WK - KCPE-KCSE



|SCHEME OF WORK FORM FOUR MATHEMATICS TERM ONE YEAR 2018 |

|WK |L/NO |TOPIC / SUBTOPIC |LESSON / SPECIFIC |TEACHING / LEARNING |MATERIALS |REFERE- | REMARKS |

|NO. | | |OBJECTIVES |ACTIVITIES |/ |NCES | |

| | | | | |RESOURCES | | |

|1 |1 |MATRICES & TRANSFORMA-TIONS |By the end of the lesson, the learner should | | | | |

| | |Definition of a |be able to: |Questioning to review position vectors; | | | |

| | |transformation. | |Drawing objects and their images on the |Geo – board, | | |

| | |Reflection in the |Define a transformation. |Cartesian plane; |Graph papers, |KLB BK IV | |

| | |y-axis. |Obtain image of an object by reflection in |Inferring the matrix of transformation for |mirrors. |Pgs 1-2 | |

| | | |the y-axis. |reflection in the y-axis. | | | |

| | | | |Written exercise. | | | |

| |2 |Reflection in the |Obtain image of an object by reflection in |Drawing object and image on the Cartesian | |KLB BK IV | |

| | |x-axis. |the x-axis. |plane; |Geo – board, |Pgs 2 - 3 | |

| | | | |Inferring the matrix of transformation for |Graph papers, | | |

| | | | |reflection in the x-axis. |mirrors. | | |

| | | | |Written exercise. | | | |

| |3 |Reflection in the |Obtain image of an object by reflection in a |Review equation of a line; | |KLB BK IV | |

| | |Lines y = x, |given line. |Draw the line y = x; |Geo – board, |Pgs 2-3 | |

| | |y = - x and other lines. | |Reflect an object in the line |Graph papers, | | |

| | | |Obtain the object given its image and line of |y = x; |mirrors. | | |

| | | |reflection. |Infer the matrix of transformation | | | |

| | | | |Written exercise. | | | |

| |4 |Rotation matrix. |Obtain image of an object by rotation through |Guided discovery; |Geo – board, |KLB BK IV | |

| | |(positive angle) |a positive angle. |Worked example; |Graph papers. |Pgs 3-4 | |

| | | |Obtain the object given its image and |Written exercise. | | | |

| | | |positive rotation angle. | | | | |

| |5 |Rotation matrix. |Obtain image of an object by rotation through |Guided discovery; |Geo – board, |KLB BK IV | |

| | |(negative angle) |a negative angle. |Worked example; |Graph papers. |Pgs 3-4 | |

| | | | |Written exercise. | | | |

| |6 |The unit circle. |Use the unit circle to identify a |Guided discovery; |Geo – board, |KLB BK IV | |

| | | |transformation represented by a given matrix. |Worked example; |Graph papers. |Pgs 9-13 | |

| | | | |Written exercise. | | | |

| |7 |Finding matrix of |Find matrix of transformation given an object |Review simultaneous equations and matrix |Geo – board, |KLB BK IV | |

| | |transformation. |and image. |multiplication; |Graph papers. |Pgs 6-8 | |

| | | |Describe the transformation fully. |Worked examples; | | | |

| | | | |Written exercise. | | | |

|2 |1 |Enlargement matrix. |Identify an enlargement matrix. |Review scale factor and centre of |Geo – board, |KLB BK IV | |

| | | |Perform operations involving enlargement |enlargement; |Graph papers. |Pgs 11-12 | |

| | | |matrices. |Worked examples; | | | |

| | | | |Written exercise. | | | |

| | | | | | | | |

| |2 |Two successive |Perform two successive transformations. |Guided discovery of order of operation; |Geo – board, |KLB BK IV | |

| | |transformations. | |Written exercise. |Graph papers. |Pgs 16-17 | |

| |3 |Several successive |Perform several successive transformations. |Previous exercise review; |Geo – board, |KLB BK IV | |

| | |transformations. | |Guided discovery of order of operation; |Graph papers. |Pgs 16-17 | |

