Relevant texts

TOPIC 2: POLINOMIALS

SUB TOPIC LEARNING OB- CONTENT (Atti- SUGGESTED SUGGESTED RE- JECTIVES Learner tudes, Knowldege NOTES AND ACTIV- SOURCES should be able to: and Skills) ITIES Polynomials • define a polyno- • Polynomials: • Discussing • ICT tools mial - Definition polynomials • Brailel materials • carryout basic op- - Operations • Performing basic and equipment erations involving operations with • Talking books or polynomials polynomials of software order not more • Relevant texts than three

Remainder Theorem • state the remain- • Remainder theorem • Using the remain- • ICT tools der theorem der theorem in • Braille material • find the remainder identifying factor and equipment of a polynomial and remainder • Talking books or when divisible by • Using the remain- software a given factor der theorem to • Relevant texts solve problems involving polynomials

Factor Theorem • Factorise given • Factor theorem • Identifying factors • ICT tools polynomials - factorisation for given polyno- • Braille materials mials and equipment • Talking books or software • Relevant texts

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TOPIC 3: ALGEBRAIC IDENTITIES, EQUATIONS AND INEQUALITIES

SUB TOPIC LEARNING OB- CONTENT (Atti- SUGGESTED SUGGESTED RE- JECTIVES Learner tudes, Knowldege NOTES AND ACTIV- SOURCES should be able to: and Skills) ITIES Identities • distinguish • Identities: • Comparing • ICT tools identities from - Definition given polynomial • Brail materials equations - unknown coefficient expressions and equipment • determine un- • Comparing coeffi- • Talking books or known coefficients cients of identical software using identities expressions • Relevant texts

Equations (up to • solve given • Equations: • solving equations • ICT tools order 3) equations - Linear ( up to order 3) • Brail materials • solve a pair of - Simultaneous • Solving simulta- and equipment simultaneous - Quadratic neous equations • Talking books or equations with at - cubic with at least one software least one linear linear and at most • Relevant texts and at most one one quadratic quadratic

Inequalities • Solve given • Inequalities • Solving problems • ICT tools inequalities - Linear involving inequal- • Brail materials - Quadratic ities and equipment • Talking books or software • Relevant texts

TOPIC 4: SEQUENCE AND SERIES

SUB TOPIC LEARNING OB- CONTENT (Atti- SUGGESTED SUGGESTED RE- JECTIVES Learner tudes, Knowldege NOTES AND ACTIV- SOURCES should be able to: and Skills) ITIES Sequence • define a sequence • Sequences • Discussing • ICT tools • identify the - notation and identifying • Brail materials elements of a • Behaviour of sequences and equipment sequence sequences • Observing and • Talking books or • identify the - Periodic discussing the software behaviour of - Oscillatory behavioural • Relevant texts sequences - Convergent nature of given - divergent sequences

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TOPIC 4: SEQUENCE AND SERIES

SUB TOPIC LEARNING OB- CONTENT (Atti- SUGGESTED SUGGESTED RE- JECTIVES Learners tudes, Knowldeg NOTES AND ACTIV- SOURCES should be able to: and Skills) ITIES Series • define sigma • Series • Finding sum of • ICT tools notation - Notation sequential terms • Brail materials • use the sigma • Arithmetic progres- using the sigma and equipment notation to solve sion (AP) notation () • Talking books or problems involv- • Geometric progres- • Using the AP or software ing series sion (GP) GP to find the nth • Relevant texts • recognise term and sum of arithmetic and the n terms geometric • Using the formula progressions to find sum to • find the nth term infinity and sum of the • Representing life first n terms of an phenomena using AP and GP mathematical • find sum to infinity models involving of a geometric series and progression exploring their • solve problems applications in life involving series

