ytp additional mathematics form 4

8/14/2019 YTP Additional Mathematics Form 4

1/9

SMK Dato Zulkifli Muhammad, Slim River, Perak

1

YEARLY TEACHING PLAN ADDITIONAL MATHEMATICS FORM 4

SyllabusWeek Learning Objective Learning Outcomes

Suggested Teaching and LearningActivities

Functions

1.1Understand the conceptof relations.

(i) Represent a relation using :

a) arrow diagrams

b) ordered pairs

c) graphs

(ii) Identify domain, codomain, object, image

and range of a relation.

(iii) Classify a relation show on a mapped

diagram as: one to one, many to one, one to

many or many to many relation.

Use pictures, role-play andcomputer software to introduce the

concept of relations.

1.2Understand the conceptof functions.

(i) Recognise functions as a special relation.(ii) Express functions using function notation.(iii) Determine domain, object, image and range of a function.(iv) Determine image of a function given the objects and vice versa. Use graphing calculator and

computer software to explore the

image of a function.

1.3Understand the conceptof composite functions

(i) Determine composition of two functions.(ii) Determine image of composite functions given the object and vice

versa.

(iii) Determine one of the functions in a given composite function given theother related function.

Use arrow diagrams or algebraicmethod to determine composite

functions.

3 Weeks

22/1 9/2

1.4Understand the conceptof inverse functions.

(i) Find object by inverse mapping given its image and function.(ii) Determine inverse function using algebra.(iii) Determine and state the condition for existence of an inverse function. Use sketches of graphs to show therelationship between a function

and its inverse.

2 Weeks

12/2

23/2

Quadratic

Equation

2.1 Understand the concept

of quadratic equation

and its roots.

(i) Recognise quadratic equation and express it in general form.(ii) Determine whether a given value is the root of a quadratic equation by:

a) substitution

Use graphing calculator orcomputer software such as the

Geometers Sketchpad and


2/9


2

b) Inspection.

(iii) Determine roots of a quadratic equation by trial and improvementmethod.

spreadsheet to explore the concept

of quadratic equations.


of quadratic equations.

(i) Determine the roots of a quadratic equation by:a)factorisationb)completing the squarec)using the formula.

(ii) Form a quadratic equation from given roots.2.3 Understand and use the

conditions for quadratic

equation to have

a) two different roots.

b) two equal roots.

c) no roots.

(i) Determine types of roots of quadratic equations from the value ofacb 42

(ii)

Solve problems involving acb 4

2

in quadratic equations toa) find an unknown value,b) derive a relation.

26/2

28/2UJIAN RASMI 1

Quadratic

Functions


of quadratic functionsand their graphs.

(i) Recognise quadratic functions.(ii) Plot quadratic function graphs

a) based on given tabulated values;b) by tabulating values based on given functions.

(iii) Recognise shapes of graphs of quadratic functions.(iv) Relate the position of quadratic function graphs with types of roots for

f(x) = 0.

Use graphing calculator orcomputer software such as theGeometers Sketchpad to explore

the graphs of quadratic functions.

Use examples of everydaysituations to introduce graphs of

quadratic functions.

3.2 Find maximum and

minimum values of


(i) Determine the maximum or minimum value of a quadratic function bycompleting the square.

Use graphing calculator ordynamic geometry software such

as the Geometers Sketchpad toexplore the graphs of quadratic

functions.

2 Weeks

5/3 23/3

3.3 Sketch graphs of


(i) Sketch quadratic function graphs by determining the maximum orminimum point and two other points.


as the Geometers Sketchpad to

reinforce the understanding of


3/9


3

graphs of quadratic functions.

3.4 Understand and use the

concept of quadraticinequalities.

(i) Determine the ranges of values of x that satisfies quadratic inequalities. Use graphing calculator ordynamic geometry software suchas the Geometers Sketchpad to

explore the concept of quadratic

inequalities.

10/3

18/3CUTI PERTENGAHAN PENGGAL 1

1 Weeks

26/3

30/3

Simultaneous

Equation

4.1 Solve simultaneous

equation in two

unknowns one linear

equation and one non-

linear equation.

(i) Solve simultaneous equations using the substitution method.(ii) Solve simultaneous equations involving real-life situations.



explore the concept of

simultaneous equations.

Use examples in real-life situationssuch as area, perimeter and others.

10/4

12/4UJIAN RASMI 2

Indices and

Logarithms


concept of indices and

laws of indices to

solve

problems.

(i) Find the values of numbers given in the form of;a) integer indicesb) fractional indices

(ii) Use laws of indices to find the values of numbers in index form thatare multiplied divided, or raised to a power.

(iii) Use laws of indices to simplify algebraic expressions.