| | | | |Written exercise. | | | |

| |4 |Combined matrix of |Find combined matrix of several |Previous exercise review; |Geo – board, |KLB BK IV | |

| | |transformations. |transformations. |Guided discovery of order of operation; |Graph papers. |Pgs 21-22 | |

| | | | |Written exercise. | | | |

| |5 |Inverse of a transformation |Identify the identity matrix. |Worked examples using several methods; |Geo – board, |KLB BK IV | |

| | |matrix. |Determine the inverse of a transformation |Supervised practice; |Graph papers. |Pgs 24-26 | |

| | | |matrix. |Written exercise. | | | |

| |6 |Inverse of several |Determine the inverse of several combined |Worked; |Geo – board, |KLB BK IV | |

| | |transformation matrices. |transformation matrices. |Supervised practice; |Graph papers. |Pgs 24-26 | |

| | | | |Written exercise. | | | |

| |7 |A.S.F. and determinant of a |State the relation between A.S.F. and |Finding area of object, image, ASF; |Geo – board, |KLB BK IV | |

| | |transformation matrix. |determinant of a transformation matrix. |Guided discovery; |Graph papers. |Pgs 26-27 | |

| | | | |Written exercise. | | | |

|3 |1 |Shear transformation. |Identify a shear transformation. (x-axis |Drawing object and image under a shear |Geo – board, |KLB BK IV | |

| | |(x-axis invariant) |invariant) |transformation; |Graph papers. |Pgs 28-32 | |

| | | |Describe a shear fully. |Oral exercise; | | | |

| | | | |Written exercise. | | | |

| |2 |Shear transformation. |Identify a shear transformation. (y-axis |Drawing object and image under a shear |Geo – board, |KLB BK IV | |

| | |(y-axis invariant) |invariant) |transformation; |Graph papers. |Pgs 28-31 | |

| | | |Describe a shear fully. |Oral exercise; | | | |

| | | | |Written exercise. | | | |

| |3 |Finding shear matrix. |Find shear matrix given the object and image. |Worked examples; |Geo – board, |KLB BK IV | |

| | | | |Written exercise. |Graph papers. |Pgs 31-2 | |

| |4 |One-way stretch. |Describe a one-way stretch. |Guided discovery; |Geo – board, |KLB BK IV | |

| | |(x-axis invariant) |(x-axis invariant) |Worked examples and discussion. |Graph papers. |Pgs 32-34 | |

| | | |Find the scale factor of a stretch. | | | | |

| |5 |One-way stretch. |Describe a one-way stretch. |Guided discovery; |Geo – board, |KLB BK IV | |

| | |(y-axis invariant) |(y-axis invariant). |Worked examples and discussion. |Graph papers. |Pgs 32-34 | |

| | | |Find the scale factor of a stretch. | | | | |

| |6 |Isometric and non-isometric |Classify transformations as either isometric |Review types of transformations; | |KLB BK IV | |

| | |transformation. |or non-isometric. |Probing questions on size and shape of | |Pg 35 | |

| | | | |objects and images. | | | |

| |7 |Test / mixed exercise. | | |Past exam papers. | | |

|4 |1 |STATISTICS II | |Simple worked examples; |Calculator. |KLB BK IV | |

| | | | |Exposition of method involving an assumed | |Pgs 38-39 | |

| | |Mean and assumed mean. |Find mean of ungrouped data using an assumed |mean; | | | |

| | |(frequency 1) |mean. |Written exercise. | | | |

| | | |(frequency 1) | | | | |

| |2 |Mean and assumed mean. |Find mean of ungrouped data using an assumed |Simple worked examples; |Calculator. |KLB BK IV | |

| | |(frequency > 1) |mean. |Written exercise. | |Pg 40 | |

| | | |(frequency > 1) | | | | |

| |3 |Mean of grouped data. |Find mean of grouped data. |Review previous exercise; |Calculator. |KLB BK IV | |

| | | | |Completing table; | |Pgs 40-41 | |

| | | | |Worked examples. | | | |

| |4 |Mean of grouped data. |Find mean of grouped data. |Completing table; |Calculator. |KLB BK IV | |