TOPIC 5: COORDINATE GEOMETRY IN TWO DIMENSIONS

SUB TOPIC LEARNING OB- CONTENT (Atti- SUGGESTED SUGGESTED RE- JECTIVES Learners tudes, Knowldeg NOTES AND ACTIV- SOURCES should be able to: and Skills) ITIES Coordinate • calculate the • Distance between • Calculating • ICT tools Geometry in two distance between two points gradient between • Brail materials Dimensions two given points • Gradient two points in a and equipment • calculate gradient • Equation of a straight line • Talking books or between two straight line • Discussing and software points • Parallel and deducing the • Relevant texts • find the equation perpendicular relationship of a straight line lines between gradients • find the equation • Equation of a of parallel and of a normal to the normal perpendicular given straight line lines • Finding equations of parallel or perpendicular lines using the above relationships

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TOPIC 6: FUNCTIONS

SUB TOPIC LEARNING OBJEC- CONTENT (Atti- SUGGESTED SUGGESTED TIVES Learners tudes, Knowldeg NOTES AND RESOURCES should be able to: and Skills) ACTIVITIES FUNCTIONS • define a function • Definitions • Discussing and • ICT tools • find the domain • Domain deducing the • Brail materials and range • Range concept of a and equipment • distinguish a • One to one function. • Talking books or function from mapping • Identifying do- software given relations • Inverse functions mains and ranges • Relevant texts • recognise a one • Composite of functions to one mapping function • Deducing an • find inverse • Graphical illustra- inverse function and composite tion • Sketching graphs functions using function • represent func- properties such tions graphically as one to one function

TOPIC 7: QUADRATIC FUNCTIONS

SUB TOPIC LEARNING OB- CONTENT (Atti- SUGGESTED SUGGESTED RE- JECTIVES Learners tudes, Knowldege NOTES AND ACTIV- SOURCES should be able to: and Skills) ITIES Quadratic Func- • state the quadratic • Quadratic expres- • Discussing • ICT tools tions expression sion and identifying • Brail materials • solve quadratic • Quadratic equation quadratic relations and equipment equations • Quadratic function as a function • Talking books or • recognise a • Maximum / • Sketching the software quadratic function minimum value graphs to identify • Relevant texts as a two to one • Nature of roots the maximum and mapping minimum values • find its maximum • Solving problems /minimum involving quadrat- using the graph ic equations or completion of a • Using the algebra- square ic approach such • use the discrimi- as the coefficient nant to determine of the quadratic the nature of variable to deter- the roots of the mine the nature quadratic equation of the turning point and line of symmetry

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TOPIC 8: LOGARITHMIC FUNCTIONS

SUB TOPIC LEARNING OBJEC- CONTENT (Atti- SUGGESTED SUGGESTED RE- TIVES Learners tudes, Knowldege NOTES AND ACTIV- SOURCES should be able to: and Skills) ITIES Logarithmic and Ex- • define a logarith- • Logarithms: • Discussing • ICT tools ponential Functions mic function - Definition logarithmic • Brail materials • use laws of - Laws function and equipment - Sketch graphs and logarithms to • Discussing the • Talking books or their inverse solve logarithmic • Logarithmic equa- laws of logarithms software and exponential tions • Solving Logarith- • Relevant texts equations • Exponential equa- mic and exponen- • express loga- tions tial equations rithms as expo- • Using logarithmic nential functions properties to and vice versa sketch graphs • sketch logarithmic graph and its inverse • solve the logarithmic and exponential equations

TOPIC 9: TRIGONOMETRY

SUB TOPIC LEARNING OB- CONTENT (Atti- SUGGESTED SUGGESTED RE- JECTIVES Learners tudes, Knowldege NOTES AND ACTIV- SOURCES should be able to: and Skills) ITIES Trigonometry • state the three • Trigonometry: • Discussing the • ICT tools basic trigonomet- - Ratios three basic • Braille materials ric ratios - Simple identities trigonometric and equipment • deduce the other - Simple equations ratios • Talking books or three trigonomet- • Trigonometric • Using quadrants software ric ratios Functions of a circle to • Relevant texts • identify trigono- deduce trigonometric relations as metric ratios functions • Sketching graphs • sketch graphs trigonometric of trigonometric functions functions • Using simple • prove simple identities to solve trigonometric trigonometric identities equations • solve trigonometric equations using some identities

