ylp maths f4

SMK LUTONG SEKOLAH KLUSTER KECEMERLANGANYEARLY TEACHING PLAN – 2014

MATHEMATICS FORM 41 A expression 1 Circle2 L eqution 2 Solid geometry3 A formulae 3 Simultaneous l eqn4 Poligon 15 Transformatio

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1. Standard form2. Quadratic eqn 3. Set4. M reasoning5. S line6. Statistic7. Probability 18. Circle9 Trigo

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Angle o ele dan depre

11.

Line and planes in 3d

Week/Date

LearningArea

Learning Objectives

Learning Outcomes CCTS Remarks

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2/1

Chapter 1: Standard Form

1.1Understand and use the concept of significant figure

Students will be able to:i. round off positive numbers to a

given number of significant figures when the numbers are:a) greater than 1

- contextual

- working out mentally

- finding

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b) less than 1ii. perform operations of addition,

subtraction, multiplication and division, involving a few numbers and state the answer in specific significant figures

iii. solve problems involving significant figure

all possible solutions

- identifying relations

1.2Understand and use the concept of standard form to solve problem

i. state positive numbers in standard form when the numbers are:a) greater than or equal to 10b) less than 1

ii. convert numbers in standard form to single numbers

iii. perform operations of addition, subtraction, multiplication and division, involving any two numbers and state the answers in standard form

iv. solve problems involving numbers in standard form



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14/1

Chapter 2: Quadratic Expressions and Equations

2.1 Understand the concept of Quadratic Expression

2.2 Factorization quadratic expression

i. Identify quadratic expressions

ii. Form quadratic expressions by multiplying any two linear expressions

iii. Form quadratic expressions based on specific situations

i Factorise quadratic expressions of the form ax2+bx+c=0, where b= 0 or c= 0 ii Factorise quadratic expressions of the form px2 – q, p and q are the perfect squares

- classifying

- arranging sequentially

- translating

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iii Factorise quadratic expressions of the form ax2+ bx + c, where a, b and c not equal to zero


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2.3 Understand the concept of Quadratic Equation

iv Factorise quadratic expressions containing coefficients with common factors

i. Identify quadratic equations with one unknown

ii. Write quadratic equations in general form i.e.

ax2 + bx + c = 0iii. Form quadratic equations based

on specific situations


- classifying

- translating

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28/1

2.4 Understand the concept of Roots of quadratic equations

i. determine whether a given value is a root of a specific quadratic equation

ii. determine the solutions for quadratic equations by:a) trial and error methodb) factorization

iii. solve problems involving quadratic equation

- comparing & differentiatingfinding all possible solutions

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4/2

Chapter 3: Sets

3.1 Understand the concept of Set

i. sort given objects into groups

ii. define sets bya) descriptionsb) using set notation

iii identify whether a given object is an element of a set and use the symbol oriv. represent sets by using Venn diagramsv. list the elements and state the number of elements of a setvi. determine whether a set is an empty setvii. determine whether two sets are equal

- making generalizations

- working out mentallyclassifying

-comparing and differentiating

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17/2/13 CUTI TAHUN BARU CINA

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3.2 Understand and use the concept of Subset, universal set and the complement of a set

i. determine whether a given set is a subset of a specific set and use the symbol or .

ii. represent subset by using Venn diagram

iii. list the subsets for a specific setiv. illustrate the relationship

between set and universal set using Venn diagram

v. determine the complement of a given set

vi. determine the relationship between set, subset, universal set and the complement of a set

- classifying

- finding all possible solutions

- drawing diagrams


- interpreting

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3.3 Perform Operations on set

i. determine the intersection ofa) two setsb) three setsand use the symbol

ii. represent the intersection of sets using Venn diagram

iii. state the relationship betweena) and Ab) and B

iv. determine the complement of the intersection of sets

v. solve problems involving the intersection of sets.

