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FORM 4 MATHS SCHEMES OF WORK FOR TERM 1-3.
| SCHEME OF WORK FORM FOUR MATHEMATICS TERM ONE YEAR | |||||||
WKNO. | L/NO | TOPIC / SUBTOPIC | LESSON / SPECIFIC OBJECTIVES | TEACHING / LEARNING ACTIVITIES | MATERIALS / RESOURCES | REFERE- NCES | REMARKS |
| 1 | 1 | MATRICES & TRANSFORMA-TIONS Definition of a transformation. Reflection in the y-axis. | By the end of the lesson, the learner should be able to:
Define a transformation. Obtain image of an object by reflection in the y-axis. | Questioning to review position vectors; Drawing objects and their images on the Cartesian plane; Inferring the matrix of transformation for reflection in the y-axis. Written exercise.
|
Geo – board, Graph papers, mirrors. |
KLB BK IV Pgs 1-2 | |
| 2 | Reflection in the x-axis. | Obtain image of an object by reflection in the x-axis. | Drawing object and image on the Cartesian plane; Inferring the matrix of transformation for reflection in the x-axis. Written exercise.
| Geo – board, Graph papers, mirrors. | KLB BK IV Pgs 2 – 3 | ||
| 3 | Reflection in the Lines y = x, y = – x and other lines. | Obtain image of an object by reflection in a given line.
Obtain the object given its image and line of reflection.
| Review equation of a line; Draw the line y = x; Reflect an object in the line y = x; Infer the matrix of transformation Written exercise.
| Geo – board, Graph papers, mirrors. | KLB BK IV Pgs 2-3 | ||
| 4 | Rotation matrix. (positive angle) | Obtain image of an object by rotation through a positive angle. Obtain the object given its image and positive rotation angle.
| Guided discovery; Worked example; Written exercise. | Geo – board, Graph papers.
| KLB BK IV Pgs 3-4 | ||
| 5 | Rotation matrix. (negative angle) | Obtain image of an object by rotation through a negative angle.
| Guided discovery; Worked example; Written exercise. | Geo – board, Graph papers.
| KLB BK IV Pgs 3-4 | ||
| 6 | The unit circle. | Use the unit circle to identify a transformation represented by a given matrix. | Guided discovery; Worked example; Written exercise. | Geo – board, Graph papers.
| KLB BK IV Pgs 9-13 | ||
| 7 | Finding matrix of transformation. | Find matrix of transformation given an object and image. Describe the transformation fully. | Review simultaneous equations and matrix multiplication; Worked examples; Written exercise. | Geo – board, Graph papers.
| KLB BK IV Pgs 6-8 | ||
| 2 | 1 | Enlargement matrix. | Identify an enlargement matrix. Perform operations involving enlargement matrices.
| Review scale factor and centre of enlargement; Worked examples; Written exercise.
| Geo – board, Graph papers.
| KLB BK IV Pgs 11-12 | |
| 2 | Two successive transformations. | Perform two successive transformations. | Guided discovery of order of operation; Written exercise. | Geo – board, Graph papers.
| KLB BK IV Pgs 16-17 | ||
| 3 | Several successive transformations. | Perform several successive transformations. | Previous exercise review; Guided discovery of order of operation; Written exercise. | Geo – board, Graph papers.
| KLB BK IV Pgs 16-17 | ||
| 4 | Combined matrix of transformations. | Find combined matrix of several transformations. | Previous exercise review; Guided discovery of order of operation; Written exercise. | Geo – board, Graph papers.
| KLB BK IV Pgs 21-22 | ||
| 5 | Inverse of a transformation matrix. | Identify the identity matrix. Determine the inverse of a transformation matrix. | Worked examples using several methods; Supervised practice; Written exercise.
| Geo – board, Graph papers.
| KLB BK IV Pgs 24-26 | ||
| 6 | Inverse of several transformation matrices. | Determine the inverse of several combined transformation matrices. | Worked; Supervised practice; Written exercise.
| Geo – board, Graph papers.
| KLB BK IV Pgs 24-26 | ||
| 7 | A.S.F. and determinant of a transformation matrix. | State the relation between A.S.F. and determinant of a transformation matrix. | Finding area of object, image, ASF; Guided discovery; Written exercise.
| Geo – board, Graph papers.