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TOPIC 10: DIFFERENTIATION

SUB TOPIC LEARNING OB- CONTENT (Atti- SUGGESTED SUGGESTED RE- JECTIVES Learners tudes, Knowldege NOTES AND ACTIV- SOURCES should be able to and Skills) ITIES Differentiation • find the gradient • Differentiation: • Discussing and • ICT tools of a straight line - Gradient of a curve deducing the • Brail materials • approximate - Derivative notation gradient of curve and equipment the gradient of - Rules of derivatives at a point • Talking books or a tangent on - Derivative of simple • Using operating software the curve at the functions rules to derive • Relevant texts point of contact • Stationery Points given functions using gradients - Maximum such as axn, Inx, of sequence of - Minimum sin x, cos x, tan chords (from first • Application: x,1/x,ex principles) - Tangent and normal • Using appropriate • recognize appro- Rates of change notation such as priate notation f/ (x),dy(dx,) (d^2 for the derivation y)/(dx^2 ) for the process of given derivation process functions of given functions • differentiate • Determining the using quotient and nature of the product rules stationery points • apply differen- using change of tiation to find sign or second gradients and derivative test equations of • Applying differenti- a normal and ation to determine tangent to the rates of change curve • use differentiation to identify stationery points and their nature • apply differentiation to determine rates of change and approxima- tions

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TOPIC 11: INTEGRATION

SUB TOPIC LEARNING OB- CONTENT (Atti- SUGGESTED SUGGESTED RE- JECTIVES Learners tudes, Knowldege NOTES AND ACTIV- SOURCES should be able to: and Skills) ITIES Integration • recognize • Reverse process • Discussing the • ICT tools integration as the of differentiation relationship between • Braille materials reverse process of • Notation differentiation and and equipment differentiation • Integration of integration • Talking books or • integrate basic simple functions • Integrating sim- software functions such as xn ple functions which • Relevant texts • apply integration (including the case includes the following to find area and where n= -1), (ax+b)n, eax+b, sin volume under a cosx, sinx,e^x (ax+b) (Integration curve • Application is restricted to linear - Area under the substitution) curve • Finding volumes and area under the curve using integration

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FORM FOUR (4)

9.0 COMPETENCY MATRIX: FORM 4

PROBABILITY AND STATISTICS

TOPIC 1: PROBABILITY

SUB TOPIC LEARNING OB- CONTENT (Atti- SUGGESTED SUGGESTED RE- JECTIVES Learners tudes, Knowldege NOTES AND ACTIV- SOURCES should be able to: and Skills) ITIES Sets and Notation • define probabil- • Trial • Discussing • ICT tools ity, trial, sample • Sample space probability terms • Braille materials space, outcome • Outcomes and • Carrying out and equipment and events events experiments to • Talking books or • illustrate different • Venn diagrams illustrate proba- software sample spaces bility space and • Relevant texts • relate sets to outcome events • Discussing Venn • illustrate two or diagrams more events using • Demonstrating Venn diagrams events on Venn diagrams

Approaches to • describe the basic • Objective proba- • Discussing the • ICT tools Probability approaches to bility various types of • Braille materials probability - Experimental probabilities and equipment - Classical • Talking books or • Subjective proba- software bility • Relevant texts

Addition amd Prod- • apply addition • Mutually exclusive • Discussing the • ICT tools uct Rules rule for mutually events concepts of • Brail materials exclusive events • Independent mutually events and equipment • apply the product events and Independent • Talking books or rule for indepen- • Outcome tables events software dent events • Tree diagrams • Calculating • calculate • Addition rule probabilities probability using • Product rule using outcome tree diagrams and tables and/ or tree outcome tables diagrams

Conditional Proba- • define conditional • Conditional • Discussing • ICT tools bility probability probability conditional • Brail materials • solve probability • Diagrams probability and equipment problems involv- • Solving problems • Talking books or ing conditional on conditional software probabilities probabilities • Relevant texts

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TOPIC 2: DATA COLLECTION AND PRESENTATION