vi. determine the union ofa) two setsb) three setsand use the symbol

vii. represent the union of sets

- comparing and differentiating

- drawing diagrams


- interpreting

- translating

- making generalization

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using Venn diagramviii. state the relationship between

a) and Ab) and B

ix. determine the complement of the union of sets

x. solve problems involving the union of sets

xi. determine the outcome of combined operations on sets

xii. solve problems involving combined operations on sets

1111/3

Chapter 4: Mathematical Reasoning

4.1 Understand the concept of Statement

i. determine whether a given sentence is a statement

ii. determine whether a given statement is true or false

iii. construct true or false statement using given numbers and mathematical symbols

[PEPERIKSAAN PERTENGAHAN PENGGAL 1]

[CUTI PERTENGAHAN PENGGAL PERTAMA]

- Classifying

- Working out mentally

- Translating

- Interpreting

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141/4

4.2 Understand the concept of Quantifiers “all” and “some”

i. construct statements using quantifier

a) allb) some

ii. determine whether a statement that contains the quantifier “all” is true or false

iii. determine whether a statement can be generalized to cover all cases by using the quantifier “all”

iv. construct a true statement using the quantifier “all” or “some” given an object and a property”


- Identifying relations

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4.3 Perform Operations Involving the words “not” or “ no” statements

i. change the truth value of a given statement by placing the word “not” into the original statement

ii. identify two statements from a compound statement that contains the word “and”

iii. form a compound statement by combining two given statements using the word “and”

iv. identify two statement from a compound statement that contains the word “or”

v. form a compound statement by combining two given statements using the word “or”

vi. determine the truth value of a compound statement which is the combination of two statements with the word “and”

vii. determine the truth value of a compound statement which is the combination of two statements with the word “or”


- classifying

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4.4 Understand the concept of Implication

i. identify the antecedent and consequent of an implication “if p, then q”

ii. write two implications from a compound statement containing “if and only if”

iii. construct mathematical statements in the form of implication:a) If p, then qb) p if and only if q

iv. determine the converse of a given implication

v. determine whether the converse of an implication is true or false


- classifying

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4.5 Understand the concept of Argument

i. identify the premise and conclusion of a given simple argument

ii. make a conclusion based on two given premises for:a) Argument Form Ib) Argument Form IIc) Argument Form III

iii. complete an argument given a premise and the conclusion

- Classifying

- Making inferences

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4.6 Understand and use the concept of Deduction and Induction

i. determine whether a conclusion is made through:a) reasoning by deductionb) reasoning by induction

ii. make a conclusion for a specific case based on a given general statement, by deduction

iii. make a generalization based on the pattern of a numerical sequence, by induction

iv. use deduction and induction in problem solving

- classifying

- making inferences

- making generalization

- looking for patterns

- making analogy

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Chapter 5: The Straight Line

5.l Understant the concept of gradient of a straight line

i. determine the vertical and horizontal distances between two given points on a straight line

ii. determine the ratio of vertical distance to horizontal distance

- Interpreting

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5.2 Understant the concept of gradient of a straight line in Cartesian coordinates

i. derive the formula for the gradient of a straight line

ii. calculate the gradient of a straight line passing through two points

iii. determine the relationship between the value of the gradient and the:a) steepnessb) direction of inclinationof a straight line

- interpreting

- classifying

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5.3 Understand i. determine the x-intercept and - interpreti -

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the concept of intercept

the y-intercept of a straight lineii. derive the formula for the

gradient of a straight line in terms of the x-intercept and the y-intercept

iii. perform calculations involving gradient x-intercept and y-intercept

ng

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5.4Understand and use the concept of Equation of a straight line

i. draw the graph given an equation of the form y = mx + c

ii. determine whether a given point lies on a specific straight line

iii. write the equation of the straight line given the gradient and y-intercept

iv. determine the gradient and y-intercept of the straight line which equation is of the form:a) y = mx + cb) ax + by = c

v. find the equation of the straight line which:a) is parallel to the x-axisb) is parallel to the y-axisc) passes through a given point and

has a specific gradientd) passes through two given points

vi. find the point of the intersection of two straight lines by:a) drawing the two straight linese) solving simultaneous equations

- drawing diagrams



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5.5 Understand and use the concept of Parallel line

i. verify that two parallel lines have the same gradient and vice versa

ii. determine from the given equations whether two straight lines are parallel

iii. find the equation of the straight line which passes through a


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given point and is parallel to another straight line

iv. solve problems involving equations of straight lines

[PEPERIKSAAN PENGGAL 1]

