Ylp Maths f4
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Transcript of 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
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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
- working out mentally
- identifying relations
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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
- arranging sequentially
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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
- arranging sequentially
- classifying
- translating
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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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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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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
- identifying relations
- 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
- identifying relations
- 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
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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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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”
- Working out mentally
- 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”
- working out mentally
- 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
- working out mentally
- 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
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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
- comparing and differentiating
- working out mentally
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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
- comparing and differentiating
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given point and is parallel to another straight line
iv. solve problems involving equations of straight lines
[PEPERIKSAAN PENGGAL 1]
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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
- working out mentally
- 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
- Working out mentally
- Making inferences
- Identifying relations
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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
- working out mentally
- 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
- identifying relations
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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
- Finding all possible solutions
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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.
- identifying relations
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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
- Working out mentally
- Drawing diagrams
- Identifying relations
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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
- identifying relations
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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
- comparing and differentiating
- Finding all possible solutions
- Identifying relations
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tangents and common tangent
[PEPERIKSAAN PERTENGAHAN PENGGAL 2]
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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)
- working out mentally
- interpreting
- identifying relations
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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]
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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
- comparing and differentiating
- 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
- working out mentally
- 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
- Working out mentally
- Identifying relations
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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
- working out mentally
- drawing diagrams
- identifying relations
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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
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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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