Use examples in real-life situationsto introduce the concept of indices.

Use computer software such as thespreadsheet to enhance the

understanding of indices.


concept of logarithms

and laws of logarithmsto solve problems.

(i) Express equation in index form to logarithm form and vice versa.(ii) Find logarithm of a number.(iii) Find logarithm of numbers by using laws of logarithm.(iv) Simplify logarithmic expressions to the simplest form.

Use scientific calculator toenhance the understanding of the

concept of logarithm.


change of base of

logarithms to solve

problems.

(i) Find the logarithm of a number by changing the base of the logarithm toa suitable base.

(ii) Solve problems involving the change of base and laws of logarithms.

3 Weeks

16/4 4/5

5.4 Solve equations (i) Solve equations involving indices.


4/9


4

involving indices and

logarithms.

(ii) Solve equations involving logarithms.7/5 18/5

REVISION AND PREPARATION FOR MID YEAR EXAMINATIONS15/55/5 PEPERIKSAAN PERTENGAHAN TAHUN

26/5-10/ 6 CUTI PERTENGAHAN TAHUNCoordinate

Geometry

6.1 Find distance between

two points.

(i) Find distance between two points using formula. Use examples of real-life situationsto find the distance between two

points.


of division of a line

segment.

(i) Find midpoint of two given points.(ii) Find coordinates of a point that divides a line according to a given ratio

m : n.

6.3 Find areas of polygons. (i) Find area of a triangle based on the area of specific geometrical shapes.(ii) Find area of a triangle y using formula.(iii) Find area of a quadrilateral using formula.

Use dynamic geometry softwaresuch as the Geometers Sketchpad

to explore the concept of area of

polygons.

Use4321

1321

21

yyyy

xxxx

for substitution

of coordinates into the formula.


concept of equation of a

straight line.

(i) Determine thex-intercept and they-intercept of a line.(ii) Find the gradient of a straight line that passes through two points.(iii) Find the gradient of a straight line using thex-intercept andy-intercept.(iv) Find the equation of a straight line given;

a) gradient and one point;b) two points;c) x-intercept andy-intercept.

(v) Find the gradient and the intercepts of a straight line given the equation.(vi) Change the equation of a straight line to the general form.(vii)Find the point of intersection of two lines.

a) Use dynamic geometry softwaresuch as the Geometers Sketchpad

to explore the concept of equation

of a straight line.

3 Weeks

11/6

29/6


concept of parallel and

perpendicular lines.

(i) Determine whether two straight lines are parallel when gradients of bothlines are known and vice versa.

(ii) Find the equation of a straight line that passes through a fixed point andparallel to a given line.

Use examples of real-life situationsto explore parallel and



5/9


5

(iii) Determine whether two straight lines are perpendicular when gradientsof both lines are known and vice versa.

(iv) Determine the equation of a straight line that passes through a fixedpoint and perpendicular to a given line.

(v) Solve problems involving equations of straight lines.

Use graphic calculator anddynamic geometry software such

as Geometers Sketchpad toexplore the concept of parallel and



concept of equation of

locus involving

distance

between two points.

(i) 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.

(ii) Solve problems involving loci.

Use examples of real-life situationsto explore equation of locus

involving distance between two

points.

Use graphic calculator anddynamic geometry software such


explore the concept of parallel and


Statistics


concept of measures of

central tendency to

solve problems.

(i) Calculate mean of ungrouped data.(ii) Determine mode of ungrouped data.(iii) Determine median of ungrouped data.(iv) Determine modal class of grouped data from the frequency distribution

table.(v) Find mode from histogram.(vi) Calculate mean of grouped data.(vii)Calculate median of grouped data from the cumulative frequency

distribution table.

(viii) Estimate median of grouped data from an ogive.(ix) Determine the effects on mode, median and mean for a set of data when:

a) each data is changed uniformly,b) extreme values exist,c) certain data is added or removed.

(x) Determine the most suitable measure of central tendency for givendata.

Use scientific calculator, graphingcalculators and spreadsheets to

explore measures of central

tendency.

Students collect data from real-lifesituations to investigate measures

of central tendency.

3 Weeks

2/7 20/7


concept of measures of

dispersion to solve

problems.

(i) Find the range of ungrouped data.(ii) Find the interquartile range of ungrouped data.(iii) Find the range of grouped data.(iv) Find the interquartile range of grouped data from the cumulative


6/9


6

frequency table.

(v) Determine the interquartile range of grouped data from an ogive.(vi) Determine the variance of

a) ungrouped data;b) grouped data.