2013/5

Chapter 6: Statistics

6.1 Understand the concept of class Interval

i. complete the class interval for a set of data given one of the class intervals

ii. determine:a) the upper limit an lower limitb) the upper boundary and lower

boundaryof a class in a group data

iii. calculate the size of a class interval


- classifying

- making inferences

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iv. determine the class interval, given a set of data and the numbers of classes

v. determine a suitable class interval for a given set of data

i. construct a frequency table for given set of data

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6.2Understand and use the concept of Mode and mean of grouped data

i. determine the modal class from the frequency table of grouped dataii. calculate the midpoint of a classiii. verify the formula for the mean of

grouped dataiv. calculate the mean from the

frequency table of grouped datav. discuss the effect of the size of

class interval on the accuracy of the mean for a specific set of grouped data

[CUTI PERTENGAHAN TAHUN]

- Interpreting


- Making inferences


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6.3 represent and interpret

i. draw a histogram based on the frequency table of a grouped data

- drawing diagrams

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data in histograms with class intervals

ii. interpret information from given histogram

iii. solve problems involving histograms

- interpreting

6.4Represent and interpret data in Frequency polygons to solve problem

i. draw the frequency polygon based on:a) a histogramb) a frequency table

ii. interpret information from a given frequency polygon

iii. solve problems involving frequency polygon

- drawing diagrams

- interpreting

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6.5 Understand the concept of Cumulative frequency

i. construct the cumulative frequency table for:a) ungrouped datab) grouped data

ii. draw the ogive for:a) ungrouped datab) grouped data


- drawing diagrams

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6.6Understand and use the concept of Measures of dispersion

i. determine the range of a set data

ii. determine:a) the medianb) the first quartilec) the third quartiled) the interquartile rangefrom the ogive

iii. interpret information from an ogiveiv. solve problems involving data

representations and measures of dispersion

- interpreting


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Chapter 7: Probability I

7.1Understand the concept of Sample space

i. determine whether an outcome is a possible outcome of an experiment

ii. list all the possible outcomes of an experiment:a) from activitiesb) by reasoning

- Finding all possible solutions

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iii determine the sample space of an experimentiv write the sample space by using set notations

7.2 Understand the concept of Events

i. identify the elements of a sample space which satisfy given conditions

ii. list all the elements of a sample which satisfy certain conditions using set notations

iii determine whether an event is possible for a sample space


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7.3Understand and use the concept of Probability of an event

i. find the ratio of the number of times an event occurs to the number of trials

ii. find the probability of an event from a big enough of trials

iii calculate the expected number of times an event will occur, given the probability of the use event and number of trialsiii. solve problems involving

probabilityiv. predict the occurrence of an

outcome and make a decision based on known information

v.


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Chapter 8:Circles III

8.1 Understand and use the concept of Tangents of a circle

i. identify tangents to a circle

ii. make inference that the tangent to a circle is a straight line perpendicular to the radius that passes through the contact point

iii construct the tangent to a circle passing through a point:

a) on the circumference of the circleb) outside the circle


- Drawing diagrams


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iv. determine the properties related to two tangents to a circle from a given point outside the circlev. solve problems involving tangents to a circle

8.2 Understand and use the properties of Angle between tangent and chord

i. identify the angle in the alternate segment which is subtended by the chord through the contact point of the tangent

ii. verify the relationship between the angle formed by the tangent and the chord with the angle in the alternate segment which is subtended by the chord

iii. perform calculations involving the angle in alternate segment

iv. solve problems involving tangent to a circle and angle in alternate segment


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8.3 Understand and use the properties of common tangents to solve problem

i. determine the number of common tangents which can be drawn to two circles which:a) intersect at two pointsb) intersect only at one pointc) do not intersect

ii. determine the properties related to the common tangent to two circles which:a) intersect at two pointsb) intersect only at one pointc) do not intersect

iii. solve problems involving common tangents to two circles

iv. solve problems involving




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tangents and common tangent

[PEPERIKSAAN PERTENGAHAN PENGGAL 2]

