RPT Math Form4 2011

RPT Math Form 4

By tjgan Week/

Date

Learning

Area

Learning Objectives Learning Outcomes CCTS Remarks

1

4/1-8/1/10

Chapter 1: Standard Form

1.1 Understand and use the concept of significant figure

Students will be able to:

1. round off positive numbers to a given number of significant figures when the numbers are:

a) greater than 1

b) less than 1

1. 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

- contextual

- working out mentally

- finding all possible solutions

- identifying relations

2

11/1-15/1/10

1.2 Understand

and use the concept of standard form to solve problem

1. state positive numbers in standard form when the numbers are:

a) greater than or equal to 10

b) less than 1

1. convert numbers in standard form to single numbers

2. perform operations of addition,



subtraction, multiplication and division, involving any two numbers and state the answers in standard form

3. solve problems involving numbers in standard form

3

18/1-22/1/10

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

1. 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

-

4

25/1/-29/1/10

2.3 Understand the concept of Quadratic Equation

iii Factorise quadratic expressions of the form ax2+ bx +

c, where a, b and c not equal to zero

iv Factorise quadratic expressions containing



- classifying

-

coefficients

with common factors

1. Identify quadratic equations with one unknown

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

ax2 + bx + c = 0

1. Form quadratic equations based on specific situations

- translating

5

1/2-5/2/10

2.4 Understand the concept of Roots of quadratic equations

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

2. determine the solutions for quadratic equations by:

a) trial and error method

b) factorization

iii. solve problems involving quadratic equation

- comparing & differentiating

finding all possible solutions

6

8/2-12/2/10

Chapter 3: Sets

3.1 Understand the concept of Set

1. sort given objects into groups2. define sets by

a) descriptions

- making generalizations


classifying

-

b)using set notation

iii identify whether a given object is an element of a set

and use the symbol or

iv. represent sets by using Venn diagrams

v. list the elements and state the number of elements of a set

vi. determine whether a set is an empty set

vii. determine whether two sets are equal

-comparing and differentiating

7

14/2-21/10

CUTI TAHUN BARU CINA

8

22/2-26/2/10

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

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

2. represent subset by using Venn diagram3. list the subsets for a specific set4. illustrate the relationship between set and

universal set using Venn diagram5. determine the complement of a given set6. determine the relationship between set,

subset,

universal set and the complement of a set

- classifying

- finding all possible solutions

- drawing diagrams


- interpreting

9 3.3 Perform Operations on set

1. determine the intersection of - comparing and differentiating

-

10

1/3-12/3/10

a) two sets

b) three sets

and use the symbol

1. represent the intersection of sets using Venn diagram

2. state the relationship between

a) and A

b) and B

1. determine the complement of the intersection of sets

2. solve problems involving the intersection of sets.

3. determine the union of

a) two sets

b) three sets

and use the symbol

vii. represent the union of sets using Venn diagram

viii.state the relationship between

- drawing diagrams


- interpreting

- translating

- making generalization

a) and A

b) and B

1. determine the complement of the union of sets

2. solve problems involving the union of sets3. determine the outcome of combined

operations on sets

xii. solve problems involving combined operations on sets

CUTI PERTENGAHAN PENGGAL 1 [ 13-21 MAC 2010]

12

22/3-26/3/10

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

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

- Classifying

- Working out mentally

- Translating

- Interpreting

-

12 4.2 Understand the concept of Quantifiers “all” and “some”

i. construct statements using quantifier

a) all


- Identifying relations

-

b) some

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

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

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

13

29/3-2/4/10

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”

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

2. 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”

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


- classifying

-

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

13

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”

1. construct mathematical statements in the form of implication:

a) If p, then q

b) p if and only if q

1. determine the converse of a given implication

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


- classifying

-

14

5/4-9/4/10

4.5 Understand the concept of Argument

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

2. make a conclusion based on two given premises for:

a) Argument Form I

b) Argument Form II

c) Argument Form III

- Classifying

- Making inferences

-

1. complete an argument given a premise and the conclusion

14

4.6 Understand and use the concept of Deduction and Induction

1. determine whether a conclusion is made through:

a) reasoning by deduction

b) reasoning by induction

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

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

3. use deduction and induction in problem solving

- classifying

- making inferences

- making generalization

- looking for patterns

- making analogy

-

15

12/4-16/4/10

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 -

15

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

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

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

3. determine the relationship between the value of the gradient and the:

- interpreting

- classifying

-

a) steepness

b) direction of inclination

of a straight line

16

19/4-23/4/10

5.3 Understand the concept of intercept

1. determine the x-intercept and the y-intercept of a straight line

2. derive the formula for the gradient of a straight line in terms of the x-intercept and the y-intercept

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

- interpreting -

17

26/4-30/4/10

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

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

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

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

4. determine the gradient and y-intercept of the straight line which equation is of the form:

a) y = mx + c

b) ax + by = c

1. find the equation of the straight line which:

a) is parallel to the x-axis

- drawing diagrams

- comparing and differentiating


-

b) is parallel to the y-axis

c) passes through a given point and has a specific gradient

d) passes through two given points

1. find the point of the intersection of two straight lines by:

a) drawing the two straight lines

e) solving simultaneous equations18

3/5-7/5/09

19

10/5-114/5/10

5.5 Understand and use the concept of Parallel line

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

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

3. find the equation of the straight line which passes through a given point and is parallel to another straight line

4. solve problems involving equations of straight lines

ULANGKAJI

PEPERIKSAAN PENGGAL 1 [ ]


(WEEK 20-21)

