If this scheme pleases you, click here to download.
| WK | LSN | TOPIC | SUB-TOPIC | OBJECTIVES | T/L ACTIVITIES | T/L AIDS | REFERENCE | REMARKS |
|---|---|---|---|---|---|---|---|---|
| 1 | 3 |
Circles: Chords and tangents
|
Length of an arc
Chords |
By the end of the
lesson, the learner
should be able to:
Calculate the length of an arc |
Discussions
Solving Demonstrating Explaining |
Geometrical set,calculator
Geometrical set ,calculator |
KLB Mathematics
Book Three Pg 124-125 |
|
| 1 | 4 |
Circles: Chords and tangents
|
Parallel chords
Equal chords |
By the end of the
lesson, the learner
should be able to:
Calculate the perpendicular bisector Find the value of parallel chords |
Discussions
Solving Demonstrating Explaining |
Geometrical set ,calculator
|
KLB Mathematics
Book Three Pg 129-131 |
|
| 1 | 5 |
Circles: Chords and tangents
|
Intersecting chords
|
By the end of the
lesson, the learner
should be able to:
Calculate the length of intersecting chords |
Discussions
Solving Demonstrating Explaining |
Geometrical set ,calculator
|
KLB Mathematics
Book Three Pg 132-135 |
|
| 1 | 6 |
Circles: Chords and tangents
|
Tangent to a circle
|
By the end of the
lesson, the learner
should be able to:
Construct a tangent to a circle |
Discussions
Solving Demonstrating Explaining |
Geometrical set ,calculator
|
KLB Mathematics
Book Three Pg 139-140 |
|
| 1 | 7 |
Circles: Chords and tangents
|
Properties of tangents to a circle from an external point
Tangents to two circles |
By the end of the
lesson, the learner
should be able to:
State the properties of tangents to a circle from an external point |
Discussions
Solving Demonstrating Explaining |
Geometrical set ,calculator
|
KLB Mathematics
Book Three Pg 142-144 |
|
| 2 | 1 |
Circles: Chords and tangents
|
Tangents to two circles
Contact of circles |
By the end of the
lesson, the learner
should be able to:
Calculate the tangents of transverse common tangents |
Discussions
Solving Demonstrating Explaining |
Geometrical set ,calculator
|
KLB Mathematics
Book Three Pg 150-151 |
|
| 2 | 2 |
Circles: Chords and tangents
|
Contact of circles
Problem solving |
By the end of the
lesson, the learner
should be able to:
Calculate the radii of contact circles |
Discussions
Solving Demonstrating Explaining |
Geometrical set ,calculator
|
KLB Mathematics
Book Three Pg 153-154 |
|
| 2 | 3 |
Circles: Chords and tangents
|
Angle in alternate segment
|
By the end of the
lesson, the learner
should be able to:
Calculate the angles in alternate segments |
Discussions
Solving Demonstrating Explaining |
Geometrical set ,calculator
|
KLB Mathematics
Book Three Pg 157-160 |
|
| 2 | 4 |
Circles: Chords and tangents
|
Circumscribed circle
Escribed circles |
By the end of the
lesson, the learner
should be able to:
Construct circumscribed circles |
Discussions
Solving Demonstrating Explaining |
Geometrical set ,calculator
|
KLB Mathematics
Book Three Pg 165 |
|
| 2 | 5 |
Circles: Chords and tangents
|
Centroid
Orthocenter |
By the end of the
lesson, the learner
should be able to:
Construct centroid |
Discussions
Solving Demonstrating Explaining |
Geometrical set ,calculator
|
KLB Mathematics
Book Three Pg 166 |
|
| 2 | 6 |
Compound proportions and rate of work
|
Compound proportions
|
By the end of the
lesson, the learner
should be able to:
Find the compound proportions |
Discussions
Solving Demonstrating Explaining |
Calculators
|
KLB Mathematics
Book Three Pg 288-290 |
|
| 2 | 7 |
Compound proportions and rate of work
|
Proportional parts
Rates of work |
By the end of the
lesson, the learner
should be able to:
Calculate the proportional parts |
Discussions
Solving Demonstrating Explaining |
Calculators
|
KLB Mathematics
Book Three Pg 291-293 |
|
| 3 | 1 |
Compound proportions and rate of work
|
Rates of work
|
By the end of the
lesson, the learner
should be able to:
Calculate the rate of work |
Discussions
Solving Demonstrating Explaining |
Calculators
|
KLB Mathematics
Book Three Pg 295-296 |
|
| 3 | 2 |
Graphical methods
|
Tables of given relations
Graphs of given relations |
By the end of the
lesson, the learner
should be able to:
Draw tables of given relations |
Discussions
Solving Demonstrating Explaining |
Geoboard & graph books
|
KLB Mathematics
Book Three Pg 299 |
|
