rpt maths f4 2015

SMK ..Yearly Lesson Plan MathematicsForm Four

LEARNING AREA/ WEEKLEARNING OBJECTIVESSUGGESTED TEACHING AND LEARNING ACTIVITIESLEARNING OUTCOMENOTES/ I-THINK/ KBAT

Students will be taught to:Students will be able to:

112.1.15 - 16.1.15Orientation week

1 STANDARD FORM219.1.15 - 23.1.15a) understand and use the concept of significant figure;

Discuss the significance of zero in a number.

1. round off positive numbers to a given number of significant figures when the numbers are:2. greater than 1;2. less than 1;

Discuss the use of significant figures in everyday life and other areas.

perform operations of addition, subtraction, multiplication and division, involving a few numbers and state the answer in specific significant figures;

solve problems involving significant figures;Analysing

326.1.15 30.1.15

b) c) understand and use the concept of standard form to solve problems.Use everyday life situations such as in health, technology, industry, construction and business involving numbers in standard form.1. state positive numbers in standard form when the numbers are:a) greater than or equal to 10;b) less than 1;

Use the scientific calculator to explore numbers in standard form.convert numbers in standard form to single numbers;perform operations of addition, subtraction, multiplication and division, involving any two numbers and state the answers in standard form;solve problems involving numbers in standard form.

Analysing

WEEKLEARNING OBJECTIVESSUGGESTED TEACHING AND LEARNING ACTIVITIESLEARNING OUTCOMENOTES/ I-THINK/ KBAT


42.2.15 - 6.2.15UJIAN KEFAHAMAN TINGKATAN 4

2 QUADRATIC EXPRESIONS AND EQUATIONS59.2.15 13.2.15c) understand the concept of quadratic expression;Discuss the characteristics of quadratic expressions of the form, where a, b and c are constants, a 0 and x is an unknown.

1. identify quadratic expressions; 1. form quadratic expressions by multiplying any two linear expressions; 1. form quadratic expressions based on specific situations;

a) b) factorise quadratic expression;Discuss the various methods to obtain the desired product.1. factorise quadratic expressions of the form , where b = 0 or c = 0;

factorise quadratic expressions of the form px2 q, p and q are perfect squares;

Begin with the case a = 1.Explore the use of graphing calculator to factorise quadratic expressions.factorise quadratic expressions of the form , where a, b and c not equal to zero; factorise quadratic expressions containing coefficients with common factors;

616.2.15 20.2.15CUTI TAHUN BARU CINA

723.2.15- 27.2.157. 7. 7. understand the concept of quadratic equation;Discuss the characteristics of quadratic equations.1. identify quadratic equations with one unknown;

(ix) write quadratic equations in general form i.e.

;

(x) form quadratic equations based on specific situations;

Applying



82.3.15 6.3.1510. 10. 10. 10. understand and use the concept of roots of quadratic equations to solve problems.1. determine whether a given value is a root of a specific quadratic equation;

Discuss the number of roots of a quadratic equation.(xii) determine the solutions for quadratic equations by:12. trial and error method;12. factorisation;

Use everyday life situations.(xiii) solve problems involving quadratic equations.

Analysing

3 SETS99.3.15 13.3.1513. understand the concept of set;Use everyday life examples to introduce the concept of set.1. sort given objects into groups;

(xv) define sets by:15. descriptions;15. using set notation;Circle Map

(xvi) identify whether a given object is an element of a set and use the symbol or ;

Discuss the difference between the representation of elements and the number of elements in Venn diagrams.