| | |(alternative methods) |(alternative methods) |Worked examples. | |Pgs 40-46 | |

| | | | |Written exercise. | | | |

| |5 |Median. |Find median of grouped data. |Worked examples; |Calculator. |KLB BK IV | |

| | | | |Written exercise. | |Pgs 46-7 | |

| |6 |Quartiles. |Find upper and lower quartiles. |Exposition; |Calculator. |KLB BK IV | |

| | | | |Worked examples; | |Pgs 47-8 | |

| | | | |Written exercise. | | | |

| |7 |Deciles and Percentiles. |Define a decile and percentile. |Exposition; |Calculator. |KLB BK IV | |

| | | |Find nth decile / percentile. |Worked examples; | |Pgs 47-8 | |

| | | | |Written exercise. | | | |

|5 |1 |Cumulative frequency curve. |Draw a cumulative frequency curve. |Q/A to review upper and lower limits of |Calculator, graph |KLB BK IV | |

| | | | |class boundaries; |papers. |Pgs 38-40 | |

| | | | |Complete a table by finding cumulative | | | |

| | | | |totals; | | | |

| | | | |Draw an ogive. | | | |

| |2 |Median and quartiles from an|Estimate median and quartiles from an ogive. |Probing questions to make inferences from an|Calculator, graph |KLB BK IV | |

| | |ogive. | |ogive. |papers. |Pgs 48-50 | |

| |3 |Deciles and percentiles from|Estimate deciles and percentiles from an |Probing questions to make inferences from an|Calculator, graph |KLB BK IV | |

| | |an ogive. |ogive. |ogive. |papers. |Pgs 53-55 | |

| |4 |Range, inter-quartile range |Find range and inter-quartile range of a set |Exposition and oral exercise. |Calculator. |KLB BK IV | |

| | |and quartile deviation. |of data. | | |Pgs 55-56 | |

| |5 |Mean absolute deviation. |Determine mean absolute deviation. |Exposition; |Calculator. |KLB BK IV | |

| | | | |Worked examples. | |Pgs 56-7 | |

| |6 |Variance. |Define variance. |Exposition; |Calculator. |KLB BK IV | |

| | | |Determine variance of a set of data. |Worked examples. | |Pgs 57-59 | |

| |7 |Standard deviation. |Determine standard deviation of a set of data.|Exposition; |Calculator. |KLB BK IV | |

| | | | |Worked examples; | |Pgs 59-60 | |

| | | | |Written exercise. | | | |

|6 |1-4 |Formulae for standard |Use various methods of finding std deviation. |Exposition; |Calculator. |KLB BK IV | |

| | |deviation. | |Worked examples; | |Pgs 60-3 | |

| | | | |Written exercise. | | | |

| |5 |LOCI | | | |KLB BK IV | |

| | | | | | |Pgs 66-7 | |

| | |Definition of a locus. |Define locus of a point. |Illustrative examples; |Door, clock, see saw, | | |

| | | | |Exposition of meaning of locus of a point. |etc. | | |

| |6 |Sketching locus of a point. |Sketch locus of a point. |Oral exercise; | |KLB BK IV | |

| | | | |Supervised practice; | |Pgs 67-8 | |

| | | | |Written exercise. | | | |

| |7 |Perpendicular bisector |Describe perpendicular bisector locus. |Geometrical construction; |Geometrical sets. |KLB BK IV | |

| | |locus. |(two dimensions) |Guided discovery; | |Pgs 68-9 | |

| | |(two dimensions) | |Written exercise. | | | |

|7 |1 |Perpendicular bisector |Describe perpendicular bisector locus. |Geometrical construction; |Geometrical sets. |KLB BK IV | |

| | |locus. |(three dimensions) |Guided discovery; | |Pg 69 | |

| | |(three dimensions) | |Supervised practice; | | | |

| | | | |Written exercise. | | | |

| |2 |Locus of points at a given |Describe locus of points at a given distance |Geometrical construction; |Geometrical sets. |KLB BK IV | |