(vii)Determine standard deviation ofa) ungrouped datab) grouped data

(viii) Determine the effects on range, interquartile range, variance andstandard deviation for a set of data when

a) each data is changed uniformly,b) extreme values exist,c) certain data is added or removed.

(ix) Compare the measures of central tendency and dispersion between twosets of data.

24/7

26/7UJIAN RASMI 3

Circular

Measures

8.1 Understand theconcept of radian.

(i) Convert measurements in radians to degrees and vice versa. Use dynamic geometry softwaresuch as Geometers Sketchpad to

explore the concept of circular

measure.


concept of length of

arc of a circle to solve

problems.

(i) Determine:a) length of arcb) radius andc) angle subtended at the centre of a circle based on given

information.(ii) Find perimeter of segments of circles(iii) Solve problems involving lengths of arcs.

Use examples of real-lifesituations to explore circular

measure.

3 Weeks

30/7

17/8


concept of area of

sector of a circle to

solve problems.

(i) Determine:b) area of sectorc) radius andd) angle subtended at the centre of a circle based on given

information.


7/9


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(ii) Find area of segments of circles.(iii) Solve problems involving area of sectors.

18/8

26/8 CUTI PERTENGAHAN PENGGAL 2Differentiation


concept of gradients of

curve and

differentiation

(i) Determine value of a function when its variable approaches a certainvalue.

(ii) Find gradient of a chord joining two points on a curve.(iii) Find the first derivative of a functiony = f(x) as gradient of tangent to

its graph.

(iv) Find the first derivative for polynomial using first principles.(v) Deduce the formula for first derivative of functiony = f(x) by induction.


as Geometers Sketchpad to

explore the concept of

differentiation.


concept of first

derivative of

polynomial functions

to solve problems.

(i) Determine first derivative of the function naxy = using formula.(ii) Determine value of the first derivative of the function naxy = for a

given value ofx.

(iii) Determine first derivative of a function involving:a) addition, orb) subtraction of algebraic terms.

(iv)

Determine first derivative of a product of two polynomials.(v) Determine first derivative of a quotient of two polynomials.(vi) Determine first derivative of composite function using chain rule.(vii)Determine gradient of tangent at a point on curve.(viii)Determine equation of tangent at a point on a curve.

Determine equation of normal at a point on a curve.


concept of maximum

and minimum values

to solve problems.

(i) Determine coordinates of turning points of a curve.(ii) Determine whether a turning point is a maximum or minimum point.(iii) Solve problems involving maximum or minimum values.

Use graphing calculator ordynamic geometry software to

explore the concept of maximum

and minimum values.


concept of rates of

change to solve

problems

(i) Determine rates of change for related quantities. Use graphing calculator withcomputer base ranger to explore

the concept of rates of change.

4 Weeks

27/8

21/9


concept of small

changes and

(i) Determine small changes in quantities.(ii) Determine approximate values using differentiation.


8/9


8

approximations to

solve problems.


concept of second

derivative to solve

problems.

(i) Determine second derivative of function )(xfy = .(ii) Determine whether a turning point is maximum or minimum point of a

curve using the second derivative.

Solution of

Triangles

10.1 Understand and use

the concept of sine

rule to solve

problems.

(i) Verify sine rule.(ii) Use sine rule to find unknown sides or a triangle(iii) Find unknown sides and angles of a triangle in a ambiguous case.(iv) Solve problems involving sine rule.


to explore the sine rule.

Use examples of real-life situationsto explore the sine rule.


the concept of cosine

rule to solve

problems.

(i) Verify cosine rules.

(ii) Use cosine rule to find unknown sides or angles of a triangle.

(iii)Solve problem involving cosine rule.

(iv)Solving problems involving sine and cosine rules.


to explore the cosine rule.

Use examples of real-life situationsto explore the cosine rule

2 Weeks

24/9

5/10


the formula for areaof triangles to solve

problems.

(i) Find area of triangles using formula Cabsin2

1

or its equivalent.

(ii) Solve problems involving three-dimensional objects.


to explore the concept of area

triangles.

Use examples of real-life situationsto explore area of triangles.

Index Number


the concept of indexnumber to solve

problems.

(i) Calculate index number.(ii)Calculate price index(iii) Find oQ or 1Q given relevant information.

Use examples of real-life situationsto explore index numbers.

1 Week

8/10

12/10


the concept of

composite index to

solve problems.

(i) Calculate composite index.

(ii) Find index number or weightage given relevant information.

(iii) Solve problems involving index number and composite index. Use examples of real-life situations

to explore composite index.

15/10 REVISION AND PREPARATION FOR THE END OF THE YEAR EXAMINATIONS


9/9


9

31/10

1/11

16/11END OF THE YEAR EXAMINATION

ytp additional mathematics form 4

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