(xvii) represent sets by using Venn diagrams;

Discuss why { 0 } and { } are not empty sets.(xviii) list the elements and state the number of elements of a set;Circle Map

(xix) determine whether a set is an empty set;

(xx) determine whether two sets are equal;



20. 20. understand and use the concept of subset, universal set and the complement of a set;Begin with everyday life situations.1. determine whether a given set is a subset of a specific set and use the symbol or ;

(xxii) represent subset using Venn diagram;

(xxiii) list the subsets for a specific set;Circle Map

Discuss the relationship between sets and universal sets.(xxiv) illustrate the relationship between set and universal set using Venn diagram;

(xxv) determine the complement of a given set;

(xxvi) determine the relationship between set, subset, universal set and the complement of a set;Bridge Map

CUTI PENGGAL 1 (16.3.15 20.3.15)

1023.3.15 27.3.15

26. 26. 26. perform operations on sets: the intersection of sets; the union of sets.1. determine the intersection of:27. two sets;27. three sets;and use the symbol ;

Discuss cases when: A B = A B(xxviii) represent the intersection of sets using Venn diagram;

(xxix) state the relationship between29. A B and A ;29. A B and B ;

(xxx) determine the complement of the intersection of sets;

(xxxi) solve problems involving the intersection of sets;



(xxxii) determine the union of:32. two sets;32. three sets;and use the symbol ;

(xxxiii) represent the union of sets using Venn diagram;

(xxxiv) state the relationship betweena) A B and A ;b) A B and B ;

(xxxv) determine the complement of the union of sets;

(xxxvi) solve problems involving the union of sets;Analysing

(xxxvii) determine the outcome of combined operations on sets;

(xxxviii) solve problems involving combined operations on sets.

4 MATHEMATICAL REASONING1130.3.15 3.4.1538. understand the concept of statement;Introduce this topic using everyday life situations.

Focus on mathematical sentences.

1. determine whether a given sentence is a statement;

1. determine whether a given statement is true or false;

Discuss sentences consisting of: words only; numbers and words; numbers and mathematical symbols;

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



41. 41. understand the concept of quantifiers all and some;Start with everyday life situations.1. construct statements using the quantifier:42. all;42. some;

126.4.15 10.4.151. determine whether a statement that contains the quantifier all is true or false;

1. determine whether a statement can be generalised to cover all cases by using the quantifier all;

1. construct a true statement using the quantifier all or some, given an object and a property.

1313.4.15 17.4.1545. 45. 45. perform operations involving the words not or no, and and or on statements;Begin with everyday life situations.1. change the truth value of a given statement by placing the word not into the original statement; 1. 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;

1. identify two statement from a compound statement that contains the word or ;

1. 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;



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

52. 52. 52. 52. understand the concept of implication;Start with everyday life situations.1. identify the antecedent and consequent of an implication if p, then q;

1. write two implications from a compound statement containing if and only if;

1. construct mathematical statements in the form of implication:55. If p, then q;55. p if and only if q;

1. determine the converse of a given implication;

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

1420.4.15 24.4.1557. 57. 57. 57. 57. understand the concept of argument;Start with everyday life situations.1. identify the premise and conclusion of a given simple argument;

1. make a conclusion based on two given premises for:59. Argument Form I;59. Argument Form II;59. Argument Form III;

Encourage students to produce arguments based on previous knowledge.

1. complete an argument given a premise and the conclusion.Analysing



60. 60. 60. 60. 60. 60. understand and use the concept of deduction and induction to solve problems.Use specific examples/activities to introduce the concept.1. determine whether a conclusion is made through:61. reasoning by deduction;61. reasoning by induction;

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

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

1. use deduction and induction in problem solving.

5 THE STRAIGHT LINE1527.4.15 1.5.1564. understand the concept of gradient of a straight line;Use technology such as the Geometers Sketchpad, graphing calculators, graph boards, magnetic boards, topo maps as teaching aids where appropriate.1. determine the vertical and horizontal distances between two given points on a straight line.

VerticaldistanceBegin with concrete examples/daily situations to introduce the concept of gradient.

Horizontal distance

1. determine the ratio of vertical distance to horizontal distance.



Discuss: the relationship between gradient and tan . the steepness of the straight line with different values of gradient.Carry out activities to find the ratio of vertical distance to horizontal distance for several pairs of points on a straight line to conclude that the ratio is constant.

