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- 1. ANNUAL PLANNING FOR MATHEMATICS FORM 4 / 2011 WEEK TOPICS/LEARNING AREA LEARNING OUTCOMES POINTS TO NOTE3 Jan – • Registration Day 7 Jan • Orientation Week1 WEEK CHAPTER 1 : STANDARD FORM(10 Jan – 13 Students will be taught to Students will be able to: Discuss the significance of zero in a Jan) understand and use the concept of i. Round off positive numbers number. significant figure to a given number of significant figures when the numbers are a. greater than 1 b. less than 1 Discuss the use of significant ii. Perform operations of figures in everyday life and other addition, subtraction, areas multiplication and division involving a few numbers and state the answer in specific significant figures. iii. solve problems involving significant figures. Students will be taught to Students will be able to: understand and use the concept of i. State positive numbers in Use everyday life situations such as standard form to solve problems standard form when the in health, technology, industry, numbers are construction and business involving a) greater than or equal to numbers in standard form 10 b) less than 1 ii. convert numbers in Use the scientific calculator to standard form to single explore numbers in standard form 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
- 2. 2 CHAPTER 2 : QUADRATICWEEKS EXPRESSIONS AND EQUATIONS(17 Jan – 28 Students will be taught to Students will be able to : Discuss the characteristics of Jan) understand the concept of quadratic i. Identify quadratic quadratic expressions of the form expressions expressions ax2 + bx + c = 0 where a, b and are ii. Form quadratic constants, a ≠ 0 and x is an unknown expressions by multiplying any two linear expressions iii. Form quadratic expressions based on specific situations Students will be taught how to Students will be able to : factorise quadratic expressions i. Factorise quadratic Discuss the various methods to expressions of the form obtain the desired product. ax2+bx+c =0 or c=0; ii. Factorise quadratic expressions of the form Begin with the case a=1. px2-q, p and q are perfect Explore the use of graphing squares; calculator to factorise quadratic iii. Factorise quadratic expressions expressions of the form ax2+bx+c, where a, b and c not equal to zero; iv. Factorise quadratic expressions containing coefficients with common factors; Students will be taught to Students will be able to : understand the concept of quadratic i. Identify quadratic Discuss the characteristics of equation equations with one quadratic equations. unknown; ii. write quadratic equations in general form i.e. ax2 + bx + c = 0 ; iii. form quadratic equations based on specific situations ;
- 3. Students will be taught to Students will be able to : understand and use the concept of i. Determine whether a given roots of quadratic equations to solve value is a root of a specific problems. quadratic equation ii. Determine the solutions for quadratic equations by: Discuss the number of roots of a a) trial and error method ; quadratic equation. b) factorization ; iii. solve the problems Use everyday life situations. involving quadratic equations 3 CHAPTER 3 : SETSWEEKS Use everyday life examples to(31 Jan Students will be taught to Students will be able to : introduce the concept of set. – 18 understand the concept of set i. sort given objects into Feb) group ii. define set by : a. descriptions; b. using set notation; iii. identify whether a given object is anelement of a set and use the symbol ∈ or ∉ ; iv. represent sets by using Discuss the difference between the Venn diagrams; representation of element and the v. list the element and state number of element in Venn diagrams. the number of element of a Discuss why { 0 } and { Ø } are not set; empty sets. vi. determine whether a set is an empty set; vii. determine whether two sets are equal; Students will be taught to Students will be able to : Begin with everyday life situations. understand and use the concept of i. determine whether a given subset, universal set and the set is a subset of a specific complement of a set set and use the symbol ⊂ or ⊄ ; ii. represent subset using Venn diagram; iii. list the subsets for a specific set;
- 4. iv. illustrate the relationship between set and universal Discuss the relationship between set using Venn diagram; sets and universal sets. v. determine the complement of a given set ; vi. determine the relationship between set, subset, universal set and the complement of a set;Students will be taught to perform Students will be able to:operations on sets: i. determine the intersection• the intersection of sets; of:• the union of sets a) two sets; b) three sets; and use the symbol ∩ ; ii. represent the intersection of sets using Venn Discuss cases when: diagram; • A∩ B= Ø iii. state the relationship • A⊂ B between i. A ∩ B and A , ii. A ∩ B and B ; iv. determine the complement of the intersection of sets; v. solve problems involving the intersection of sets; vi. 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 a) A ∪ B and A , b) A ∪ B and B ; ix. determine the complement of the union of sets x. solve problems involving the union of sets xi. determine the outcome of