| KLB BK IV Pgs 26-27 | ||
| 3 | 1 | Shear transformation. (x-axis invariant) | Identify a shear transformation. (x-axis invariant) Describe a shear fully. | Drawing object and image under a shear transformation; Oral exercise; Written exercise.
| Geo – board, Graph papers.
| KLB BK IV Pgs 28-32 | |
| 2 | Shear transformation. (y-axis invariant) | Identify a shear transformation. (y-axis invariant) Describe a shear fully. | Drawing object and image under a shear transformation; Oral exercise; Written exercise.
| Geo – board, Graph papers.
| KLB BK IV Pgs 28-31 | ||
| 3 | Finding shear matrix. | Find shear matrix given the object and image. | Worked examples; Written exercise. | Geo – board, Graph papers.
| KLB BK IV Pgs 31-2 | ||
| 4 | One-way stretch. (x-axis invariant) | Describe a one-way stretch. (x-axis invariant) Find the scale factor of a stretch. | Guided discovery; Worked examples and discussion.
| Geo – board, Graph papers.
| KLB BK IV Pgs 32-34 | ||
| 5 | One-way stretch. (y-axis invariant) | Describe a one-way stretch. (y-axis invariant). Find the scale factor of a stretch. | Guided discovery; Worked examples and discussion.
| Geo – board, Graph papers.
| KLB BK IV Pgs 32-34 | ||
| 6 | Isometric and non-isometric transformation. | Classify transformations as either isometric or non-isometric. | Review types of transformations; Probing questions on size and shape of objects and images.
| KLB BK IV Pg 35 | |||
| 7 | Test / mixed exercise. | Past exam papers. | |||||
| 4 | 1 | STATISTICS II
Mean and assumed mean. (frequency 1) |
Find mean of ungrouped data using an assumed mean. (frequency 1) | Simple worked examples; Exposition of method involving an assumed mean; Written exercise.
| Calculator. | KLB BK IV Pgs 38-39 | |
| 2 | Mean and assumed mean. (frequency > 1) | Find mean of ungrouped data using an assumed mean. (frequency > 1) | Simple worked examples; Written exercise.
| Calculator. | KLB BK IV Pg 40 | ||
| 3 | Mean of grouped data. | Find mean of grouped data. | Review previous exercise; Completing table; Worked examples. | Calculator. | KLB BK IV Pgs 40-41 | ||
| 4 | Mean of grouped data. (alternative methods) | Find mean of grouped data. (alternative methods) | Completing table; Worked examples. Written exercise. | Calculator. | KLB BK IV Pgs 40-46 | ||
| 5 | Median. | Find median of grouped data. | Worked examples; Written exercise. | Calculator. | KLB BK IV Pgs 46-7 | ||
| 6 | Quartiles. | Find upper and lower quartiles. | Exposition; Worked examples; Written exercise. | Calculator. | KLB BK IV Pgs 47-8 | ||
| 7 | Deciles and Percentiles. | Define a decile and percentile. Find nth decile / percentile. | Exposition; Worked examples; Written exercise. | Calculator. | KLB BK IV Pgs 47-8 | ||
| 5 | 1 | Cumulative frequency curve. | Draw a cumulative frequency curve. | Q/A to review upper and lower limits of class boundaries; Complete a table by finding cumulative totals; Draw an ogive.
| Calculator, graph papers. | KLB BK IV Pgs 38-40 | |
| 2 | Median and quartiles from an ogive. | Estimate median and quartiles from an ogive. | Probing questions to make inferences from an ogive.
| Calculator, graph papers. | KLB BK IV Pgs 48-50 | ||
| 3 | Deciles and percentiles from an ogive. | Estimate deciles and percentiles from an ogive. | Probing questions to make inferences from an ogive.
| Calculator, graph papers. | KLB BK IV Pgs 53-55 | ||
| 4 | Range, inter-quartile range and quartile deviation. | Find range and inter-quartile range of a set of data. | Exposition and oral exercise. | Calculator. | KLB BK IV Pgs 55-56 | ||
| 5 | Mean absolute deviation. | Determine mean absolute deviation. | Exposition; Worked examples. | Calculator. | KLB BK IV Pgs 56-7 | ||
| 6 | Variance. | Define variance. Determine variance of a set of data. | Exposition; Worked examples. | Calculator. | KLB BK IV Pgs 57-59 | ||
| 7 | Standard deviation. | Determine standard deviation of a set of data. | Exposition; Worked examples; Written exercise. | Calculator. | KLB BK IV Pgs 59-60 | ||
| 6 | 1-4 | Formulae for standard deviation. | Use various methods of finding std deviation. | Exposition; Worked examples; Written exercise. | Calculator. | KLB BK IV Pgs 60-3 | |
| 5 | LOCI
Definition of a locus. |
Define locus of a point. |
Illustrative examples; Exposition of meaning of locus of a point.