66. 66. understand the concept of gradient of a straight line in Cartesian coordinates;Discuss the value of gradient if P is chosen as (x1, y1) and Q is (x2,y2); P is chosen as (x2, y2) and Q is (x1,y1).1. derive the formula for the gradient of a straight line; 1. calculate the gradient of a straight line passing through two points; 1. determine the relationship between the value of the gradient and the:69. steepness,69. direction of inclination,of a straight line;

Evaluating

164.5.15 8.5.1569. understand the concept of intercept;1. determine the x-intercept and the y-intercept of a straight line;

1. derive the formula for the gradient of a straight line in terms of the x-intercept and the y-intercept; 1. perform calculations involving gradient, x-intercept and y-intercept;Creating



72. 72. 72. 72. understand and use equation of a straight line;

Discuss the change in the form of the straight line if the values of m and c are changed.1. draw the graph given an equation of the formy = mx + c ;

Carry out activities using the graphing calculator, Geometers Sketchpad or other teaching aids.1. determine whether a given point lies on a specific straight line;

Verify that m is the gradient and c is the y-intercept of a straight line with equation y = mx + c .1. write the equation of the straight line given the gradient and y-intercept;

1. determine the gradient and y-intercept of the straight line which equation is of the form:76. y = mx + c;76. ax + by = c;

1. find the equation of the straight line which:77. is parallel to the x-axis;77. is parallel to the y-axis;77. passes through a given point and has a specific gradient;77. passes through two given points;

Discuss and conclude that the point of intersection is the only point that satisfies both equations.Use the graphing calculator and Geometers Sketchpad or other teaching aids to find the point of intersection.1. find the point of intersection of two straight lines by:78. drawing the two straight lines;78. solving simultaneous equations.



1711.5.15 15.5.15PEPERIKSAAN PERTENGAHAN TAHUN TINGKATAN 4 2015 (11.5.15 21.5.15)

1818.5.15 22.5.15PEPERIKSAAN PERTENGAHAN TAHUN TINGKATAN 4 2015 (11.5.15 21.5.15)

1925.5.1578. 78. 78. understand and use the concept of parallel lines.Explore properties of parallel lines using the graphing calculator and Geometers Sketchpad or other teaching aids.1. verify that two parallel lines have the same gradient and vice versa;Analysing

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

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

1. solve problems involving equations of straight lines.

Applying

CUTI PERTENGAHAN TAHUN 2015 (1.6.15 12.6.15)

6 STATISTICS2015.6.15 19.6.1582. understand the concept of class interval;Use data obtained from activities and other sources such as research studies to introduce the concept of class interval.1. complete the class interval for a set of data given one of the class intervals;

1. determine:84. the upper limit and lower limit;84. the upper boundary and lower boundaryof a class in a grouped data;

1. calculate the size of a class interval;

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



1. determine a suitable class interval for a given set of data;

Discuss criteria for suitable class intervals.1. construct a frequency table for a given set of data.

88. 88. understand and use the concept of mode and mean of grouped data;1. determine the modal class from the frequency table of grouped data;

1. calculate the midpoint of a class;

1. verify the formula for the mean of grouped data;Evaluating

1. calculate the mean from the frequency table of grouped data;

1. discuss the effect of the size of class interval on the accuracy of the mean for a specific set of grouped data..Evaluating

2122.6.15 26.6.1593. 93. 93. represent and interpret data in histograms with class intervals of the same size to solve problems;Discuss the difference between histogram and bar chart.

Use graphing calculator to explore the effect of different class interval on histogram.1. draw a histogram based on the frequency table of a grouped data; 1. interpret information from a given histogram; 1. solve problems involving histograms.

Applying

96. 96. 96. 96. represent and interpret data in frequency polygons to solve problems.1. draw the frequency polygon based on:97. a histogram;97. a frequency table;

1. interpret information from a given frequency polygon;

1. solve problems involving frequency polygon.