CUTI GAWAI– [ 31/5-6/6 ]

(WEEK 22)

CUTI PERTENGAHAN TAHUN [7-20 JUN20 10]

(WEEK 23-24)

25

21/6-25/6/10

Chapter 6: Statistics

6.1 Understand the concept of class Interval

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

2. determine:

a) the upper limit an lower limit

b) the upper boundary and lower boundary

of a class in a group data

1. calculate the size of a class interval


- classifying

- making inferences

-

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

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

3. construct a frequency table for given set

of data

25

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

i. determine the modal class from the frequency table of grouped data

1. calculate the midpoint of a class2. verify the formula for the mean of

grouped data3. calculate the mean from the frequency

table of grouped data4. discuss the effect of the size of class

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

- Interpreting


- Making inferences


-

25

6.3 represent and interpret data in histograms with class intervals

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

2. interpret information from given histogram

3. solve problems involving histograms

- drawing diagrams

- interpreting

-

26

28/6-2/7/10

6.4Represent and interpret data in Frequency polygons to solve problem

1. draw the frequency polygon based on:

a) a histogram

b) a frequency table

1. interpret information from a given frequency polygon

2. solve problems involving frequency polygon

- drawing diagrams

- interpreting

-

26 6.5 Understand the 1. construct the cumulative frequency table - working out -

concept of Cumulative frequency

for:

a) ungrouped data

b) grouped data

1. draw the ogive for:

a) ungrouped data

b) grouped data

mentally

- drawing diagrams

27

5/7-9/7/10

6.6Understand and use the concept of Measures of dispersion

1. determine the range of a set data2. determine:

a) the median

b) the first quartile

c) the third quartile

d) the interquartile range

from the ogive

1. interpret information from an ogive2. solve problems involving data

representations and measures of dispersion

- interpreting


-

27 Chapter 7: Probability I

7.1Understand the concept of Sample space

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

- Finding all possible solutions

-

ii. list all the possible outcomes of an experiment:

a) from activities

b) by reasoning

iii determine the sample space of an experiment

iv write the sample space by using set notations 28

12/7- 16/7/10

7.2 Understand the concept of Events

1. 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


-

28 7.3Understand and use the concept of Probability of an event

1. 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 trials

1. solve problems involving probability2. predict the occurrence of an outcome and

make a decision based on known information


-

v.

29

19/7-23/7/10

Chapter 8:

Circles III

8.1 Understand and use the concept of Tangents of a circle

1. 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 circle

b) outside the circle

iv. determine the properties related to two tangents to a circle from a given point outside the circle

v. solve problems involving tangents to a circle


- Drawing diagrams


-

29

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

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

2. 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

3. perform calculations involving the angle in alternate segment

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


-

30

26/7-30/7/10

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

1. determine the number of common tangents which can be drawn to two circles which:

a) intersect at two points

b) intersect only at one point

c) do not intersect

1. determine the properties related to the common tangent to two circles which:

a) intersect at two points

b) intersect only at one point

c) do not intersect

1. solve problems involving common tangents to two circles

2. solve problems involving tangents and common tangent




-

31

2/8-6/8/10

Chapter 9:

Trigonometry II

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

1. identify the quadrants and angles in the unit circle

2. determine:

a) the value of y-coordinate

b) the value of x-coordinate


- interpreting


-

c) the ratio of y-coordinate to x-coordinate

of several points on the circumference of the unit circle

1. verify that, for an angle in quadrant I of the unit circle:

a)

b)

c)

1. determine the value of:

a) sine

b) cosine

c) tangent

of an angle in quadrant I of the unit circle

1. determine the values of:

a) sin θ

b) cos θ

c) tan θ

32

3/8-7/8/09

for

1. determine whether the values of:

a) sine

b) cosine

c) tangent

of an angle in a specific quadrant is positive or negative

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

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

1. State the relationships between the values of:

a) sine

b) cosine, and

c) tangent

of angles in quadrant II, III and IV with their respective values of the corresponding angle in

quadrant I

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

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

3. Solve problems involving sine, cosine and tangent

33

16/8-20/8/10

9.2Draw and use Graphs of sine, cosine and tangent

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

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

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

- drawing diagrams


- interpreting

-

34

23/8-27/8/10

35

36

Chapter 10: Angles of Elevation and Depression

10.1Understand and use the concept of Angle of elevation and angle of depression

1. identify:

a) the horizontal line

b) the angle of elevation

c) the angle of depression

1. represent a particular situation involving

a) the angle of elevation

b) the angle of depression, using diagrams


- drawing diagrams


1. solve problems involving the angle of elevation and the angle of depression

second mid semester Test

CUTI PERTENGAHAN PENGGAL 2 [24-30 OGOS]

37

13/9-17/9/10

Chapter 11: Lines and Planes in 3-dimensions

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

1. identify planes2. identify horizontal planes, vertical planes

and inclined planes3. sketch a three dimensional shape and

identify the specific planes4. identify5. identify normals to a given plane6. determine the orthogonal projection of a

line on a plane7. draw and name the orthogonal projection

of line on plane8. determine the angle between a line and a

plane

solve problems involving the angle between a line and a plane

- Comparing and differentiating



-

38,39

20/9-1/10/10

11.2Understand and the concept of Angle between two planes

1. identify the line of intersection between two planes

2. 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

3. determine the angle between two planes


- drawing diagrams


-

on a model and a given diagram

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

40,41,42

4/10- 22/10/10

ULANGKAJI

- - Revision

PEPERIKSAAN PENGGAL II [

]-

Documents

RPT Math Form4 2011