Week No Learning Objectives Pupils will be taught to..... Learning Outcomes Pupils will be able to… No of Periods Suggested Teaching & Learning activities/Learning Skills/Values Points to Note Topic/Learning Area Al : FUNCTION --- 2 weeks First Term 1 1. Understand the concept of relations. 1 Represent relations using 2 arrow diagrams 3 ordered pairs 4 graphs 5 Identify domain, co domain, object, image and range of a relation. 1.3 Classify a relation shown on a mapped diagram as: one to one, many to one, one to many or many to many relation. 1 Use pictures, role-play and computer software to introduce the concept of relations. Skill : Interpretation, observe connection between domain, co domain, object, image and range of a relation. Discuss the idea of set and introduce set notation. 2. Understand 2.1 Recognise functions as a Give examples of finding Represent functions using arrow diagrams, ordered pairs or 1 Yearly Plan – Additional Mathematics Form 4
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2. Find the maximum and minimum values of quadratic functions.
2.1 Determine the maximum or minimum value of a quadratic function by completing the square.
Use graphing calculators or dynamic geometry software such as the Geometer’s Sketchpad to explore the graphs of quadratic functions
Skills : mental process , interpretation
Students be reminded of the steps involved in completing square and how to deduce maximum or minimum value from the function and also the corresponding values of x.
3. Sketch graphs of quadratic functions.
3.1 Sketch quadratic function graphs by determining the maximum or minimum point and two other points.
Use graphing calculators or dynamic geometry software such as the Geometer’s Sketchpad to reinforce the understanding of graphs of quadratic functions.
Steps to sketch quadratic graphs:a) Determining the form“” or “”b) finding maximum or minimum point and axis of symmetry. c) finding the intercept with x-axis and y-axis.d) plot all points e) write the equation of the axis of symmetry
Emphasise the marking of maximum or minimum point and two other points on the graphs drawn or by finding the axis of symmetry and the intersection with the y-axis.Determine other points by finding the intersection with the x-axis (if it exists).
4. Understand and use the concept of quadratic inequalities.
4.1 Determine the ranges of values of x that satisfies quadratic inequalities.
Use graphing calculators or dynamic geometry software such as the Geometer’s Sketchpad to explore the concept of quadratic inequalities.
Emphasise on sketching graphs and use of number lines when necessary.
1. Solve simultaneous equations in two unknowns: one linear equation and one non-linear equation.
1.1 Solve simultaneous equations using the substitution method.
Use graphing calculators or dynamic geometry software such as the Geometer’s Sketchpad to explore the concept of simultaneous equations.Value: systematicSkills: interpretation of mathematical problem
Limit non-linear equations up to second degree only.
5.3 Determine whether two straight lines are perpendicular when the gradients of both lines are known and vice versa.
5.4 Determine the equation of a straight line that passes through a fixed point and perpendicular to a given line.
5.5 Solve problems involving equations of straight lines.
Students to be exposed to SPM exam type of questions.
Values : hard work, cooperative
Pedagogy : Mastery learning
Emphasise that for perpendicular lines
.
Derivation of is not required.
6 Understand and use the concept of equation of locus involving distance between two points.
6.1 Find the equation of locus that satisfies the condition if:
a)the distance of a moving point from a fixed point is constant;
b) the ratio of the distances of a moving point from two fixed points is constant
6.2 Solve problems involving loci.
Use examples of real-life situations to explore equation of locus involving distance between two points.Use graphic calculators and dynamic geometry software such as the Geometer’s Sketchpad to explore the concept of parallel and perpendicular lines.
Value : Patience, hard workingPedagogy: contextual learningSkill : drawing relevant diagrams
Use dynamic geometry software such as the Geometer’s Sketchpad to explore the concept of circular measure.Students measure angle subtended at the centre by an arc length equal the length of radius. Repeat with different radius.Skill : contextual learningValue : Accurate, making conclusion.
Discuss the definition of one radian.“rad” is the abbreviation of radian.Include measurements in radians expressed in terms of π.
rad = 1800
2. Understand and use the concept of length of arc of a circle to solve problems.bulatan
2.1 Determine:
i) length of arc;
ii) radius; and
iii) angle subtended at the centre of a circle
based on given information.
Use examples of real-life situations to explore circular measure.Derivation of S = j θ by use of ratio or by deduction using definition of radian.Skill : Making conclusion or deduction, application of formula
Major and minor arc lengths discussed
Emphasize that the angle must be in radian.Students can also use formula
2. Understand and use the concept of logarithms and laws of logarithms to solve problems.
2.1 Express equation in index form to logarithm form and vice versa.
2.2 Find logarithm of a number
Use scientific calculators to enhance the understanding of the concept of logarithm.Explain definition of logarithm.N = ax; loga N = x with a > 0, a ≠ 1.
Value : systematic, abide by the laws
Pedagogy:Mastery learning
Emphasise that:loga 1 = 0; loga a = 1.