| | |distance from a fixed point.|from a fixed point. |Guided discovery; | |Pg 70 | |

| | |(two dim) | |Written exercise. | | | |

| |3 |Locus of points at a given |Describe locus of points at a given distance |Geometrical construction; |Geometrical sets. |KLB BK IV | |

| | |distance from a fixed point.|from a fixed point. |Guided discovery; | |Pg 71 | |

| | |(three dim) | |Written exercise. | | | |

| |4 |Locus of points at a given |Describe locus of points at a given distance |Geometrical construction; |Geometrical sets. |KLB BK IV | |

| | |distance from a line. |from a fixed point. |Guided discovery; | |Pg 69 | |

| | |(two dim) | |Written exercise. | | | |

| |5 |Locus of points at a given |Describe locus of points at a given distance |Geometrical construction; |Geometrical sets. |KLB BK IV | |

| | |distance from a line. |from a fixed point. |Guided discovery; | |Pg 70 | |

| | |(three dim) | |Written exercise. | | | |

| |6 |Angle bisector locus. |Construct the angle bisector locus. |Geometrical construction; |Geometrical sets. |KLB BK IV | |

| | | | |Guided discovery; | |Pg 70 | |

| | | | |Written exercise. | | | |

| |7 |Constant angle locus. |Construct constant angle locus. |Probing questions to review angle properties|Geometrical sets. |KLB BK IV | |

| | | | |of a circle; | |Pgs 72-4 | |

| | | | |Geometrical construction; | | | |

| | | | |Guided discovery; | | | |

| | | | |Written exercise. | | | |

|8 |1 |Constant angle locus. |Construct constant angle locus. |Probing questions to review previous |Geometrical sets. |KLB BK IV | |

| | |(contd) | |exercise; | |Pgs 72-4 | |

| | | | |Geometrical construction; | | | |

| | | | |Guided discovery; | | | |

| | | | |Written exercise. | | | |

| |2 |Intersecting loci involving |Construct intersecting loci involving lines |Geometrical construction; |Geometrical sets. |KLB BK IV | |

| | |lines and angles. |and angles. |Supervised practice; | |Pgs 72-4 | |

| | | | |Written exercise. | | | |

| |3 |Circumcircle locus. |Construct a circumcircle. |Geometrical construction; |Geometrical sets. |KLB BK IV | |

| | | | |Supervised practice; | |Pg 78 | |

| | | | |Written exercise. | | | |

| |4 |In-circle locus. |Construct an in-circle locus. |Geometrical construction; |Geometrical sets. |KLB BK IV | |

| | | | |Supervised practice; | |Pg 78 | |

| | | | |Written exercise. | | | |

| |5 |Ex-circle locus. |Construct an ex-circle locus. |Geometrical construction; |Geometrical sets. |KLB BK IV | |

| | | | |Supervised practice; | |Pg 78 | |

| | | | |Written exercise. | | | |

| |6 |Intersecting loci in plane |Construct intersecting loci in plane figures. |Problem solving. |Geometrical sets. |KLB BK IV | |

| | |figures. | | | |Pgs 79-81 | |

| |7 |Loci of inequalities. |Draw locus of points that satisfy various |Q/A to review simple and compound |Geometrical sets. |KLB BK IV | |

| | | |inequalities. |inequalities; | |Pgs 81-2 | |

| | | | |Worked examples; | | | |

| | | | |Written exercise. | | | |

|9 |1 |Loci of inequalities. |Draw locus of points that satisfy various |Review previous exercise; |Geometrical sets. |KLB BK IV | |

| | |(contd) |inequalities. |Further worked examples; | |Pg 83 | |

| | | | |Written exercise. | | | |

| |2 |Locus involving chords. |Construct locus involving chords. |Worked examples; |Geometrical sets. |KLB BK IV | |

| | | | |Written exercise. | |Pgs 96-97 | |

| |3 |TRIGONOMETRY | | | | | |

| | |III | | | | | |

| | | | | | | | |

| | |Some trigonometric ratios. |Rearrange |Exposition and worked examples; | | | |