31323435

1/8

Chapter 9:Trigonometry II

9.1 Values of sin θ, cos θ and tan θ .

i. identify the quadrants and angles in the unit circle

ii. determine:a) the value of y-coordinateb) the value of x-coordinatec) the ratio of y-coordinate to x-

coordinateof several points on the circumference of the unit circle

iii. verify that, for an angle in quadrant I of the unit circle:a)b)


- interpreting


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c)iv. determine the value of:

a) sineb) cosinec) tangentof an angle in quadrant I of the unit circle

v. determine the values of:a) sin θb) cos θc) tan θfor

vi. determine whether the values of:a) sineb) cosinec) tangentof an angle in a specific quadrant is positive or negative

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vii. determine the values of sine, cosine and tangent for special angles

viii. determine the values of the angles in quadrant I which correspond to the values of the angles in other quadrants

ix. State the relationships between the values of:a) sineb) cosine, andc) tangentof angles in quadrant II, III and IV with their respective values of the corresponding angle in quadrant I

x. Find the values of sine, cosine and tangent of the angles between 90º and 360º

xi. Find the angles between 0º and 360º, given the values of sine, cosine and tangent

xii. Solve problems involving sine, cosine and tangent

[CUTI PERTENGAHAN PENGGAL 2]

362/9

9.2Draw and use Graphs of sine, cosine and tangent

i. draw the graphs of sine, cosine and tangent for angles between 0º and 360º

ii. compare the graphs of sine, cosine and tangent for angles between 0º and 360º

iii. solve problems involving graphs of sine, cosine and tangent

- drawing diagrams


- interpreting

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Chapter 10: Angles of

10.1Understand and use the concept of Angle

i. identify:a) the horizontal lineb) the angle of elevation


- drawi

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Elevation and Depression

of elevation and angle of depression

c) the angle of depressionii. represent a particular

situation involvinga) the angle of elevationb) the angle of depression, using

diagramsiii. solve problems involving

the angle of elevation and the angle of depression

ng diagrams- identi

fying relations

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Chapter 11: Lines and Planes in 3-dimensions

11.1Understand and use the concept of Angle between lines and planes

i. identify planesii. identify horizontal planes,

vertical planes and inclined planesiii. sketch a three dimensional

shape and identify the specific planesiv. identifyv. identify normals to a given

planevi. determine the orthogonal

projection of a line on a planevii. draw and name the

orthogonal projection of line on planeviii. determine the angle

between a line and a planesolve problems involving the angle between a line and a plane

- Comparing and differentiating



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11.2Understand and the concept of Angle between two planes

i. identify the line of intersection between two planes

ii. draw a line on each plane which is perpendicular to the line of intersection of the two planes at a point on the line of intersection

iii. determine the angle between two planes on a model and a given diagram

iv. solve problems involving lines and planes in 3-dimensional shapes


- drawing diagrams


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NUMBER BASES

1. Understand and use the concept of number in base two, eight and five.

Student will be able toi. State zero, one, two, three,…, as a number in base :a) twob)eightc)fiveii. State the value of a digit of a number in base :a) twob)eightc)fiveiii. Write a number in base :a) twob)eightc)fivein expanded notation.iv. Convert a number in base:a) twob)eightc)five(v) Convert a number in a certain base to a number in another base.(vi) Perform computations involving:

a) additionalb) subtraction

of two numbers in base two.

AnalyzingProblem solvingMaking conclusion working out mentally, find all possible solution, iii)comparing and contrasting

Teaching aids :GSP

Teaching aids :CD courseware

Teaching aids :CD courseware

417/10

8.0 BEARING 8.1 Understand and use the concept of bearing.

i) Draw and label the eight main compass directions: a) North, South, East, Westb) North-East, North-West, South-East, South-

Westii) State the compass angle of any compass direction.iii) Draw a diagram of a point which shows the direction

of B relative to another point A given the bearing of B from A.

iv) State the bearing of point A from point B based on given information.

v) Solve problems involving bearing.

[ULANGKAJI: 14-24/10][PEPERIKSAAN AKHIR TAHUN: 25-31/10]

Identifying RelationsDrawing DiagramsGenerating IdeasTranslating

Teaching AidsComputer/NotebookGSPProtractor

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ylp maths f4

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