Emphasise that:a) logarithm of negative numbers
is undefined;b) logarithm of zero is undefined.Discuss cases where the given number is in:a) index formb) numerical form.
2.3 Find logarithm of numbers by using laws of logarithms
2.4 Simplify logarithmic expressions to the simplest form.
Activities : DemonstrationValue : systematic and organised
Skill : recognising pattern and relationship, application of laws
Discuss laws of logarithms
3 Understand and use the change of base of logarithms to solve problems.
3.1 Find the logarithm of a number by changing the base of the logarithm to a suitable base.
Aktivities : DemonstrationPedagogy: Mastery learning, problem solving
Discuss:
3.2 Solve problems involving the change of base and laws of logarithms.
Aktivities : DemonstrationPedagogy: Mastery learning, problem solving.
4. Solve equations involving indices and logarithms
4.1 Solve equations involving indices.
Aktivities : Demonstration
Pedagogy: Mastery learning
, problem solving.
Equations that involve indices and logarithms are limited to equations with single solution only. Solve equations involving indices by: a) comparison of indices and
bases;b) using logarithms.
. 4.2 Solve equations involving logarithms.
Additional/reinforcement Exercises on this topic
Values : Systematic & logical thinking
Topic S1: Statistics ---4 Weeks
1 Understand and use the concept of measures of central tendency to solve problems.
1.1 Calculate the mean of ungrouped data.
1.2 Determine the mode of ungrouped data.
1.3 Determine the median of ungrouped data
1.4Determine the modal class of grouped data from frequency distribution tables.
1.5 Find the mode from histograms.
1.6 Calculate the mean of grouped data
1.7 Calculate the median of grouped data from cumulative frequency distribution tables.
Use scientific calculators, graphing calculators and spreadsheets to explore measures of central tendency.
Students collect data from real-life situations to investigate measures of central tendency.Eg. 1) Length of leaves in school compound2). Marks for Add maths in the class.
1.8 Estimate the median of grouped data from an ogive
1.9 Determine the effects on mode, median and mean for a set of data when:
i) each data is changed uniformly;
ii) extreme values exist;
iii) certain data is added or removed
1.10 Determine the most suitable
measure of central tendency for given data.
2. Constructivism3. Multiple intelligence
Skills : Classification; observing relationship, course and effect, able to analise and make conclusion
Ogive is also known as cumulative frequency curve.
Involve grouped and ungrouped data
2. Understand and use the concept of measures of dispersion to solve problems.
2.1 Find the range of ungrouped data.
2.2 Find the interquartile range of ungrouped data.
2.3 Find the range of grouped data
Activities : 1. Teacher gives real life examples where values of mean, mode adn medium are more or less the same and not sufficient to determine the consistency of the data and that lead to the need of finding measures of dispersion
2.4 Find the interquartile range of grouped data from the cumulative frequency table
Values :1. Honest2. cooperative
Determine the upper and lower quartiles by using the first principle.
Use dynamic geometry software such as the Geometer’s Sketchpad to explore the concept of areas of triangles.Skills : Recognising RelationshipAnalising data Use examples of real-life situations to explore area of triangles.
Value : Systematic
Topic ASS1: INDEX NUMBER---1 week
1. Understand and use the concept of index number to solve problems
1.1 Calculate index number.1.2 Calculate price index.
Find Q0 or Q 1 given relevant information.
Use examples of real-life situations to explore index numbers.Skill : Analise, problem solvingValue : Systematic Q0 = Quantity at base time.
Q1 = Quantity at specific time.
2. Understand and use the concept of composite index to solve problems
2.1 Calculate composite index.2.2 Find index number or weightage given relevant information.
2.3 Solve problems involving index number and composite index.
Additional Exercises or past year questions
Use examples of real-life situations to explore composite index. Eg Composite index of share.
Skill : Analise, problem solvingValue : Systematic
3. Understand and use the concept of maximum and minimum values to solve problems.
3.1 Determine coordinates of turning points of a curve.
3.2 Determine whether a turning point is a maximum or a minimum point.
3.3 Solve problems involving maximum or minimum values.
Use graphing calculators or dynamic geometry software to explore the concept of maximum and minimum values Pedagogy : Constructivism
Skills : Interpretation of problem; Application of approprate method/formula
Emphasise the use of first derivative to determine the turning points.Limit problems to two variables only.Exclude points of inflexion.
Limit problems to two variables only
4. Understand and use the concept of rates of change to solve problems.
4.1 Determine rates of change for related quantities.
Use graphing calculators with computer base ranger to explore the concept of rates of change.Skills : Interpretation of problem; Application of approprate method/formula
Limit problems to 3 variables only.
5. Understand and
use the concept of small changes and approximations to solve problems.
5.1 Determine small changes in quantities
5.2 Determine approximate values using differentiation.
Skills : Interpretation of problem; Application of approprate method/formula
Exclude cases involving percentage change.
6. Understand and use the concept of second derivative to solve problems.
6.1 Determine the second derivative of .
6.2 Determine whether a turning point is maximum or minimum point of a curve using the second derivative