| 3 | 3 |
Graphical methods
|
Graphical solution of cubic equations
|
By the end of the
lesson, the learner
should be able to:
Draw tables of cubic functions |
Discussions
Solving Demonstrating Explaining |
Geoboard & graph books
|
KLB Mathematics
Book Three Pg 301 |
|
| 3 | 4 |
Graphical methods
|
Average rates of change
Rate of change at an instant |
By the end of the
lesson, the learner
should be able to:
Calculate the average rates of change |
Discussions
Solving Demonstrating Explaining |
Geoboard & graph books
|
KLB Mathematics
Book Three Pg 304-306 |
|
| 3 | 5 |
Graphical methods
|
Empirical graphs
Reduction of non-linear laws to linear form |
By the end of the
lesson, the learner
should be able to:
Draw the empirical graphs |
Discussions
Solving Demonstrating Explaining |
Geoboard & graph books
|
KLB Mathematics
Book Three Pg 315-316 |
|
| 3 | 6 |
Graphical methods
|
Reduction of non-linear laws to linear form
|
By the end of the
lesson, the learner
should be able to:
Draw the graphs of reduction of non-linear laws to linear form |
Discussions
Solving Demonstrating Explaining |
Geoboard & graph books
Geoboard & graph bookss |
KLB Mathematics
Book Three Pg 318-321 |
|
| 3 | 7 |
Graphical methods
|
Equation of a circle
|
By the end of the
lesson, the learner
should be able to:
Find the equation of a circle |
Discussions
Solving Demonstrating Explaining |
Geoboard & graph books
|
KLB Mathematics
Book Three Pg 325-326 |
|
| 4 | 1 |
Graphical methods
|
Equation of a circle
|
By the end of the
lesson, the learner
should be able to:
Find the equation of a circle |
Discussions
Solving Demonstrating Explaining |
Geoboard & graph books
|
KLB Mathematics
Book Three Pg 327-328 |
|
| 4 | 2 |
Loci
|
Introduction to Loci
|
By the end of the
lesson, the learner
should be able to:
-Define locus and understand its meaning -Distinguish between locus of points, lines, and regions -Identify real-world examples of loci -Understand the concept of movement according to given laws |
-Demonstrate door movement to show path traced by corner -Use string and pencil to show circular locus -Discuss examples: clock hands, pendulum swing -Students trace paths of moving objects |
Exercise books
-Manila paper -String -Chalk/markers |
KLB Secondary Mathematics Form 4, Pages 73-75
|
|
| 4 | 3 |
Loci
|
Basic Locus Concepts and Laws
|
By the end of the
lesson, the learner
should be able to:
-Understand that loci follow specific laws or conditions -Identify the laws governing different types of movement -Distinguish between 2D and 3D loci -Apply locus concepts to simple problems |
-Physical demonstrations with moving objects -Students track movement of classroom door -Identify laws governing pendulum movement -Practice stating locus laws clearly |
Exercise books
-Manila paper -String -Real objects |
KLB Secondary Mathematics Form 4, Pages 73-75
|
|
| 4 | 4 |
Loci
|
Perpendicular Bisector Locus
|
By the end of the
lesson, the learner
should be able to:
-Define perpendicular bisector locus -Construct perpendicular bisector using compass and ruler -Prove that points on perpendicular bisector are equidistant from endpoints -Apply perpendicular bisector to solve problems |
-Construct perpendicular bisector on manila paper -Measure distances to verify equidistance property -Use folding method to find perpendicular bisector -Practice with different line segments |
Exercise books
-Manila paper -Compass -Ruler |
KLB Secondary Mathematics Form 4, Pages 75-82
|
|
| 4 | 5 |
Loci
|
Properties and Applications of Perpendicular Bisector
|
By the end of the
lesson, the learner
should be able to:
-Understand perpendicular bisector in 3D space -Apply perpendicular bisector to find circumcenters -Solve practical problems using perpendicular bisector -Use perpendicular bisector in triangle constructions |
-Find circumcenter of triangle using perpendicular bisectors -Solve water pipe problems (equidistant from two points) -Apply to real-world location problems -Practice with various triangle types |
Exercise books
-Manila paper -Compass -Ruler |
KLB Secondary Mathematics Form 4, Pages 75-82
|
|
| 4 | 6 |
Loci
|
Locus of Points at Fixed Distance from a Point
|
By the end of the
lesson, the learner
should be able to:
-Define circle as locus of points at fixed distance from center -Construct circles with given radius using compass -Understand sphere as 3D locus from fixed point -Solve problems involving circular loci |
-Construct circles of different radii -Demonstrate with string of fixed length -Discuss radar coverage, radio signal range -Students create circles with various measurements |
Exercise books
-Manila paper -Compass -String |
KLB Secondary Mathematics Form 4, Pages 75-82
|
|
| 4 | 7 |
Loci
|
Locus of Points at Fixed Distance from a Line
|
By the end of the
lesson, the learner
should be able to:
-Define locus of points at fixed distance from straight line -Construct parallel lines at given distances -Understand cylindrical surface in 3D -Apply to practical problems like road margins |
-Construct parallel lines using ruler and set square -Mark points at equal distances from given line -Discuss road design, river banks, field boundaries -Practice with various distances and orientations |
Exercise books
-Manila paper -Ruler -Set square |
KLB Secondary Mathematics Form 4, Pages 75-82
|
|
| 5 | 1 |
Loci
|
Angle Bisector Locus
|
By the end of the
lesson, the learner
should be able to:
-Define angle bisector locus -Construct angle bisectors using compass and ruler -Prove equidistance property of angle bisector -Apply angle bisector to find incenters |
-Construct angle bisectors for various angles -Verify equidistance from angle arms -Find incenter of triangle using angle bisectors -Practice with acute, obtuse, and right angles |
Exercise books
-Manila paper -Compass -Protractor |
KLB Secondary Mathematics Form 4, Pages 75-82
|
|
| 5 | 2 |
Loci
|
Properties and Applications of Angle Bisector
|
By the end of the
lesson, the learner
should be able to:
-Understand relationship between angle bisectors in triangles -Apply angle bisector theorem -Solve problems involving inscribed circles -Use angle bisectors in geometric constructions |
-Construct inscribed circle using angle bisectors -Apply angle bisector theorem to solve problems -Find external angle bisectors -Solve practical surveying problems |
Exercise books
-Manila paper -Compass -Ruler |
KLB Secondary Mathematics Form 4, Pages 75-82
|
|
| 5 | 3 |
Loci
|
Constant Angle Locus
|
By the end of the
lesson, the learner
should be able to:
-Understand constant angle locus concept -Construct constant angle loci using arc method -Apply circle theorems to constant angle problems -Solve problems involving angles in semicircles |
-Demonstrate constant angle using protractor -Construct arc passing through two points -Use angles in semicircle property -Practice with different angle measures |
Exercise books
-Manila paper -Compass -Protractor |
KLB Secondary Mathematics Form 4, Pages 75-82
|
|
| 5 | 4 |
Loci
|
Advanced Constant Angle Constructions
|
By the end of the
lesson, the learner
should be able to:
-Construct constant angle loci for various angles -Find centers of constant angle arcs -Solve complex constant angle problems -Apply to geometric theorem proving |
-Find centers for 60°, 90°, 120° angle loci -Construct major and minor arcs -Solve problems involving multiple angle constraints -Verify constructions using measurement |
Exercise books
-Manila paper -Compass -Protractor |
KLB Secondary Mathematics Form 4, Pages 75-82
|
|
| 5 | 5 |
Loci
|
Introduction to Intersecting Loci
|
By the end of the
lesson, the learner
should be able to:
-Understand concept of intersecting loci -Identify points satisfying multiple conditions -Find intersection points of two loci -Apply intersecting loci to solve practical problems |
-Demonstrate intersection of two circles -Find points equidistant from two points AND at fixed distance from third point -Solve simple two-condition problems -Practice identifying intersection points |
Exercise books
-Manila paper -Compass -Ruler |
KLB Secondary Mathematics Form 4, Pages 83-89
|
|
| 5 | 6 |
Loci
|
Intersecting Circles and Lines
|
By the end of the
lesson, the learner
should be able to:
-Find intersections of circles with lines -Determine intersections of two circles -Solve problems with line and circle combinations -Apply to geometric construction problems |
-Construct intersecting circles and lines -Find common tangents to circles -Solve problems involving circle-line intersections -Apply to wheel and track problems |