|
Door, clock, see saw, etc. | KLB BK IV Pgs 66-7 | ||
| 6 | Sketching locus of a point. | Sketch locus of a point. | Oral exercise; Supervised practice; Written exercise. | KLB BK IV Pgs 67-8 | |||
| 7 | Perpendicular bisector locus. (two dimensions) | Describe perpendicular bisector locus. (two dimensions) | Geometrical construction; Guided discovery; Written exercise. | Geometrical sets. | KLB BK IV Pgs 68-9 | ||
| 7 | 1 | Perpendicular bisector locus. (three dimensions) | Describe perpendicular bisector locus. (three dimensions) | Geometrical construction; Guided discovery; Supervised practice; Written exercise. | Geometrical sets. | KLB BK IV Pg 69 | |
| 2 | Locus of points at a given distance from a fixed point. (two dim) | Describe locus of points at a given distance from a fixed point. | Geometrical construction; Guided discovery; Written exercise. | Geometrical sets. | KLB BK IV Pg 70 | ||
| 3 | Locus of points at a given distance from a fixed point. (three dim) | Describe locus of points at a given distance from a fixed point. | Geometrical construction; Guided discovery; Written exercise. | Geometrical sets. | KLB BK IV Pg 71 | ||
| 4 | Locus of points at a given distance from a line. (two dim) | Describe locus of points at a given distance from a fixed point. | Geometrical construction; Guided discovery; Written exercise. | Geometrical sets. | KLB BK IV Pg 69 | ||
| 5 | Locus of points at a given distance from a line. (three dim) | Describe locus of points at a given distance from a fixed point. | Geometrical construction; Guided discovery; Written exercise. | Geometrical sets. | KLB BK IV Pg 70 | ||
| 6 | Angle bisector locus. | Construct the angle bisector locus. | Geometrical construction; Guided discovery; Written exercise. | Geometrical sets. | KLB BK IV Pg 70 | ||
| 7 | Constant angle locus. | Construct constant angle locus. | Probing questions to review angle properties of a circle; Geometrical construction; Guided discovery; Written exercise. | Geometrical sets. | KLB BK IV Pgs 72-4 | ||
| 8 | 1 | Constant angle locus. (contd) | Construct constant angle locus. | Probing questions to review previous exercise; Geometrical construction; Guided discovery; Written exercise. | Geometrical sets. | KLB BK IV Pgs 72-4 | |
| 2 | Intersecting loci involving lines and angles. | Construct intersecting loci involving lines and angles. | Geometrical construction; Supervised practice; Written exercise. | Geometrical sets. | KLB BK IV Pgs 72-4 | ||
| 3 | Circumcircle locus. | Construct a circumcircle. | Geometrical construction; Supervised practice; Written exercise. | Geometrical sets. | KLB BK IV Pg 78 | ||
| 4 | In-circle locus. | Construct an in-circle locus. | Geometrical construction; Supervised practice; Written exercise. | Geometrical sets. | KLB BK IV Pg 78 | ||
| 5 | Ex-circle locus. | Construct an ex-circle locus. | Geometrical construction; Supervised practice; Written exercise. | Geometrical sets. | KLB BK IV Pg 78 | ||
| 6 | Intersecting loci in plane figures. | Construct intersecting loci in plane figures. | Problem solving. | Geometrical sets. | KLB BK IV Pgs 79-81 | ||
| 7 | Loci of inequalities. | Draw locus of points that satisfy various inequalities. | Q/A to review simple and compound inequalities; Worked examples; Written exercise. | Geometrical sets. | KLB BK IV Pgs 81-2 | ||
| 9 | 1 | Loci of inequalities. (contd) | Draw locus of points that satisfy various inequalities. | Review previous exercise; Further worked examples; Written exercise. | Geometrical sets. | KLB BK IV Pg 83 | |
| 2 | Locus involving chords. | Construct locus involving chords. | Worked examples; Written exercise.