- 5. combined operations on sets xii solve problems involving combined operations on sets 2 CHAPTER 4 :WEEKS MATHEMATICAL REASONING(21 Feb –4 Students will be taught to Students will be able to:March) understand the concept of i. determine whether a given Introduce this topic using everyday statement; sentence is a statement; life situations ii. determine whether a given Focus on mathematical sentences statement is true or false; iii. construct true or false Discuss sentences consisting of: statement using given • words only; numbers and mathematical • numbers and words; symbols; • numbers and mathematical symbols;. Students will be taught Students will be able to: understand the concept of i. construct statements using the Start with everyday life situations. quantifiers “all” and “some”; quantifier: a) all; b) some; ii. determine whether a statement that contains the quantifier “all” is true or false; iii. determine whether a statement can be generalised 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. TEST 1 Will be prepared by: (7 Mac – 11 Mac) PN. SURIANI
- 6. 2 Students will be taught to Students will be able to :WEEKS perform operations involving Begin with everyday life situations. i. change the truth value of a(21 Mar the words “not” or “no”, “and” given statement by placing the– 1 Apr) and “or” on statements; 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”. Students will be taught to Students will be able to; understand the concept of i. identify the antecedent and implication; Start with everyday life situations. 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 q; b) p if and only if q
- 7. Students will be taught to Students will be able to: understand the concept of Start with everyday life situations. i. identify the premise and argument; conclusion of a given simple argument; ii. make a conclusion based on two given premises for a) Argument Form I; b) Argument Form II; c) Argument Form III; iii. complete an argument given a Encourage students to produce premise and the conclusion. arguments based on previous knowledge. Students will be taught to Students will be able to: understand and use the concept i. determine whether a conclusion Use specific examples/activities to of deduction and induction to is made through: introduce the concept. solve problems. a) reasoning by deduction; b) 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. 3 CHAPTER 5 : THE STRAIGHT LINEWEEKS(4 Apr Students will be taught to Students will be able to: Use technology such as the -22 understand the concept of gradient i. determine the vertical and Geometers Sketchpad , graphing Apr) of a straight line horizontal distances between calculators, graph boards, magnetic two given points on a straight boards, topo maps as teaching aid line where appropriate. Begin with concrete examples /daily ii. determine the ratio of vertical situations to introduce the concept of distance to horizontal distance gradient. Vertical distance
- 8. θ Horizontal distance Discuss: • the relationship between gradient and tan θ • the steepness of th straight line with different values of gradient Carry out activities to find the ratios of vertical distance to horizontal distance for several pairs of points on a straight line to conclude that the ratio is constant.Students will be taught to Students will be able to: Discuss the value of gradient ifunderstand the concept of gradient i. derive the formula for the • P is chosen as (x1 ,y1 ) and Qof a straight line in Cartesian gradient of a straight line is (x2 ,y2 ) ;coordinates ii. calculate the gradient of a • P is chosen as (x2 ,y2 ) and straight line passing through Q is (x1 ,y1 ) two points; iii. determine the relationship between the value of the gradient and the : a) steepness; b) direction of inclination, of a straight lineStudents will be taught to Students will be able to: Students will be taught tounderstand the concept of intercept; i. determine the x-intercept and understand the concept of intercept; the y-intercept of a straight line ii. 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