Exercise books
-Manila paper -Compass -Ruler |
KLB Secondary Mathematics Form 4, Pages 83-89
|
|
| 5 | 7 |
Loci
|
Triangle Centers Using Intersecting Loci
|
By the end of the
lesson, the learner
should be able to:
-Find circumcenter using perpendicular bisector intersections -Locate incenter using angle bisector intersections -Determine centroid and orthocenter -Apply triangle centers to solve problems |
-Construct all four triangle centers -Compare properties of different triangle centers -Use triangle centers in geometric proofs -Solve problems involving triangle center properties |
Exercise books
-Manila paper -Compass -Ruler |
KLB Secondary Mathematics Form 4, Pages 83-89
|
|
| 6 | 1 |
Loci
|
Complex Intersecting Loci Problems
|
By the end of the
lesson, the learner
should be able to:
-Solve problems with three or more conditions -Find regions satisfying multiple constraints -Apply intersecting loci to optimization problems -Use systematic approach to complex problems |
-Solve treasure hunt type problems -Find optimal locations for facilities -Apply to surveying and engineering problems -Practice systematic problem-solving approach |
Exercise books
-Manila paper -Compass -Real-world scenarios |
KLB Secondary Mathematics Form 4, Pages 83-89
|
|
| 6 | 2 |
Loci
|
Introduction to Loci of Inequalities
|
By the end of the
lesson, the learner
should be able to:
-Understand graphical representation of inequalities -Identify regions satisfying inequality conditions -Distinguish between boundary lines and regions -Apply inequality loci to practical constraints |
-Shade regions representing simple inequalities -Use broken and solid lines appropriately -Practice with distance inequalities -Apply to real-world constraint problems |
Exercise books
-Manila paper -Ruler -Colored pencils |
KLB Secondary Mathematics Form 4, Pages 89-92
|
|
| 6 | 3 |
Loci
|
Distance Inequality Loci
|
By the end of the
lesson, the learner
should be able to:
-Represent distance inequalities graphically -Solve problems with "less than" and "greater than" distances -Find regions satisfying distance constraints -Apply to safety zone problems |
-Shade regions inside and outside circles -Solve exclusion zone problems -Apply to communication range problems -Practice with multiple distance constraints |
Exercise books
-Manila paper -Compass -Colored pencils |
KLB Secondary Mathematics Form 4, Pages 89-92
|
|
| 6 | 4 |
Loci
|
Combined Inequality Loci
|
By the end of the
lesson, the learner
should be able to:
-Solve problems with multiple inequality constraints -Find intersection regions of inequality loci -Apply to optimization and feasibility problems -Use systematic shading techniques |
-Find feasible regions for multiple constraints -Solve planning problems with restrictions -Apply to resource allocation scenarios -Practice systematic region identification |
Exercise books
-Manila paper -Ruler -Colored pencils |
KLB Secondary Mathematics Form 4, Pages 89-92
|
|
| 6 | 5 |
Loci
|
Advanced Inequality Applications
|
By the end of the
lesson, the learner
should be able to:
-Apply inequality loci to linear programming introduction -Solve real-world optimization problems -Find maximum and minimum values in regions -Use graphical methods for decision making |
-Solve simple linear programming problems -Find optimal points in feasible regions -Apply to business and farming scenarios -Practice identifying corner points |
Exercise books
-Manila paper -Ruler -Real problem data |
KLB Secondary Mathematics Form 4, Pages 89-92
|
|
| 6 | 6 |
Loci
|
Introduction to Loci Involving Chords
|
By the end of the
lesson, the learner
should be able to:
-Review chord properties in circles -Understand perpendicular bisector of chords -Apply chord theorems to loci problems -Construct equal chords in circles |
-Review chord bisector theorem -Construct chords of given lengths -Find centers using chord properties -Practice with chord intersection theorems |
Exercise books
-Manila paper -Compass -Ruler |
KLB Secondary Mathematics Form 4, Pages 92-94
|
|
| 6 | 7 |
Loci
|
Chord-Based Constructions
|
By the end of the
lesson, the learner
should be able to:
-Construct circles through three points using chords -Find loci of chord midpoints -Solve problems with intersecting chords -Apply chord properties to geometric constructions |
-Construct circles using three non-collinear points -Find locus of midpoints of parallel chords -Solve chord intersection problems -Practice with chord-tangent relationships |
Exercise books
-Manila paper -Compass -Ruler |
KLB Secondary Mathematics Form 4, Pages 92-94
|
|
| 7 | 1 |
Loci
|
Advanced Chord Problems
|
By the end of the
lesson, the learner
should be able to:
-Solve complex problems involving multiple chords -Apply power of point theorem -Find loci related to chord properties -Use chords in circle geometry proofs |
-Apply intersecting chords theorem -Solve problems with chord-secant relationships -Find loci of points with equal power -Practice with tangent-chord angles |
Exercise books
-Manila paper -Compass -Ruler |
KLB Secondary Mathematics Form 4, Pages 92-94
|
|
| 7 | 2 |
Loci
|
Advanced Chord Problems
|
By the end of the
lesson, the learner
should be able to:
-Solve complex problems involving multiple chords -Apply power of point theorem -Find loci related to chord properties -Use chords in circle geometry proofs |
-Apply intersecting chords theorem -Solve problems with chord-secant relationships -Find loci of points with equal power -Practice with tangent-chord angles |
Exercise books
-Manila paper -Compass -Ruler |
KLB Secondary Mathematics Form 4, Pages 92-94
|
|
| 7 | 3 |
Loci
|
Integration of All Loci Types
|
By the end of the
lesson, the learner
should be able to:
-Combine different types of loci in single problems -Solve comprehensive loci challenges -Apply multiple loci concepts simultaneously -Use loci in geometric investigations |
-Solve multi-step loci problems -Combine circle, line, and angle loci -Apply to real-world complex scenarios -Practice systematic problem-solving |
Exercise books
-Manila paper -Compass -Ruler |
KLB Secondary Mathematics Form 4, Pages 73-94
|
|
| 7 | 4 |
Trigonometry III
|
Review of Basic Trigonometric Ratios
|
By the end of the
lesson, the learner
should be able to:
-Recall sin, cos, tan from right-angled triangles -Apply Pythagoras theorem with trigonometry -Use basic trigonometric ratios to solve problems -Establish relationship between trigonometric ratios |
-Review right-angled triangle ratios from Form 2 -Practice calculating unknown sides and angles -Work through examples using SOH-CAH-TOA -Solve simple practical problems |
Exercise books
-Manila paper -Rulers -Calculators (if available) |
KLB Secondary Mathematics Form 4, Pages 99-103
|
|
| 7 | 5 |
Trigonometry III
|
Deriving the Identity sin²θ + cos²θ = 1
|
By the end of the
lesson, the learner
should be able to:
-Understand the derivation of fundamental identity -Apply Pythagoras theorem to unit circle -Use the identity to solve trigonometric equations -Convert between sin, cos using the identity |
-Demonstrate using right-angled triangle with hypotenuse 1 -Show algebraic derivation step by step -Practice substituting values to verify identity -Solve equations using the fundamental identity |
Exercise books
-Manila paper -Unit circle diagrams -Calculators |
KLB Secondary Mathematics Form 4, Pages 99-103
|
|
| 7 | 6 |
Trigonometry III
|
Applications of sin²θ + cos²θ = 1
|
By the end of the
lesson, the learner
should be able to:
-Solve problems using the fundamental identity -Find missing trigonometric ratios given one ratio -Apply identity to simplify trigonometric expressions -Use identity in geometric problem solving |
-Work through examples finding cos when sin is given -Practice simplifying complex trigonometric expressions -Solve problems involving unknown angles -Apply to real-world navigation problems |
Exercise books
-Manila paper -Trigonometric tables -Real-world examples |
KLB Secondary Mathematics Form 4, Pages 99-103
|
|
| 7 | 7 |
Trigonometry III
|
Additional Trigonometric Identities
|
By the end of the
lesson, the learner
should be able to:
-Derive and apply tan θ = sin θ/cos θ -Use reciprocal ratios (sec, cosec, cot) -Apply multiple identities in problem solving -Verify trigonometric identities algebraically |
-Demonstrate relationship between tan, sin, cos -Introduce reciprocal ratios with examples -Practice identity verification techniques -Solve composite identity problems |
