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# F5 add maths year plan 2013

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### Transcript of "F5 add maths year plan 2013"

1. 1. SMK JENJAROM, KUALA LANGAT SCHEME OF WORKS ADDITIONAL MATHEMATICS FORM 5 2013 Week (Date) Topic (Learning Area) Sub-topic (Learning Outcomes) Remarks 1-- 4 CHAPTER :1 PROGRESSIONS 1.1 Understand and use the concept of arithmetic progression 1. Identify characteristics of arithmetic progressions. 2. Determine whether a given sequence is an arithmetic progression. 3. Determine by using formula : a) specific terms in arithmetic progressions; b) the number of terms in arithmetic progressions. 4. Find : a) the sum of the first n terms of arithmetic progressions. b) the sum of a specific number of consecutive terms of arithmetic progressions. c) the value of n, given the sum of the first n terms of arithmetic progressions. 5 Solve problems involving arithmetic progressions. Include the use of formula Tn = Sn – Sn-1 Problems involving real- life situations 1.2 Understand and use the concept of geometric progression 1 Identify characteristics of geometric progressions. 2. Determine whether a given sequence is an geometric progression. 3. Determine by using formula : a) specific terms in geometric progressions; b) the number of terms in geometric progressions. 4 Find : a) the sum of the first n terms of geometric progressions.
2. 2. Week (Date) Topic (Learning Area) Sub-topic (Learning Outcomes) Remarks b) the sum of a specific number of consecutive terms of geometric progressions. c) the value of n, given the sum of the first n terms of geometric progressions. 5. Find : a) the sum to infinity of geometric progressions. b) the first term or common ratio, given the sum to infinity of geometric progressions. 6. Solve problems involving geometric progressions. Discuss: As n → α, rn → 0, then Sα = r a −1 . Exclude: combination of arithmetic progressions and geometric progressions. 5 –6 CHAPTER 2 : LINEAR LAW 2.1 Understand and use the concept of lines of best fit. 2.2 Apply linear law to non- linear relations. ` 1. Draw lines of best fit by inspection of given data. 2. Write equations for lines of best fit. 3 Determine values of variables from : a) lines of best fit b) equations of lines of best fit. 2.1 Reduce non-linear relations to linear form. 2.2 Determine values of constants of non-linear relations given : a) lines of best fit b) data. 2.3 Obtain information from : a) lines of best fit b) equations of lines of best fit. Limit data to linear relations between two variables.
3. 3. Week (Date) Topic (Learning Area) Sub-topic (Learning Outcomes) Remarks 7 -- 10 CHAPTER 3 : INTEGRATION 3.1 Understand and use the concept of indefinite integral. 1. Determine integrals by reversing differentiation. 2. Determine integrals of axn , where a is a constant and n is an integer, n ≠ -1. 3. Determine integrals of algebraic expressions. 4. Find constants of integration, c, in indefinite integrals. 5. Determine equations of curves from functions of gradients. 6. Determine by substitution the integrals of expressions of the form (ax + b)n , where a and b are contants, n is an integer and n ≠ -1. Limit intregration of ∫ dxun , where u = ax + b 3.2 Understand and use the concept of indefinite integral. 1 Find definite integrals of algebraic expressions. 2 Find areas under curves as the limit of a sum of areas. 3 Determine areas under curves using formula. 4 Find volumes of revolutions when region bounded by a curve is rotated completely about the a) x-axis b) y-axis as the limit of a sum of volumes. 5 Determine volumes of revolutions using formula. Include ∫ ∫= a b a dxxfkdxxkf )()( ∫ ∫−= b a a b dxxfdxxf )()( Deriavation of formula not required. Lomit volume of revolution about the x axis or y axis. 12 – 15 CHAPTER 4: VECTORS 4.1 Understand and use the conceptof vector 1. Differentiate between vector and scalar quantity. 2. draw and label directed line segments tu represent vectors. 3. Determine the magnitude and direction of vectors represented by directed line segments. 4. Determine whether two vectors are equal. 5. Multiply vectors by scalars 6. Determine whether two vectors are parallel. Use notations: Vector: a, AB Zero vector : 0 Emphasis negative vector: -AB = BA Include negative scalar. Week 7 1st Monthly Test First Semester Break Week 11
4. 4. Week (Date) Topic (Learning Area) Sub-topic (Learning Outcomes) Remarks 4.2 Understand and use the concept of addition and subtraction of vectors 1. Determine the resultant vector of two parallel vectors. 2. Determine the resultant vector of two non-parallel vectors using: a. triangle law b. parallelelogram law 3. Determine the resultant vector of three or more vectors using the polygon law. 4. Subtract two vectors which are: a. parallel b. non-parallel 5. Solve problems involving addition and subtraction of vectors. 4.3 Understand and use vectors in the Cartesian plane 1 Express vectors in the form: a. x i + y ) b. 2 Determine magnitudes of vectors. 3 Determine unit vectors in given directions. 4 Add two or more vectors. 5 Subtract two vectors. 6 Multiply vectors by scalars. 7 Perform combined operations on vectors. 8 Solve problems involving vectors. Relate unit vector i and j to Cartesian coordinates. Emphasise: vector i =       0 1 and vector j =       1 0 xy Week 15 Second Monthly Test