| | | |trigonometric expressions. |Written exercise. | | | |

| | | | | |Geometrical sets. |KLB BK IV | |

| | | | | | |Pgs 90-91 | |

| |4 |Trigonometric identities. |Prove some trigonometric identities. |Problem solving. |Geometrical sets. |KLB BK IV | |

| | | | | | |Pgs 100-1 | |

| |5 |Period and amplitude of |Determine period and amplitude of waves. |Exposition and worked examples. |Geometrical sets. |KLB BK IV | |

| | |waves. | | | |94-5 | |

| |6 |Tables for trigonometric |Complete tables for trigonometric functions. |Exposition and worked examples. |Calculator. |KLB BK IV | |

| | |functions. | | | |Pgs 96-7 | |

| |7 |Graphs for trig. functions. |Plot graphs for trigonometric functions. |Drawing graphs; supervised practice; make |Geometrical sets, graph|KLB BK IV | |

| | | | |inferences from the graphs. |papers. |Pgs 96-7 | |

|10 |1 |Further graphs for trig. |Plot graphs for trigonometric functions. |Drawing graphs; supervised practice; make |Geometrical sets, graph|KLB BK IV | |

| | |functions. | |inferences from the graphs. |papers. |Pgs 96-7 | |

| |2 |Transformations of waves. |Describe some transformations of waves. |Supervised practice; |Geometrical sets, graph|KLB BK IV | |

| | | | |Exposition and worked examples; |papers. |Pgs 96-97 | |

| | | | |Written exercise. | | | |

| |3 |Waves with a phase angle. |Determine the phase angle (positive) for two |Guided discovery; |Geometrical sets, graph|KLB BK IV | |

| | |(positive) |waves. |Written exercise. |papers. |Pgs 97-8 | |

| |4 |Waves with a phase angle. |Determine the phase angle (negative) for two |Guided discovery; |Geometrical sets, graph|KLB BK IV | |

| | |(negative) |waves. |Written exercise. |papers. |Pgs 97-8 | |

| |5 |Trigonometric equations. |Solve trigonometric equations. |Q/A to review trig. ratios for complementary|Geometrical sets, graph|KLB BK IV | |

| | | | |angles; |papers. |Pgs 100-3 | |

| | | | |Worked examples; | | | |

| | | | |Supervised practice; | | | |

| | | | |Written exercise. | | | |

| |6 |Further trig. equations. |Solve trigonometric equations. |Exercise review; |Geometrical sets, graph|KLB BK IV | |

| | | | |Problem solving. |papers. |Pgs 100-3 | |

| |7 |Graph of a trig. function |Draw the graph of a trig. function and a line |Worked examples; |Geometrical sets, graph|KLB BK IV | |

| | |and a line. |to solve an equation. |Supervised practice; |papers. |Pgs 100-3 | |

| | | | |Written exercise. | | | |

|11 |1 |Graphs of two trig. |Draw graphs of two trig. functions to solve |Worked examples; |Geometrical sets, graph|KLB BK IV | |

| | |functions. |some equations. |Supervised practice; |papers. |Pgs 100-3 | |

| | | | |Written exercise. | | | |

| |2 |THREE DIMENSIONAL GEOMETRY | | | | | |

| | | | | | | | |

| | |Dimensions of figures. | | | | | |

| | | |State the dimensions of figures. | |Common planes and | | |

| | | |Identify faces, edges, and vertices of common |Probing questions; |solids. |KLB BK IV | |

| | | |figures. |Oral exercise. | |Pgs 104-6 | |

| |3 |Angle between a line and a |Identify the angle between a line and a plane.|Exposition; |Cuboid wire mesh. |KLB BK IV | |

| | |plane. | |Oral exercise. | |Pgs 106-7 | |

| |4 |Finding the angle between a |Find the angle between a line and a plane. |Guided discovery; |Models of solids. |KLB BK IV | |