2229.6.15 3.7.1599. 99. 99. 99. 99. understand the concept of cumulative frequency;1. construct the cumulative frequency table for:100. ungrouped data;100. grouped data;

1. draw the ogive for:101. ungrouped data;101. grouped data;

236.7.15 10.7.15101. 101. 101. 101. understand and use the concept of measures of dispersion to solve problems.Discuss the meaning of dispersion by comparing a few sets of data. Graphing calculator can be used for this purpose. 1. determine the range of a set of data.

1. determine:103. the median;103. the first quartile;103. the third quartile;103. the interquartile range;from the ogive.Tree Map

1. interpret information from an ogive;Circle Map

Carry out a project/research and analyse as well as interpret the data. Present the findings of the project/research.Emphasise the importance of honesty and accuracy in managing statistical research.

1. solve problems involving data representations and measures of dispersionApplying



7 PROBABILITY 124 13..7.15 17.7.15105. understand the concept of sample space;Use concrete examples such as throwing a die and tossing a coin.1. determine whether an outcome is a possible outcome of an experiment; 1. list all the possible outcomes of an experiment:107. from activities;107. by reasoning;

1. determine the sample space of an experiment;Circle Map

1. write the sample space by using set notations.

109. 109. understand the concept of events.Discuss that an event is a subset of the sample space.Discuss also impossible events for a sample space.1. identify the elements of a sample space which satisfy given conditions;

1. list all the elements of a sample space which satisfy certain conditions using set notations;

Discuss that the sample space itself is an event.1. determine whether an event is possible for a sample space.

2520.7.15 24.7.15112. 112. 112. understand and use the concept of probability of an event to solve problems.Carry out activities to introduce the concept of probability. The graphing calculator can be used to simulate such activities.

1. find the ratio of the number of times an event occurs to the number of trials; 1. find the probability of an event from a big enough number of trials;

Discuss situation which results in: probability of event = 1. probability of event = 0.1. calculate the expected number of times an event will occur, given the probability of the event and number of trials;

Emphasise that the value of probability is between 0 and 1.1. solve problems involving probability;Applying

Predict possible events which might occur in daily situations.1. predict the occurrence of an outcome and make a decision based on known information.Creating



8 CIRCLES III2627.7.15 31.7.15117. understand and use the concept of tangents to a circle.Develop concepts and abilities through activities using technology such as the Geometers Sketchpad and graphing calculator.1. identify tangents to a circle;

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

1. construct the tangent to a circle passing through a point:120. on the circumference of the circle;120. outside the circle;

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

1. solve problems involving tangents to a circle.

Applying

122. 122. understand and use the properties of angle between tangent and chord to solve problems.Explore the property of angle in alternate segment using Geometers Sketchpad or other teaching aids.1. identify the angle in the alternate segment which is subtended by the chord through the contact point of the tangent;1. 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;

1. perform calculations involving the angle in alternate segment;

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



273.8.15 7.8.15126. 126. 126. understand and use the properties of common tangents to solve problems.Discuss the maximum number of common tangents for the three cases.

1. determine the number of common tangents which can be drawn to two circles which:127. intersect at two points;127. intersect only at one point;127. do not intersect;Bridge Map

Include daily situations.1. determine the properties related to the common tangent to two circles which:128. intersect at two points;128. intersect only at one point;128. do not intersect;

1. solve problems involving common tangents to two circles;Applying

1. solve problems involving tangents and common tangents.

Applying

9 TRIGONOMETRY II2810.8.15 14.8.15130. understand and use the concept of the values of sin, cos and tan (0 360) to solve problems.Explain the meaning of unit circle.

0yxP (x,y)y1x Q1. identify the quadrants and angles in the unit circle;

1. determine:132. the value of y-coordinate;132. the value of x-coordinate; 132. the ratio of y-coordinate to x-coordinate;of several points on the circumference of the unit circle;



Begin with definitions of sine, cosine and tangent of an acute angle.