5. 5. Week (Date) Topic (Learning Area) Sub-topic (Learning Outcomes) Remarks 16 – 19 CHAPTER 5 : TRIGONOMETRIC FUNCTIONS 5.1 Understand the concept of positive and negative angles measured in degrees and radians. 1. Represent in a Cartesian plane, angles greater than 3600 or 2π radians for: a. positive angles b. negative angles 5.2 Understand and use the six trigonometric functions of any angle 1. Define sine, cosine and tangent of any angle in a Cartesian plane 2. Define cotangent, secant and cosecant of any angle in a Cartesian plane 3. Find values of the six trigonometric functions of any angle 4. Solve trigonometric equations Emphasis : Sin θ = cos (90 – θ), cos θ= sin (90 – θ) , tan θ = cot (90 – θ), cosec θ= sec (90 – θ), sec θ = cosec ( 90-θ), cot θ = tan (90 – θ). Emphasis the use of triangles to find trigo ratio for special angles 300 , 450 , 60 0 . 5.3 Understand and use graphs of sine, cosine and tangent functions. 1. Draw and sketch graphs of trigometric functions a. y = c + a sinbx, b. y = c + a cosbx, c. y = c + a tan bx where a, b and c are constant and b > 0. 2. Determine the number of solutions to a trigonometric equation using sketched graphs. 3. Solve trigonometric equations using drawn graphs. Use angles in (a) degrees, (b) radians, in term of Л. Include trigonometric functions involving modulus. Exclude combinations of trigonometric functions. 5.4 Understand and use basic identities 1. Prove basicidentities a. sin2 A + cos2 = 1 b. 1 + tan2 +A = sec2 A
6. 6. Week (Date) Topic (Learning Area) Sub-topic (Learning Outcomes) Remarks c. 1 + cot2 A = cosec2 A 2. Prove trigonometric identities using basic identities. 3. Solve trigonometric equations using basic identities. 5.5 Understand and use addition formulae and double-angle formulae 1. Prove trigonometric identities using addition formulae for sin (A + B), cos (A + B) and tan (A + B). 2. Derive double-angle formulae for sin 2A, cos 2A and tan 2A. 3. Prove trigonometric identities using addition formulae and/or double-angle formulae. 4. Solve trigonometric equations. Derivation of addition formulae not required. Discuss half-angle formulae. Ecclude A cos x + b sin x = c, where c ≠ 0. 25 – 27 CHAPTER: 6 PERMUTATION AND COMBINATIONS 6.1 Understand and use the concept of permutation 1. Determine the total number of ways to perform successive events using multiplication rule. 2. Determine the number of permutation of n different objects. 3. Determine the number of permutation of n different object taken r at a time. 4. Determine the number of permutation of n different objects for given conditions. 5. Determine the number of permutation of n different objects taken r at a time for given conditions. Exclude cases involving identical objects. Exclude cases involving arrangement of objects in a circle. 6.2 Understand and use the concept of combination 1 Determine the number of combinations r objects chosen from n different objects 2 Determine the number of combination r objects chosen from n different objects for given conditions Use examples to illustrate !r p c r n r n = Week 20 – 22: Mid Year Exam Week 23--24: Semester Break
7. 7. Week (Date) Topic (Learning Area) Sub-topic (Learning Outcomes) Remarks 28 – 29 CHAPTER 7 PROBABLITY 7.1 Understand and use the concept of probability. 1. Describe the sample space of an expriment. 2. Determine the number of outcome of an event. 3. Determine the probability of an event 4. Determine the probability of two event: - a) A or B occurring - b) A and B occurring Discuss : a) classical probability (Throretical probability) b) subjective probability c) relative frequency probability ( experimental prob.). Emphasis : only classical Prob is used to solve problems. 7.2 Understand and use the concept of probability of mutually exclusive events. 1 Determine whether two events are mutually exclusive. 2. Determine the probability of two or more evebts that are mutually exclusive. Include events that are mutually exclusive and exhaustive. Limits to three mutually exclusive events. 7.3 Understand and use the concept of probability of independent events. 1 Determine whether two events are independent. 2 Determine the probability of two independent events. 3 Determine the probability of three independent events. Include tree diagrams. 30 – 32 CHAPTER 8 : PROBABILITY DISTRIBUTIONS 8.1 Understand and use the concept of binomial distribution. 1. List all possible values of a discrete random variable. 2. Determine the probability of an event in a binomial distribution. 3. Plot binomial distribution graph. 4. Determine mean variance and standard deviation of a binomial distribution. 5. Solve problems involving binomial distributions.