| | |line and a plane. | |Worked examples; | |Pgs 107-113 | |

| | | | |Written exercise. | | | |

| |5 |Finding the angle between a |Find the angle between a line and a plane. |Problem solving. |Models of solids. |KLB BK IV | |

| | |line and a plane. | | | |Pgs 107-113 | |

| | |(contd) | | | | | |

| |6 |Angle between two planes. |Identify the angle between two planes. |Q/A counting planes; |Models of solids. |KLB BK IV | |

| | | | |Exposition. | |Pgs 113-118 | |

| | | | | | | | |

| | | | | | | | |

| |7 |Angle between two planes. |Find the angle between two planes. |Exposition; |Models of solids. |KLB BK IV | |

| | |(contd) | |Guided discovery; | |Pgs 113-118 | |

| | | | |Worked examples; | | | |

| | | | |Written exercise. | | | |

| | | | | | | | |

|12 | |END OF TERM EXAMS | |

|13 | | | |

|SCHEME OF WORK FORM FOUR MATHEMATICS TERM TWO YEAR 20………… |

|1 |1 |Angle between two planes. |Find the angle between two planes. |Problem solving. |Models of solids. |KLB BK IV | |

| | |(contd) | | | |Pgs 113-118 | |

| |2 |Length between two points in|Determine length between two points in three |Supervised practice, |Models of solids. |KLB BK IV | |

| | |three dimensions. |dimensions. |Problem solving. | |Pgs 119-124 | |

| |3 |Length between two points on|Determine length between two points on nets of|Making nets of solids; |Manilla off-cuts, |KLB BK IV | |

| | |nets of solids. |solids. |Supervised practice, |scissors/ Models of |Pg 118 | |

| | | | |Problem solving. |solids. | | |

| |4 |Angle between skew lines. |Find the angle between skew lines. |Exposition; |Models of solids. |KLB BK IV | |

| | | | |Guided discovery; | |Pgs 142-8 | |

| | | | |Worked examples; | | | |

| | | | |Written exercise | | | |

| |5 |LONGITUDES AND LATITUDES | | |Globe, atlas. |KLB BK IV | |

| | | | | | |Pgs 125-7 | |

| | |Great and small circles | |Probing questions; | | | |

| | | |Identify great and small circles from on a |Oral exercise. | | | |

| | | |globe. | | | | |

| |6 |Difference in longitudes and|Find the difference in longitudes and |Probing questions; |Wire globe. |KLB BK IV | |

| | |latitudes. |latitudes. |Oral exercise. | |Pgs 128-9, 131-141| |

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| | | | | | | | |

| | | | | | | | |

| |7 |Distance along a great |Calculate the distance along a great circle. |Exposition; |Wire globe, calculator. |KLB BK IV | |

| | |circle. |(in nm) |Guided discovery; | |Pgs 130-3, | |

| | |(in nm) | |Worked examples; | |131-141 | |

| | | | |Written exercise | | | |

|2 |1 |Distance along a great |Calculate the distance along a great circle. |Exposition; |Wire globe, calculator. |KLB BK IV | |

| | |circle. |(in nm) |Guided discovery; | |Pgs 130-3, | |

| | |(in km) | |Worked examples; | |131-141 | |

| | | | |Written exercise | | | |

| |2 |Distance along a small |Calculate the distance along a great circle. |Exposition; |Wire globe, calculator. |KLB BK IV | |

| | |circle. |(in nm) |Guided discovery; | |Pgs 130-3, | |

| | |(in nm) | |Worked examples; | |131-141 | |

| | | | |Written exercise | | | |

| |3 |Distance along a small |Calculate the distance along a great circle. |Review previous exercise; |Wire globe, calculator. |KLB BK IV | |

| | |circle. |(in nm) |Worked examples; | |Pgs 133-7 | |

| | |(in km) | |Written exercise | | | |

| |4 |Shortest distance between |Determine the shortest distance between two |Review previous exercise; |Wire globe, calculator. |KLB BK IV | |

| | |two points on the earth’s |points on the earth’s surface. |Worked examples; | |Pgs 137-9 | |