| Geometrical sets. | KLB BK IV Pgs 96-97 | ||
| 3 | TRIGONOMETRY III
Some trigonometric ratios. |
Rearrange trigonometric expressions.
|
Exposition and worked examples; 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 waves. | Determine period and amplitude of waves. | Exposition and worked examples. | Geometrical sets. | KLB BK IV 94-5 | ||
| 6 | Tables for trigonometric functions. | Complete tables for trigonometric functions.
| Exposition and worked examples. | Calculator.
| KLB BK IV Pgs 96-7 | ||
| 7 | Graphs for trig. functions. | Plot graphs for trigonometric functions.
| Drawing graphs; supervised practice; make inferences from the graphs. | Geometrical sets, graph papers. | KLB BK IV Pgs 96-7 | ||
| 10 | 1 | Further graphs for trig. functions. | Plot graphs for trigonometric functions.
| Drawing graphs; supervised practice; make inferences from the graphs. | Geometrical sets, graph papers. | KLB BK IV Pgs 96-7 | |
| 2 | Transformations of waves. | Describe some transformations of waves. | Supervised practice; Exposition and worked examples; Written exercise. | Geometrical sets, graph papers. | KLB BK IV Pgs 96-97 | ||
| 3 | Waves with a phase angle. (positive) | Determine the phase angle (positive) for two waves. | Guided discovery; Written exercise. | Geometrical sets, graph papers. | KLB BK IV Pgs 97-8 | ||
| 4 | Waves with a phase angle. (negative) | Determine the phase angle (negative) for two waves. | Guided discovery; Written exercise. | Geometrical sets, graph papers. | KLB BK IV Pgs 97-8 | ||
| 5 | Trigonometric equations. | Solve trigonometric equations. | Q/A to review trig. ratios for complementary angles; Worked examples; Supervised practice; Written exercise. | Geometrical sets, graph papers. | KLB BK IV Pgs 100-3 | ||
| 6 | Further trig. equations. | Solve trigonometric equations. | Exercise review; Problem solving. | Geometrical sets, graph papers. | KLB BK IV Pgs 100-3 | ||
| 7 | Graph of a trig. function and a line. | Draw the graph of a trig. function and a line to solve an equation. | Worked examples; Supervised practice; Written exercise. | Geometrical sets, graph papers. | KLB BK IV Pgs 100-3 | ||
| 11 | 1 | Graphs of two trig. functions. | Draw graphs of two trig. functions to solve some equations. | Worked examples; Supervised practice; Written exercise. | Geometrical sets, graph papers. | KLB BK IV Pgs 100-3 | |
| 2 | THREE DIMENSIONAL GEOMETRY
Dimensions of figures. |
State the dimensions of figures. Identify faces, edges, and vertices of common figures. |
Probing questions; Oral exercise. |
Common planes and solids. |
KLB BK IV Pgs 104-6 | ||
| 3 | Angle between a line and a plane. | Identify the angle between a line and a plane. | Exposition; Oral exercise. | Cuboid wire mesh. | KLB BK IV Pgs 106-7 | ||
| 4 | Finding the angle between a line and a plane. | Find the angle between a line and a plane. | Guided discovery; Worked examples; Written exercise.
| Models of solids. | KLB BK IV Pgs 107-113 | ||
| 5 | Finding the angle between a line and a plane. (contd) | Find the angle between a line and a plane. | Problem solving. | Models of solids. | KLB BK IV Pgs 107-113 | ||
| 6 | Angle between two planes. | Identify the angle between two planes. | Q/A counting planes; Exposition.
| Models of solids. | KLB BK IV Pgs 113-118 | ||
| 7 | Angle between two planes. (contd) | Find the angle between two planes. | Exposition; Guided discovery; Worked examples; Written exercise.