Exercise books
-Manila paper -Identity reference sheet -Calculators |
KLB Secondary Mathematics Form 4, Pages 99-103
|
|
| 8 | 1 |
Trigonometry III
|
Introduction to Waves
|
By the end of the
lesson, the learner
should be able to:
-Define amplitude and period of waves -Understand wave characteristics and properties -Identify amplitude and period from graphs -Connect waves to trigonometric functions |
-Use physical demonstrations with string/rope -Draw simple wave patterns on manila paper -Measure amplitude and period from wave diagrams -Discuss real-world wave examples (sound, light) |
Exercise books
-Manila paper -String/rope -Wave diagrams |
KLB Secondary Mathematics Form 4, Pages 103-109
|
|
| 8 | 2 |
Trigonometry III
|
Sine and Cosine Waves
|
By the end of the
lesson, the learner
should be able to:
-Plot graphs of y = sin x and y = cos x -Identify amplitude and period of basic functions -Compare sine and cosine wave patterns -Read values from trigonometric graphs |
-Plot sin x and cos x on same axes using manila paper -Mark key points (0°, 90°, 180°, 270°, 360°) -Measure and compare wave characteristics -Practice reading values from completed graphs |
Exercise books
-Manila paper -Rulers -Graph paper (if available) |
KLB Secondary Mathematics Form 4, Pages 103-109
|
|
| 8 | 3 |
Trigonometry III
|
Transformations of Sine Waves
|
By the end of the
lesson, the learner
should be able to:
-Understand effect of coefficient on amplitude -Plot graphs of y = k sin x for different values of k -Compare transformed waves with basic sine wave -Apply amplitude changes to real situations |
-Plot y = 2 sin x, y = 3 sin x on manila paper -Compare amplitudes with y = sin x -Demonstrate stretching effect of coefficient -Apply to sound volume or signal strength examples |
Exercise books
-Manila paper -Colored pencils -Rulers |
KLB Secondary Mathematics Form 4, Pages 103-109
|
|
| 8 | 4 |
Trigonometry III
|
Period Changes in Trigonometric Functions
|
By the end of the
lesson, the learner
should be able to:
-Understand effect of coefficient on period -Plot graphs of y = sin(bx) for different values of b -Calculate periods of transformed functions -Apply period changes to cyclical phenomena |
-Plot y = sin(2x), y = sin(x/2) on manila paper -Compare periods with y = sin x -Calculate period using formula 360°/b -Apply to frequency and musical pitch examples |
Exercise books
-Manila paper -Rulers -Period calculation charts |
KLB Secondary Mathematics Form 4, Pages 103-109
|
|
| 8 | 5 |
Trigonometry III
|
Combined Amplitude and Period Transformations
|
By the end of the
lesson, the learner
should be able to:
-Plot graphs of y = a sin(bx) functions -Identify both amplitude and period changes -Solve problems with multiple transformations -Apply to complex wave phenomena |
-Plot y = 2 sin(3x), y = 3 sin(x/2) on manila paper -Calculate both amplitude and period for each function -Compare multiple transformed waves -Apply to radio waves or tidal patterns |
Exercise books
-Manila paper -Rulers -Transformation examples |
KLB Secondary Mathematics Form 4, Pages 103-109
|
|
| 8 | 6 |
Trigonometry III
|
Phase Angles and Wave Shifts
|
By the end of the
lesson, the learner
should be able to:
-Understand concept of phase angle -Plot graphs of y = sin(x + θ) functions -Identify horizontal shifts in wave patterns -Apply phase differences to wave analysis |
-Plot y = sin(x + 45°), y = sin(x - 30°) -Demonstrate horizontal shifting of waves -Compare leading and lagging waves -Apply to electrical circuits or sound waves |
Exercise books
-Manila paper -Colored pencils -Phase shift examples |
KLB Secondary Mathematics Form 4, Pages 103-109
|
|
| 8 | 7 |
Trigonometry III
|
General Trigonometric Functions
|
By the end of the
lesson, the learner
should be able to:
-Work with y = a sin(bx + c) functions -Identify amplitude, period, and phase angle -Plot complex trigonometric functions -Solve problems involving all transformations |
-Plot y = 2 sin(3x + 60°) step by step -Identify all transformation parameters -Practice reading values from complex waves -Apply to real-world periodic phenomena |
Exercise books
-Manila paper -Rulers -Complex function examples |
KLB Secondary Mathematics Form 4, Pages 103-109