1. verify that, for an angle in quadrant I of the unit circle :133. sin = y-coordinate ;133. cos = x-coordinate; 133. ;1. determine the values of 134. sine;134. cosine;134. tangent;of an angle in quadrant I of the unit circle;

Explain that the concept sin = y-coordinate ;cos = x-coordinate;

can be extended to angles inquadrant II, III and IV.1. determine the values of 135. sin;135. cos ;135. tan ;for 90 360;

2917.8.15 21.8.1512

30o2

3

60o45o

111. determine whether the values of:136. sine;136. cosine;136. tangent,of an angle in a specific quadrant is positive or negative;

Use the above triangles to find the values of sine, cosine and tangent for 30, 45, 60.1. determine the values of sine, cosine and tangent for special angles;



Teaching can be expanded through activities such as reflection.1. determine the values of the angles in quadrant I which correspond to the values of the angles in other quadrants;

3024.8.15 28.8.15Use the Geometers Sketchpad to explore the change in the values of sine, cosine and tangent relative to the change in angles.

1. state the relationships between the values of:139. sine;139. cosine; and139. 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 90 and 360;

1. find the angles between 0 and 360, given the values of sine, cosine or tangent;

Relate to daily situations.1. solve problems involving sine, cosine and tangent.

Applying

3131.8.15 4.9.15142. 142. draw and use the graphs of sine, cosine and tangent.Use the graphing calculator and Geometers Sketchpad to explore the feature of the graphs of y = sin , y = cos , y = tan .1. draw the graphs of sine, cosine and tangent for angles between 0 and 360;

Discuss the feature of the graphs of y = sin , y = cos , y = tan .

1. compare the graphs of sine, cosine and tangent for angles between 0 and 360;

Discuss the examples of these graphs in other area.1. solve problems involving graphs of sine, cosine and tangent.Applying



10 ANGLES OF ELAVATION AND DEPRESSION327.9.15 11.9.15145. understand and use the concept of angle of elevation and angle of depression to solve problems.Use daily situations to introduce the concept.1. identify:146. the horizontal line;146. the angle of elevation; 146. the angle of depression,for a particular situation;

1. Represent a particular situation involving:147. the angle of elevation; 147. the angle of depression, using diagrams;

1. Solve problems involving the angle of elevation and the angle of depression.Applying

11 LINES AND PLANES IN 3-DIMENSIONS3314.9.15 18.9.15148. understand and use the concept of angle between lines and planes to solve problems.Carry out activities using daily situations and 3-dimensional models.

1. identify planes;

Differentiate between 2-dimensional and 3-dimensional shapes. Involve planes found in natural surroundings.1. identify horizontal planes, vertical planes and inclined planes;

1. sketch a three dimensional shape and identify the specific planes;

1. identify:152. lines that lies on a plane;152. lines that intersect with a plane;

1. identify normals to a given plane;

CUTI PENGGAL 2 (21.9.15 25.9.15)



3428.9.15 2.10.15Begin with 3-dimensional models.

1. determine the orthogonal projection of a line on a plane;

1. draw and name the orthogonal projection of a line on a plane;

1. determine the angle between a line and a plane;

Use 3-dimensional models to give clearer pictures.1. solve problems involving the angle between a line and a plane.Applying

355.10.15 9.10.15

157. 157. understand and use the concept of angle between two planes to solve problems.1. identify the line of intersection between two planes;

1. 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;

Use 3-dimensional models to give clearer pictures.1. determine the angle between two planes on a model and a given diagram;

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

36,37,38(12.10.15 30.10.15)PEPERIKSAAN AKHIR TAHUN TINGKATAN 4 (12.10.15 30.10.15)

39(2.11.15 6.11.15)PERBINCANGAN SOALAN PEPERIKSAAN

40,41PROGRAM SELEPAS PEPERIKSAAN

rpt maths f4 2015

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