SUB TOPIC LEARNING OB- CONTENT (Atti- SUGGESTED SUGGESTED RE- JECTIVES Learners tudes, Knowldege NOTES AND ACTIV- SOURCES should be able to and Skills) ITIES Statistical Key • define statistical • Definition of • Discussing • ICT tools Terms key terms statistical key statistical terms • Brail materials - statistics, terms such as: using illustarions and equipment - data - Statistics data and appropriate • Talking books or - frequency - Frequency examples software - tally system, - Tally system • Relevant texts - population and - Population - samples samples

Sources and types • state the source • Data • Discussing the • ICT tools of data of data - Sources sources, classes • Brail materials • classify data - Classification and types of data and equipment • state the types of - Types • Classifying data • Talking books or data in Statistics - merits and demerits • Distinguishing software • distinguish forms of data • Relevant texts between primary and secondary data

Data Collection • outline methods of • Data collection • Collecting data • ICT tools collecting data methods • Organising and • Brail materials • organise data in • Forms of data summarising and equipment appropriate tables presentation data through • Talking books or • summarise data appropriate tables software in appropriate and graphs forms

TOPIC 3. MEASURES OF CENTRAL TENDENCY AND DISPERSION

SUB TOPIC LEARNING OB- CONTENT (Atti- SUGGESTED SUGGESTED RE- JECTIVES Learners tudes, Knowldege NOTES AND ACTIV- SOURCES should be able to and Skills) ITIES The Measures of • calculate mean, • Mean • Discussing the • ICT tools Dentral Tendency mode and median • Mode relationship • Braille materials • Median between mean, and equipment (grouped and mode and median • Talking books or ungrouped data) • Calculating mean, software mode and median • Relevant texts of a distribution

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TOPIC 3. MEASURES OF CENTRAL TENDENCY AND DISPERSION

SUB TOPIC LEARNING OB- CONTENT (Atti- SUGGESTED SUGGESTED RE- JECTIVES Learners tudes, Knowldege NOTES AND ACTIV- SOURCES should be able to and Skills) ITIES Measures of Disper- • define measures • Variance • Calculating • ICT tools sion of dispersion • Standard deviation measures of • Braille materials • calculate • Range dispersion and equipment measures of • Interquartile range • Discussing the • Talking books or dispersion • Coefficient of use of measures software • explain the impor- Variation of dispersion • Relevant texts tance of measures of dispersion

TOPIC4 : DISCRETE AND CONTINOUS PROBABILITY DISTRIBUTIONS

SUB TOPIC LEARNING OB- CONTENT (Atti- SUGGESTED SUGGESTED RE- JECTIVES Learners tudes, Knowldege NOTES AND ACTIV- SOURCES should be able to: and Skills) ITIES Discrete random • define discrete - Discrete random • Discussing appli- • ICT tools variables random variable variables cation areas of the • Braille materials and its probability - Probability distribu- discrete random and equipment distribution tion of a discrete variables • Talking books or • use probability variable • Calculating E software distribution table - Binomial probability [x], Var [x] and • Relevant texts to find distribution unknown values - E(x) - E(x), Var(x) in the probability - Var (x) - Binomial distribution distribution table - unknown values - Mean and variance • Discussing the in the probability of binomial characteristics distribution distribution of a Binomial table distribution • state characteris- • Calculating tics of a Binomial probabilities model using the Binomial • use the Binomial probability density probability density function function to calcu- • Calculating mean late probabilities and variance of • calculate mean the distribution and variance • Representing life of the Binomial phenomena using distribution mathematical models involving series and exploring their applications in life

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TOPIC4 : DISCRETE AND CONTINOUS PROBABILITY DISTRIBUTIONS

SUB TOPIC LEARNING OB- CONTENT (Atti- SUGGESTED SUGGESTED RE- JECTIVES Learners tudes, Knowldege NOTES AND ACTIV- SOURCES should be able to: and Skills) ITIES Continuous random • define continuous • Continuous • Discussing • ICT tools variables random variable random variable application of • Braille materials and its probability • probability density the continuous and equipment density function function (pdf) random variables • Talking books or • Find the mean • Mean and • Finding E(x) and software and variance variance of Var (x) of con- • Relevant texts • calculate proba- a continuous tinuous random bilities using the random variable variables probability density • Using probability function density function to calculate the probabilities