|
|
| 9 | 1 |
Trigonometry III
|
Cosine Wave Transformations
|
By the end of the
lesson, the learner
should be able to:
-Apply transformations to cosine functions -Plot y = a cos(bx + c) functions -Compare cosine and sine transformations -Use cosine functions in modeling |
-Plot various cosine transformations on manila paper -Compare with equivalent sine transformations -Practice identifying cosine wave parameters -Model temperature variations using cosine |
Exercise books
-Manila paper -Rulers -Temperature data |
KLB Secondary Mathematics Form 4, Pages 103-109
|
|
| 9 | 2 |
Trigonometry III
|
Introduction to Trigonometric Equations
|
By the end of the
lesson, the learner
should be able to:
-Understand concept of trigonometric equations -Identify that trig equations have multiple solutions -Solve simple equations like sin x = 0.5 -Find all solutions in given ranges |
-Demonstrate using unit circle or graphs -Show why sin x = 0.5 has multiple solutions -Practice finding principal values -Use graphs to identify all solutions in range |
Exercise books
-Manila paper -Unit circle diagrams -Trigonometric tables |
KLB Secondary Mathematics Form 4, Pages 109-112
|
|
| 9 | 3 |
Trigonometry III
|
Solving Basic Trigonometric Equations
|
By the end of the
lesson, the learner
should be able to:
-Solve equations of form sin x = k, cos x = k -Find all solutions in specified ranges -Use symmetry properties of trigonometric functions -Apply inverse trigonometric functions |
-Work through sin x = 0.6 step by step -Find all solutions between 0° and 360° -Use calculator to find inverse trigonometric values -Practice with multiple basic equations |
Exercise books
-Manila paper -Calculators -Solution worksheets |
KLB Secondary Mathematics Form 4, Pages 109-112
|
|
| 9 | 4 |
Trigonometry III
|
Quadratic Trigonometric Equations
|
By the end of the
lesson, the learner
should be able to:
-Solve equations like sin²x - sin x = 0 -Apply factoring techniques to trigonometric equations -Use substitution methods for complex equations -Find all solutions systematically |
-Demonstrate substitution method (let y = sin x) -Factor quadratic expressions in trigonometry -Solve resulting quadratic equations -Back-substitute to find angle solutions |
Exercise books
-Manila paper -Factoring techniques -Substitution examples |
KLB Secondary Mathematics Form 4, Pages 109-112
|
|
| 9 | 5 |
Trigonometry III
|
Equations Involving Multiple Angles
|
By the end of the
lesson, the learner
should be able to:
-Solve equations like sin(2x) = 0.5 -Handle double and triple angle cases -Find solutions for compound angle equations -Apply to periodic motion problems |
-Work through sin(2x) = 0.5 systematically -Show relationship between 2x solutions and x solutions -Practice with cos(3x) and tan(x/2) equations -Apply to pendulum and rotation problems |
Exercise books
-Manila paper -Multiple angle examples -Real applications |
KLB Secondary Mathematics Form 4, Pages 109-112
|
|
| 9 | 6 |
Trigonometry III
|
Using Graphs to Solve Trigonometric Equations
|
By the end of the
lesson, the learner
should be able to:
-Solve equations graphically using intersections -Plot trigonometric functions on same axes -Find intersection points as equation solutions -Verify algebraic solutions graphically |
-Plot y = sin x and y = 0.5 on same axes -Identify intersection points as solutions -Use graphical method for complex equations -Compare graphical and algebraic solutions |
Exercise books
-Manila paper -Rulers -Graphing examples |
KLB Secondary Mathematics Form 4, Pages 109-112
|
|
| 9 | 7 |
Trigonometry III
|
Trigonometric Equations with Identities
|
By the end of the
lesson, the learner
should be able to:
-Use trigonometric identities to solve equations -Apply sin²θ + cos²θ = 1 in equation solving -Convert between different trigonometric functions -Solve equations using multiple identities |
-Solve equations using fundamental identity -Convert tan equations to sin/cos form -Practice identity-based equation solving -Work through complex multi-step problems |
Exercise books
-Manila paper -Identity reference sheets -Complex examples |
KLB Secondary Mathematics Form 4, Pages 109-112
|
|
| 10 |
END YEAR EXAMS AND CLOSING SCHOOL |
|||||||
Your Name Comes Here