| Models of solids. | KLB BK IV Pgs 113-118 | ||
| 12 13 | END OF TERM EXAMS | ||||||
| SCHEME OF WORK FORM FOUR MATHEMATICS TERM TWO YEAR | |||||||||||||||
| 1 | 1 | Angle between two planes. (contd) | Find the angle between two planes. | Problem solving. | Models of solids. | KLB BK IV Pgs 113-118 | |||||||||
| 2 | Length between two points in three dimensions. | Determine length between two points in three dimensions. | Supervised practice, Problem solving. | Models of solids. | KLB BK IV Pgs 119-124 | ||||||||||
| 3 | Length between two points on nets of solids. | Determine length between two points on nets of solids. | Making nets of solids; Supervised practice, Problem solving. | Manilla off-cuts, scissors/ Models of solids. | KLB BK IV Pg 118 | ||||||||||
| 4 | Angle between skew lines. | Find the angle between skew lines. | Exposition; Guided discovery; Worked examples; Written exercise | Models of solids. | KLB BK IV Pgs 142-8 | ||||||||||
|
| 5 | LONGITUDES AND LATITUDES
Great and small circles |
Identify great and small circles from on a globe. |
Probing questions; Oral exercise. | Globe, atlas. | KLB BK IV Pgs 125-7 | |||||||||
|
| 6 | Difference in longitudes and latitudes. | Find the difference in longitudes and latitudes. | Probing questions; Oral exercise.
| Wire globe. | KLB BK IV Pgs 128-9, 131-141 | |||||||||
| 7 | Distance along a great circle. (in nm) | Calculate the distance along a great circle. (in nm) | Exposition; Guided discovery; Worked examples; Written exercise | Wire globe, calculator. | KLB BK IV Pgs 130-3, 131-141 | ||||||||||
| 2 | 1 | Distance along a great circle. (in km) | Calculate the distance along a great circle. (in nm) | Exposition; Guided discovery; Worked examples; Written exercise | Wire globe, calculator. | KLB BK IV Pgs 130-3, 131-141 | |||||||||
| 2 | Distance along a small circle. (in nm) | Calculate the distance along a great circle. (in nm) | Exposition; Guided discovery; Worked examples; Written exercise | Wire globe, calculator. | KLB BK IV Pgs 130-3, 131-141 | ||||||||||
| 3 | Distance along a small circle. (in km) | Calculate the distance along a great circle. (in nm) | Review previous exercise; Worked examples; Written exercise | Wire globe, calculator. | KLB BK IV Pgs 133-7 | ||||||||||
|
| 4 | Shortest distance between two points on the earth’s surface. | Determine the shortest distance between two points on the earth’s surface. | Review previous exercise; Worked examples; Written exercise | Wire globe, calculator. | KLB BK IV Pgs 137-9 | |||||||||
| 5 | Longitudes and time. | Relate longitudes with local time. | Probing questions; Worked examples; Written exercise. | Wire globe, calculator. | KLB BK IV Pgs 141-2 | ||||||||||
| 6 | Speed (in km/h) | Calculate speed given distance and time. | Probing questions; Worked examples; Written exercise. | Wire globe, calculator. | KLB BK IV Pgs 142 | ||||||||||
| 7 | Speed (in knots) | Calculate speed given distance in nm and time. | Review previous exercise; Probing questions; Worked examples; Written exercise. | Wire globe, calculator. | KLB BK IV Pgs 142 | ||||||||||
| 3 | 1 | LINEAR PROGRAMMING
Forming inequalities. |
Form inequalities from given situations. |
Q/A to review inequalities; Worked examples; Written exercise.
|
Graph papers. |
KLB BK 1V Pgs 150-1 | |||||||||
| 2 | Forming inequalities. | Form inequalities from given situations. | Review previous exercise. Problem solving.
| Graph papers. | KLB BK IV Pgs 150-1 | ||||||||||
| 3 | Solutions of linear inequalities. | Solve linear inequalities. | Probing questions; Worked examples; Written exercise.
| Graph papers. | KLB BK IV Pgs 151-2 | ||||||||||
| 4 | Graphs of linear inequalities. | Represent situations graphically with inequalities.
| Worked examples; Supervised practice; Written exercise.
| Graph papers. | KLB BK IV Pgs 188-90 | ||||||||||
| 5 | Graphs of linear inequalities. (contd) | Represent situations graphically with inequalities.
| Exercise review; Supervised practice; Written exercise.
| Graph papers. | KLB BK IV Pgs 188-90 | ||||||||||
| 6 | Objective function. | Formulate the objective function.
| Probing questions; Oral exercise. | Graph papers. | KLB BK IV Pgs 191-4 | ||||||||||
| 7 | Optimization. | Obtain the optimum solution to inequalities. | Exposition; Guided discovery. Written exercise.