| | |surface. | |Written exercise | | | |

| |5 |Longitudes and time. |Relate longitudes with local time. |Probing questions; |Wire globe, calculator. |KLB BK IV | |

| | | | |Worked examples; | |Pgs 141-2 | |

| | | | |Written exercise. | | | |

| |6 |Speed (in km/h) |Calculate speed given distance and time. |Probing questions; |Wire globe, calculator. |KLB BK IV | |

| | | | |Worked examples; | |Pgs 142 | |

| | | | |Written exercise. | | | |

| |7 |Speed (in knots) |Calculate speed given distance in nm and time.|Review previous exercise; |Wire globe, calculator. |KLB BK IV | |

| | | | |Probing questions; | |Pgs 142 | |

| | | | |Worked examples; | | | |

| | | | |Written exercise. | | | |

|3 |1 |LINEAR PROGRAMMING | | | | | |

| | | | | | | | |

| | |Forming inequalities. | | | | | |

| | | |Form inequalities from given situations. |Q/A to review inequalities; |Graph papers. | | |

| | | | |Worked examples; | |KLB BK 1V | |

| | | | |Written exercise. | |Pgs 150-1 | |

| |2 |Forming inequalities. |Form inequalities from given situations. |Review previous exercise. |Graph papers. |KLB BK IV | |

| | | | |Problem solving. | |Pgs 150-1 | |

| |3 |Solutions of linear |Solve linear inequalities. |Probing questions; |Graph papers. |KLB BK IV | |

| | |inequalities. | |Worked examples; | |Pgs 151-2 | |

| | | | |Written exercise. | | | |

| |4 |Graphs of linear |Represent situations graphically with |Worked examples; |Graph papers. |KLB BK IV | |

| | |inequalities. |inequalities. |Supervised practice; | |Pgs 188-90 | |

| | | | |Written exercise. | | | |

| |5 |Graphs of linear |Represent situations graphically with |Exercise review; |Graph papers. |KLB BK IV | |

| | |inequalities. |inequalities. |Supervised practice; | |Pgs 188-90 | |

| | |(contd) | |Written exercise. | | | |

| |6 |Objective function. |Formulate the objective function. |Probing questions; |Graph papers. |KLB BK IV | |

| | | | |Oral exercise. | |Pgs 191-4 | |

| |7 |Optimization. |Obtain the optimum solution to inequalities. |Exposition; |Graph papers. |KLB BK IV | |

| | | | |Guided discovery. | |Pgs 194-7 | |

| | | | |Written exercise. | | | |

|4 |1 |Further Optimization. |Obtain the optimum solution to inequalities. |Guided discovery. |Graph papers. |KLB BK IV | |

| | | | |Written exercise. | |Pgs 197-201 | |

| |2 |DIFFERENTI-- | | | | | |

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| | |Average rate of change. |Define average rate of change. |Filling in a table of values for a |Graph papers, calculaors. | | |

| | | |Determine average rate of change. |curve; | |KLB BK IV | |

| | | | |Plotting the curve; | |Pgs 162-3 | |

| | | | |Finding average rate of change. | | | |

| | | | |Written exercise. | | | |

| |3 |Instantaneous rate of |Define instantaneous rate of change. |Drawing a tangent to a curve; | |KLB BK IV | |

| | |change. |Determine instantaneous rate of change. |Supervised working; | |Pg 163 | |

| | | | |Written exercise. | | | |

| |4 |Gradient of a curve at a |Find gradient of a curve at a point. |Q/A to review gradient of a line; | |KLB BK IV | |

| | |point. | |Exposition of gradient of a curve; | |Pgs 163-4 | |

| | | | |Worked examples. | | | |

| |5 |Gradient of a curve. |Determine gradient of a curve. |Exposition; | |KLB BK IV | |

| | |(first principles) |(first principles) |Probing questions. | |Pgs 164-6 | |

| |6 |Derivative of a function. |Obtain derivative of a function. (first |Exposition; | |KLB BK IV | |

| | |(first principles) |principles) |Probing questions. | |Pgs 167-9 | |

| |7 |Meaning of differentiation. |Recall the process of differentiation. |Exposition; | |KLB BK IV | |