8. 8. Week (Date) Topic (Learning Area) Sub-topic (Learning Outcomes) Remarks 8.2 Understand and use the concept of normal distribuation. 1 Describe continuous random variables using set notation. 2 Find probability of z values for standard normal distribution. 3 Convert random variable of normal distributions X to standardised variable,Z. 4 Represent probability of an event using set notation. 5 Determine probability of an event. 6 Solve problems involving normal distributions. Intregration of normal distribution function to determine probability is not required. 33 – 34 CHAPTER 9: MOTION ALONG A STRAIGHT LINE 9.1 Understand and use the concept of displacement 1. Identify direction of displacement of a particle from a fixed point. 2. Determine displacement of a particle from a from a fixed point. 3. Determine the total distace travelled by a particle over a time interval using graphical method. Emphasis the use of the following sumbols: s,v,a and t. Where s,v and a are functions of time. Emphasis the difference between displacement and distance. Discuss positive, negative and zero displacements. 9.2 Understand and use the concept of velocity 1 Determine velocity function of a particle by differentiation . 2 Determine instantaneous velocity of a particle 3 Determine displacement of a particle from velocity function by intergration. Emphasis velocity as the rate of change of velocity. Discuss : a) uniform velocity b) zero instantaneous velocity. c) positive velocity d) negative velocity.
9. 9. Week (Date) Topic (Learning Area) Sub-topic (Learning Outcomes) Remarks 9.3 Understand and use the concept of acceleration. 1 Determine acceleration function of a particle by differentiation 2 Determine instantaneous acceleration of a particle. 3 Determine instantaneous velocity of a particle from acceleration function by intergration. 4 Determine displacement of a particle from acceleration function by integration. 5 Solve problems involving motion along a staright line. Emphasis acceleration as the rate of change of velocity. Discuss : a) uniform acceleration b) zero acceleration c) positive acceleration d) negative acceleration. 33—34 CHAPTER 10: LINEAR PROGRAMMING 10.1 Understand and use the concept of graphs of linear inequalities. 1. Identity and shade the region on the graph that satisfies a linear inequality 2. Find the linear inequlity that defines a shaded region. 3. Shade region on the graph that satisfies several linear inequalities. 4. Find linear inequalities that defines a shaded region. Emphasis the use of solid lines and dashed lines. 10.2. Understand and use theconcept of linear programming 1 Solve problems related to linear programming by: a) writing linear inequalities and equations describing a situation. b) shading the region of feasible solutions. c) determining and drawing the objective function ax + by = k where a, b and k are constants. d) determining graphically the optimum value of the objective function. Optimum values refer to maximum or minimum values. Include the use of vertices to find the optimum value.
10. 10. Week (Date) Topic (Learning Area) Sub-topic (Learning Outcomes) Remarks 35 – 37 SPM TRIAL EXAMINATION 38 – 44 Discuss SPM Trial Exam. Questions Revision & Drill Past Year Questions 45 – 46 SPM EXAMINATION 47 End of Year Holidays Week 36 Second Semester Break
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