- 9. Students will be taught to i. Find the equation of the understand and use equation of a straight line which: straight line; a. is parallel to the x-axis; b. is parallel to the y-axis; c. passes through a given point and has a specific gradient; d. passes through two given points; ii. find the point of intersection Discuss and conclude that the point of two straight lines by; of intersection is the only point that a) drawing the two straight satisfies both equations lines; b) solving simultaneous Use the graphing calculator and equations Geometers Sketchpad or other teaching aids to find the point of intersection Students will be taught to Students will be able to: understand and use the concept of i. verify that two parallel Explore properties of parallel lines parallel lines lines have the same using the graphing calculator and gradient and vice versa; Geometers Sketchpad or other ii. determine from the given teaching aids. equation whether two straight lines are parallel; iii. find the equation of the straight line which passes through a given point and is parallel to another straight line; iv. solve problems involving equations of straight lines 2 CHAPTER 6 : STATISTICS III WEEKS Students will be taught to Students will be able to:(25 Apr understand the concept of class i. Complete the class interval for Use data obtained from activities and –6 interval. a set of data given one of the other sources such as research May class intervals; studies to introduce the concept of ii. Determine class interval . a) the upper limit and lower limit; b) the upper boundary and lower boundary of a
- 10. Students will be taught to represent Students will be able to:and interpret i. Draw a histogram based on the Discuss the difference betweendata in histograms with frequency table of a grouped histogram and bar chart.class intervals of the same data size to solve problems ; ii. Interpret information from a given histogram; Use graphing calculator to explore iii. Solve problems involving the effect of different class interval histograms. on histogram.Students will be taught to represent Students will be able to:and interpret data in frequency i. Draw the frequency polygonpolygons to solve based onproblems. a) a histogram ; b) a frequency table ; ii. Interpret information from a given frequency polygon ; iii. Solve problems involving frequency polygon.Students will be taught to Students will be able to:understand the concept of i. Construct the cumulativecumulative frequency frequency table for a) ungrouped data b) grouped data ii. Draw the ogive for : a) ungrouped data b) grouped data
- 11. Students will be taught to Students will be able to:understand and use the concept of i. Determine the range of a set of Discuss the meaning of dispersion bymeasures of dispersion to solve data comparing a few sets of data.problems ii. Determine Graphing calculator can be used for a) the median ; this purpose . b) the first quartile; c) the third quartile ; d) the interquartile range ; from the ogive . iii. interpret information from an Carry out a project /research and ogive analyse as well as interpret the iv. solve problems involving data data .Present the findings of the representations and project/research. measures of dispersion Emphasise the importance of honesty and accuracy in managing statistical research . MID YEAR EXAM Will be prepared by: (9 MAY – 27 MAY) PN. SURIANI & PN. SAIDANORLAILI
- 12. 2 CHAPTER 7 : PROBABILITYWEEKS(13 Students will be taught to Students will be able to: Use concrete examples such asJune – understand the concept o i. Determine whether an drawing a die and tossing a coin.24 sample space. outcome is a possibleJune) outcome of an experiment; 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. Students will be taught to Students will be able to: Discuss that an event is a subset understand the concept of i. identify the elements of a of the sample space events. sample space which Discuss also impossible events for satisfy given conditions; a sample space. ii. list all the element of a sample space which satisfy certain condition using set notations. iii. determine whether an Discuss that the sample space event is itself is an event. possible for a sample space. Students will be taught to Students will be able to: understand and use the concept i. find the ratio of the Carry out activities to introduce of probability of an event to number of the concept of probability . The solve problems times an event occurs to graphing calculator can be used the number of trials. to simulate such activities. ii. find the probability of an event from a big enough number of trials; iii. calculate the expected number of times an event will occur given the probability of the Discuss situation which results in: event an number of • probability of event = 1 trials; • probability of event = 0
- 13. iv. solve problems involving probability; Emphasise that the value ofv. predict the occurrence probability is between 0 and 1. of an outcome and make Predict possible events which a decision based on might occur in daily situations known information.