| | | | |Worked examples; | |Pgs 166-7 | |

| | | | |Supervised practice; | | | |

| | | | |Written exercise. | | | |

|5 |1 |Derivative of a polynomial. |Differentiate a polynomial. |Exposition; | |KLB BK IV | |

| | | | |Worked examples; | |Pgs 170-2 | |

| | | | |Supervised practice; | | | |

| | | | |Written exercise. | | | |

| |2 |Derivative of a polynomial |Differentiate a polynomial having a |Exposition; | |KLB BK IV | |

| | |with a denominator. |denominator. |Worked examples; | |Pgs 170-2 | |

| | | | |Supervised practice; | | | |

| | | | |Written exercise. | | | |

| |3 |Derivative of a quadratic |Differentiate a quadratic function. |Exposition; | |KLB BK IV | |

| | |function. | |Worked examples; | |Pgs 170-2 | |

| | | | |Supervised practice; | | | |

| | | | |Written exercise. | | | |

| |4 |Obtaining gradient from |Obtain gradient from gradient function. |Worked examples; | |KLB BK IV | |

| | |gradient function. | |Supervised practice; | |Pgs 170-2 | |

| | | | |Written exercise. | | | |

| |5 |Equation of a tangent to a |Find equation of a tangent to a curve at a |Q/A review gradient function; | |KLB BK IV | |

| | |curve at a point. |point. |Worked examples; | |Pgs 173-4 | |

| | | | |Written exercise. | | | |

| |6 |Equation of a normal to a |Find equation of a normal to a curve at a |Q/A review gradient function and | |KLB BK IV | |

| | |curve at a point. |point. |gradients of perpendicular lines; | |Pgs 173-4 | |

| | | | |Worked examples; | | | |

| | | | |Supervised practice; | | | |

| | | | |Written exercise. | | | |

| |7 |Stationary point ((minimum) |Determine minimum point of a curve. |Filling in a table of gradients at |Graph books. |KLB BK IV | |

| | | | |various points; | |Pgs 174-5 | |

| | | | |Probing questions; | | | |

| | | | |Discussion. | | | |

|6 |1 |Stationary point ((maximum) |Determine maximum point of a curve. |Filling in a table of gradients at |Graph books. |KLB BK IV | |

| | | | |various points; | |Pgs 175-6 | |

| | | | |Probing questions; | | | |

| | | | |Discussion. | | | |

| |2 |Stationary point (point of |Determine a point of inflexion on a curve. |Filling in a table of gradients at |Graph books. |KLB BK IV | |

| | |inflexion +ve to +ve) | |various points; | |Pgs 176-7 | |

| | | | |Probing questions; | | | |

| | | | |Discussion. | | | |

| |3 |Stationary point (point of |Determine a point of inflexion on a curve. |Filling in a table of gradients at |Graph books. |KLB BK IV | |

| | |inflexion -ve to -ve) | |various points; | |Pgs 176-7 | |

| | | | |Probing questions; | | | |

| | | | |Discussion. | | | |

| |4 |Features of a curve. |Identify points on a curve. |Probing questions; |Graph books. |KLB BK IV | |

| | | |Identify stationary points of a curve. |Oral exercise. | |Pgs 180-1 | |

| |5 |Curve sketching |Sketch curves. |Supervised practice; |Graph books. |KLB BK IV | |

| | | | |Written exercise. | |Pgs 180-2 | |

| |6 |Displacement time graphs. |Sketch and interpret displacement time graphs.|Q/A to review relation between | |KLB BK IV | |

| | | | |displacement and velocity; | |Pgs 182-3 | |

| | | | |Supervised practice; | | | |

| | | | |Discussion. | | | |

| |7 |Velocity from displacement |Determine velocity from a displacement |Worked examples; | |KLB BK IV | |

| | |function. |function. |Written exercise. | |Pgs 182-3 | |

| |7 |1 |Velocity time graphs. |Sketch and interpret velocity |

| | | | |time graphs. |

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