| Graph papers. | KLB BK IV Pgs 194-7 | ||||||||||
| 4 | 1 | Further Optimization. | Obtain the optimum solution to inequalities. | Guided discovery. Written exercise.
| Graph papers. | KLB BK IV Pgs 197-201 | |||||||||
| 2 | DIFFERENTI– ATION
Average rate of change.
|
Define average rate of change. Determine average rate of change.
|
Filling in a table of values for a curve; Plotting the curve; Finding average rate of change. Written exercise. |
Graph papers, calculaors. |
KLB BK IV Pgs 162-3 | ||||||||||
| 3 | Instantaneous rate of change. | Define instantaneous rate of change. Determine instantaneous rate of change.
| Drawing a tangent to a curve; Supervised working; Written exercise.
| KLB BK IV Pg 163 | |||||||||||
| 4 | Gradient of a curve at a point. | Find gradient of a curve at a point. | Q/A to review gradient of a line; Exposition of gradient of a curve; Worked examples.
| KLB BK IV Pgs 163-4 | |||||||||||
| 5 | Gradient of a curve. (first principles) | Determine gradient of a curve. (first principles) | Exposition; Probing questions. | KLB BK IV Pgs 164-6 | |||||||||||
| 6 | Derivative of a function. (first principles) | Obtain derivative of a function. (first principles) | Exposition; Probing questions. | KLB BK IV Pgs 167-9 | |||||||||||
| 7 | Meaning of differentiation. | Recall the process of differentiation. | Exposition; Worked examples; Supervised practice; Written exercise. | KLB BK IV Pgs 166-7 | |||||||||||
| 5 | 1 | Derivative of a polynomial. | Differentiate a polynomial. | Exposition; Worked examples; Supervised practice; Written exercise. | KLB BK IV Pgs 170-2 | ||||||||||
| 2 | Derivative of a polynomial with a denominator. | Differentiate a polynomial having a denominator. | Exposition; Worked examples; Supervised practice; Written exercise. | KLB BK IV Pgs 170-2 | |||||||||||
| 3 | Derivative of a quadratic function. | Differentiate a quadratic function. | Exposition; Worked examples; Supervised practice; Written exercise. | KLB BK IV Pgs 170-2 | |||||||||||
| 4 | Obtaining gradient from gradient function. | Obtain gradient from gradient function. | Worked examples; Supervised practice; Written exercise. | KLB BK IV Pgs 170-2 | |||||||||||
| 5 | Equation of a tangent to a curve at a point. | Find equation of a tangent to a curve at a point. | Q/A review gradient function; Worked examples; Written exercise.
| KLB BK IV Pgs 173-4 | |||||||||||
| 6 | Equation of a normal to a curve at a point. | Find equation of a normal to a curve at a point. | Q/A review gradient function and gradients of perpendicular lines; Worked examples; Supervised practice; Written exercise.
| KLB BK IV Pgs 173-4 | |||||||||||
| 7 | Stationary point ((minimum) | Determine minimum point of a curve. | Filling in a table of gradients at various points; Probing questions; Discussion. | Graph books. | KLB BK IV Pgs 174-5 | ||||||||||
| 6 | 1 | Stationary point ((maximum) | Determine maximum point of a curve. | Filling in a table of gradients at various points; Probing questions; Discussion. | Graph books. | KLB BK IV Pgs 175-6 | |||||||||
| 2 | Stationary point (point of inflexion +ve to +ve)
| Determine a point of inflexion on a curve. | Filling in a table of gradients at various points; Probing questions; Discussion. | Graph books. | KLB BK IV Pgs 176-7 | ||||||||||
| 3 | Stationary point (point of inflexion -ve to -ve)
| Determine a point of inflexion on a curve. | Filling in a table of gradients at various points; Probing questions; Discussion. | Graph books. | KLB BK IV Pgs 176-7 | ||||||||||
| 4 | Features of a curve. | Identify points on a curve. Identify stationary points of a curve. | Probing questions; Oral exercise. | Graph books. | KLB BK IV Pgs 180-1 | ||||||||||
| 5 | Curve sketching | Sketch curves. | Supervised practice; Written exercise. | Graph books. | KLB BK IV Pgs 180-2 | ||||||||||
| 6 | Displacement time graphs. | Sketch and interpret displacement time graphs. | Q/A to review relation between displacement and velocity; Supervised practice; Discussion. | KLB BK IV Pgs 182-3 | |||||||||||
| 7 | Velocity from displacement function. | Determine velocity from a displacement function. | Worked examples; Written exercise.