TOPIC 5: NORMAL DISTRIBUTION

SUB TOPIC LEARNING OB- CONTENT (Atti- SUGGESTED SUGGESTED RE- JECTIVES Learners tudes, Knowldege NOTES AND ACTIV- SOURCES should be able to: and Skills) ITIES Normal Distribution • explain the charac- • The normal • Standardising • ICT tools teristics of normal distribution curve variables • Braille materials distribution curve • Probability • Using standard and equipment • use the standard • Mean and normal tables • Talking books or normal variable to variance • Calculating software find the probabil- probabilities • Relevant texts ities • Finding mean and • use standard variance normal tables (including finding z when Φ (z) is known) • Find mean and variance

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TOPIC 6: SAMPLING

SUB TOPIC LEARNING OB- CONTENT (Atti- SUGGESTED SUGGESTED RE- JECTIVES Learners tudes, Knowldege NOTES AND ACTIV- SOURCES should be able to: and Skills) ITIES Sampling • explain the basic • Sampling tech- • Distinguishing • ICT tools sampling methods niques between the use • Braille materials • choose samples • Random and of sample and and equipment using randomness non-random population • Talking books or and non-ran- sampling • Choosing sam- software domness • Expectation and ples to represent • Relevant texts • apply the sam- sample mean a population pling methods to • Central Lmit • Solving problems identify represen- Theorem involving the use tative samples • Distribution of of Central Limit • use (without sample mean, x ̅ Theorem proof) the Central (when population of Limit Theorem X is normal)

TOPIC 7: ESTIMATION

SUB TOPIC LEARNING OB- CONTENT (Atti- SUGGESTED SUGGESTED RE- JECTIVES Learners tudes, Knowldege NOTES AND ACTIV- SOURCES should be able to: and Skills) ITIES Estimation • recognise the • Point estimation • Discussing concept • ICT tools importance of - Mean and variance of estimation and • Brail materials estimation • Interval estimation its application and equipment • calculate unbi- - Confidence interval • Calculating • Talking books or ased estimators of for mean of the unbiased software population mean population mean estimators of • Relevant texts and variance. of a normal population mean • use point and population with and variance interval estimators known variance • Calculating to a given margin and large sample standard error of of error/signifi- the mean cance level of 5% • Calculating confi- or 1 % dence interval

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10.0 COMPETENCY MATRIX: FORM 4

FORM FOUR (4) MECHANICS

TOPIC 1: KINEMATICS OF MOTION IN A STRAIGHT LINE

SUB TOPIC LEARNING OB- CONTENT (Atti- SUGGESTED SUGGESTED RE- JECTIVES Learners tudes, Knowldege NOTES AND ACTIV- SOURCES should be able to: and Skills) ITIES Kinematics of • define a vector and • Vector and scalar • Discussing the • ICT tools Motion in a Straight a scalar quantity quantity concept of change • Brail materials Line • sketch (x-t) and (v-t) • Distance and speed of the subject of the and equipment graphs - x – t graphs formulae • Talking books or • find gradient of (x-t) - Gradient as Velocity • Discussing the software and • Velocity and accel- relationship between • Relevant texts (v-t) graphs eration gradient, velocity and • distinguish between - v – t graphs acceleration velocity and acceler- - Gradient as accel- • Sketching (x-t) and ation eration (v-t) graphs • use the equations of • Equations of motion • Finding distance, motion to solve kine- velocity and acceler- matics problems ation from graphs • Solving equations of motion