- 14. 2 CHAPTER 8 : CIRCLES IIIWEEKS (27 Students will be taught to Students will be able to: Develop concepts and abilitiesJune – understand and use the concept of i. identify tangent to a through activities using technology8 July) tangent to a circle. circle; such as the Geometer`s Sketchpad ii. make inference that the and graphing calculator. 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 tangent to a circle from a given point outside the circle; v. solve problems involving tangent to a circle. Students will be taught understand Students will be able to: and use the properties of angle i. identify the angle in the Explore the properties of angle in between tangent and chord to solve alternate segment which alternate segment using Geometer`s problems. is subtended by the chord Sketchpad or other teaching aids. 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.
- 15. Students will be taught to i. find the values of sine, understand and use the concept of cosine and tangent of the the values of sin Ө, kos Ө , and angles between 90° and tan Ө (0° ≤ Ө ≤ 360°) to solve 360° problems. ii. find the angles between 0° and 360°, given the values of sine, cosine or tangent iii. solve problems involving Relate the daily situation sine, cosine and tangent Students will be taught to draw and Students will be able to: use the graphs of sine, cosine and i. Draw the graphs of sine, Use the graphing calculator and tangent. cosine and tangent for Geometer’s Sketchpad to explore the angles between 0o and feature of the graphs of 360o; ii. Compare the graphs of y = sin θ , y = cos θ , y = tan θ sine, cosine and tangent Discuss the feature of the graphs of for angles between 0o and 360o; y = sin θ , y = cos θ , y = tan θ iii. Solve problems involving Discuss the examples of these graphs of sine, cosine and graphs in other area. tangent. 3 CHAPTER 10 :WEEKS ANGLES OF ELEVATION AND(11 July DEPRESSIONS -29 July) Students will be taught to Students will be able to: Use daily situations to introduce the understand and use the concept of i. identify concept angle of elevation and angle of a) the horizontal line depression to solve problems b) the angle of elevation c) the angle of depression for a particular situation ii. Represent a particular situation involving a) the angle of elevation b) the angle of depression, using diagrams iii. Solve problems involving the angle of elevation and the angle of depression
- 16. (1 Aug REVISION –5 Aug) TEST 2 Will be prepared by: (8 AUG – 12 AUG) PN. SAIDANORLAILI 2 CHAPTER 11 :WEEKS LINES AND PLANES IN 3(15 Aug DIMENSIONS – 26 Aug) Students will be taught to Students will be able to Carry out activities using daily understand and use the concept of i. identify planes situation and 3-dimensional models. angle between lines and planes to ii. identify horizontal planes Differentiate between 2-dimensional solve problems and inclined planes an d 3-dimensional shapes. Involve iii. sketch a three dimensional planes found in natural surroundings. shape and identify the specific planes. Begin with 3-dimensional models. iv. Identify : a) lines that lies on a plane. b) Lines that intersect with a plane, v. Identify normals to a given plane, vi. Determine the orthogonal Use 3-dimensional models to give projection of a line on a clearer pictures. plane vii. Draw and the name the orthogonal projection of a line on a plane viii. Determine the angle between a line and a plane ix. Solve problems involving the angle between a line and a plane. Students will be taught to Students will be able to : understand and use the i. identify the line concept of angle between two intersection between two planes to solve problems planes, ii. draw a line on each plane which is perpendicular to the line of intersection of the two planes at a point
- 17. on the line of intersection Use 3-dimensional models to give iii. determine the angle clearer pictures. between two planes on a model and a given diagram. iv. Solve problems involving lines and planes in 3- dimensional shapes.(5 Sept • REVISION– 14Oct) • FINAL EXAM Will be prepared by: (17 OKT – 4 NOV) PN. SURIANI & PN. SUNITA

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