| KLB BK IV Pgs 182-3 | |||||||||||
| 7 | 1 | Velocity time graphs. | Sketch and interpret velocity time graphs. | Q/A to review relation between velocity and acceleration; Supervised practice; Discussion. | KLB BK IV Pgs 184-6 | ||||||||||
| 2 | Acceleration from velocity function. | Determine velocity from a displacement function. | Worked examples; Written exercise.
| KLB BK IV Pgs 184-6 | |||||||||||
| 3 | Acceleration from displacement function. | Determine acceleration from a displacement function. | Probing questions; Worked examples; Written exercise.
| KLB BK IV Pgs 184-6 | |||||||||||
| 4 | Maxima and minima. | Apply differentiation to find maxima and minima. | Exposition; Worked examples; Written exercise.
| KLB BK IV Pgs 186-9 | |||||||||||
| 5 | Maxima and minima (contd) | Apply differentiation to find maxima and minima. | Exercise review; Problem solving. | KLB BK IV Pgs 186-9 | |||||||||||
| 6 | INTEGRATION
Reverse the process of differentiation. |
Reverse the process of differentiation. |
Probing questions; Worked examples; Written exercise.
|
KLB BK IV Pgs 207-9 | |||||||||||
| 7 | Finding y given gradient function. | Find y given gradient function. | Probing questions; Worked examples; Written exercise.
| KLB BK IV Pgs 209-12 | |||||||||||
| 1 | Indefinite integral. | Obtain an indefinite integral. | Exposition; Worked examples; Written exercise.
| KLB BK IV Pgs 212-6 | |||||||||||
| 8 | 1 | Definite integral. | Obtain a definite integral. | Exposition; Worked examples; Written exercise.
| KLB BK IV Pgs 212-6 | ||||||||||
| 2 | Area bounded by a curve above x-axis. | Determine area bounded by a curve and x-axis. | Exposition; Worked examples; Written exercise.
| KLB BK IV Pgs 217-8 | |||||||||||
| 3 | Area bounded by a curve below x-axis. | Determine area bounded by a curve and x-axis. | Exposition; Worked examples; Written exercise.
| KLB BK IV Pgs 218-9 | |||||||||||
| 4 | Area bounded by a curve and a line. | Determine area bounded by a curve and a straight line. | Exposition; Worked examples; Written exercise.
| KLB BK IV Pg 220 | |||||||||||
| 5 | Displacement from velocity function. | Obtain displacement from a velocity function. | Probing questions; Worked examples; Written exercise.
| KLB BK IV Pgs 223-4 | |||||||||||
| 6 | Velocity from acceleration function. | Obtain velocity from a acceleration function. | Probing questions; Worked examples; Written exercise.
| KLB BK IV Pgs 223-4 | |||||||||||
| 7 | Exercise on kinematics. | Apply integration and differentiation in kinematics. | Exercises review; Problem solving. | KLB BK IV Pgs 225-231 | |||||||||||
| 9 | 1 | AREA APPROXIMATION
Trapezium rule. |
Derive the trapezium rule. |
Divide area under a graph into several trapezia; Guided derivation of the trapezium rule. |
Copies of area under a curve. |
KLB BK IV Pgs 196-7 | |||||||||
| 2 | Application of trapezium rule. | Apply trapezium rule in problem solving. | Worked examples; Written exercise. | KLB BK IV Pgs 197-201 | |||||||||||
| 3 | Application of trapezium rule. | Apply trapezium rule in problem solving. | Written exercise review. Problem solving. | KLB BK IV Pgs 197-201 | |||||||||||
| 4 | The mid-ordinate rule. | Derive the mid-ordinate rule. | Divide area under a graph into several strips; Guided derivation of the trapezium rule. | KLB BK IV Pgs 202-3 | |||||||||||
| 5 | Application of mid-ordinate rule. | Apply mid-ordinate rule.in problem solving. | Worked examples; Written exercise. | KLB BK IV Pgs 203-6 | |||||||||||
| 6-7 | Application of mid-ordinate rule. | Apply mid-ordinate rule in problem solving. | Review exercises; Problem solving. | KLB BK IV Pgs 203-6 | |||||||||||
| 10-13 | MOCK K.C.S.E EXAM | ||||||||||||||