TOPIC 2: FORCES AND EQUILIBRIUM

SUB TOPIC LEARNING OB- CONTENT (Atti- SUGGESTED SUGGESTED RE- JECTIVES Learners tudes, Knowldege NOTES AND ACTIV- SOURCES should be able to: and Skills) ITIES Forces and Equilib- • define force • Types of forces • Sketching and • ICT tools rium • identify the forces • Representation of labelling of forces • Braille materials acting in a given force by vectors on a plane and equipment situation • Resultants and • Identifying forces • Talking books or • represent forces components acting on a body software by vectors • Composition and in equilibrium • Relevant texts • find resultants and Resolutions components of • Equilibrium of a vectors particle • Friction

20 Additional Mathematics Syllabus Forms 3 - 4

TOPIC 2: FORCES AND EQUILIBRIUM

SUB TOPIC LEARNING OB- CONTENT (Atti- SUGGESTED SUGGESTED RE- JECTIVES Learners tudes, Knowldege- NOTES AND ACTIV- SOURCES should be able to: and Skills) ITIES Forces and Equilib- • use resultants and • Calculating • ICT tools rium components of resultant forces • Braille materials vectors to formu- and or unknown and equipment late equations variables • Talking books or • represent contact • Educational Tours software force between two • Representing life • Relevant texts surfaces by two phenomena using components, the mathematical ‘normal force’ and models involving ‘frictional forces’ series and • use the principle exploring their that, when a applications in life particle is at equilibrium the vector sum of the forces acting is zero • solving problems involving forces and equilibriums

TOPIC 3: NEWTON’S LAWS OF MOTION

SUB TOPIC LEARNING OB- CONTENT (Atti- SUGGESTED SUGGESTED RE- JECTIVES Learners tudes, Knowldege NOTES AND ACTIV- SOURCES should be able to: and Skills) ITIES Newton’s Laws of • state Newton’s • Newton’s laws of • Discussing the • ICT tools Motion laws of motion motion Newton’s laws of • Braille materials • apply Newton’s • Application motion and equipment laws of motion to • Using Newton’s • Talking books or the linear motion laws of motion in software of a body of problem solving • Relevant texts constant mass • Interpreting solu- moving under the tions in familiar action of constant and unfamiliar forces contexts

21 Additional Mathematics Syllabus Forms 3 - 4

TOPIC 4: ENERGY, WORK AND POWER

SUB TOPIC LEARNING OBJEC- CONTENT (Atti- SUGGESTED SUGGESTED RE- TIVES Learner s tudes, Knowldege NOTES AND ACTIV- SOURCES should be able to: and Skills) ITIES Energy, work and • explain the con- • Energy • Discussing the con- • ICT tools power cepts of gravitational • Work cept of total energy, • Braille materials potential energy • Power potential and kinetic and equipment • use the principle of • Principle of energy energy • Talking books or energy conservation conservation • Demonstrating software to solve problems simple experiments • Relevant texts involving energy on conservation of • calculate the work energy done by a constant • Calculating power force when its point of application under- goes a displacement • apply the definition of power as the rate at which work is done

22 Additional Mathematics Syllabus Forms 3 - 4

11.0: ASSESSMENTS 11.1 Assessment

The assessment will test candidate’s ability to: - • recall and use manipulative techniques • interpret and use mathematical data, symbols and terminology • comprehend numerical, algebraic and spatial concepts and relationships • recognise the appropriate mathematical procedure for a given situation • formulate problems into mathematical terms, select and apply appropriate techniques of solutions

11.2 Scheme of Assessment

Forms 3 to 4 Aadditional Mathematics assessment will be based on 30% continuous assessment and 70% summative assessment. The syllabus’ scheme of assessment is grounded in the principle of equalisation of opportunities hence, does not condone direct or indirect discrimination of learners. Arrangements, accommodations and modifications must be visible in both continuous and summative assessments to enable candidates with special needs to access assessments and receive accurate performance measurement of their abilities. Access arrangements must neither give these candidates an undue advantage over others nor compromise the standards being assessed. Candidates who are unable to access the assessments of any component or part of component due to disabil- ity (transitory or permanent) may be eligible to receive an award based on the assessment they would have taken. NB For further details on arrangements, accommodations and modifications refer to the assessment procedure booklet. a) Continuous Assessment Continuous assessment for Form 3 – 4 will consists of assignments, tests, projects and tasks to measure soft skills i. Topic Tasks These are activities that teachers use in their day to day teaching. These should include practical activities, assignments and group work activities. ii. Written Tests These are tests set by the teacher to assess the concepts covered during a given period of up to a month. The tests should consist of short structured questions as well as long structured questions. iii. End of term examinations These are comprehensive tests of the whole term’s or year’s work. These can be set at school, district or pro- vincial level. iv. Project This should be done from term one to term five. a. Summary of Continuous Assessment Tasks From term one to five, candidates are expected to have done the following recorded tasks: • 1 Topic task per term • 2 Written tests per term • 1 End of term test per term • 1 Project in five terms

23 Additional Mathematics Syllabus Forms 3 - 4

Detailed Continuous Assessment Tasks Table

Term Number of Number of Number of End Project Total Topic Tasks Written Tests Of Term Tests 1 1 2 1 2 1 2 1 3 1 2 1 1 4 1 2 1 5 1 2 1 Weighting 25% 25% 25% 25% 100% Actual Weight 7.5% 7.5% 7.5% 7.5% 30%

11.3 Specification Grid for Continuous Assessment

Component Skills Topic Tasks Written Tests End of Term Project Skill 1 50% 50% 50% 20% Knowledge Comprehension

Skill 2 40% 40% 40% 40% Application Analysis

Skill 3 10% 10% 10% 40% Synthesis Evaluation

Total 100% 100% 100% 100% Actual weighting 3% 7.5% 15% 4.5%

b) Summative Assessment The examination will consist of 2 papers: paper 1 and paper 2. Additional Mathematics paper 1 (Pure Mathematics) Duration: Two hours thirty minutes (2 ½ hrs) The paper consists of two sections, Section A and Section B Section A: Compulsory short answer structured questions, (marked out of 52) Section B: Long answer structured questions, candidates choose four question from a total of six questions (marked out of 48)

Additional Mathematics paper 2 (Mechanics and Statistics) Duration: Two hours thirty minutes (2 ½ hrs) The paper consists of three sections: Section A, Section B and Section C Answer all questions in Section A and any five from either section B and or Section C Section A: It will consist of 4 compulsory questions selected from Mechanics and Statistics (marked out of 40) Section B: It will consist of 7 questions from Mechanics Section of the syllabus where candidates choose at most 5 questions each carrying 12 marks (marked out of 60) Section C: It will consist of 7 questions from Probability and Statistics Section of the syllabus where candidates choose at most 5 questions each carrying 12 marks (marked out of 60)

24 Additional Mathematics Syllabus Forms 3 - 4

The tables below show the information on weighting, types of papers to be offered and the time allowed for each paper.

P1 P2 Total Weighting 50% 50% 100% Actual weighting 35% 35% 70% Type of Paper Section A (52 Marks) Section A (40 Marks) 4 compulsory short 4 structured questions answers structured questions Section B (60 Marks) 5 structured questions Section B (48 Marks) 4 structured questions Section C (60 Marks) 5 structured questions

Marks 100 100

Specification Grid for Summative Assessment

P1 P2 Actual Weighing Skill 1 50% 40% 31.5% Knowledge & Comprehension

Skill 2 40% 45% 29.75% Application & Analysis

Skill 3 10% 15% 8.75% Synthesis & Evaluation

Total 100% 100% Weighting 35% 35% 70%

25 Additional Mathematics Syllabus Forms 3 - 4

9.3 ASSESSMENT MODEL

Learners will be assessed using both continuous and summative assessments.

Assessment of learner performance in Addi- tional Mathematics 100%

Continuous Summative assessment assessment 30% 70%

Profiling Topic Written End of Project P1 P2 Tasks Tests term Tests 7.5% 35% 35% 7.5% 7.5% 7.5%

Continuous assessment mark Examination mark 70% 30% Profiling

Exit Pro- FINAL MARK 100% filing