Gr 11 Tech Math ATP 2023 24

2023/24 ANNUAL TEACHING PLANS: TECHNICAL MATHEMATICS: GRADE 11 2023/24 ANNUAL TEACHING PLANS: TECHNICAL MATHEMATICS: GRADE 11 (TERM 1) TERM 1 WEEK 1 WEEK 2 WEEK 3 WEEK 4 WEEK 5 WEEK 6 WEEK 7 WEEK 8 WEEK 9 WEEK 10 WEEK 11 DATE COMPLETED CAPS TOPICS ANALYTICAL GEOMETRY EXPONENTS AND SURDS LOGARITHMS EQUATIONS AND INEQUALITIES REVISION/ASSESSMENT TOPICS/CONCEPTS, Use a Cartesian co-ordinate system to: 1. Apply the laws of exponents to expressions involving rational 1. Demonstrate an understanding of the Solve SKILLS AND 1. Revise the equation of a exponents where: definition of a logarithm and any laws 1. Quadratic equations (by factorisation and by using the quadratic VALUES linethrough two given points 𝑝 𝑞 needed to solve real life problems formula) • 𝑥 𝑞 = √𝑥 𝑝 𝑥 > 0; 𝑞 ≥ 2 2. Determine the equation of a line through 2. Define a logarithm and 2. Quadratic inequalities (interpret solutions graphically) 2. Add, subtract, multiply and divide simple surds convertlogarithmic expressions to one point and parallel or perpendicular to 3. Equations in two unknowns, one of which is linear and the other a given line 3. Solve exponential equations exponential form and vice versa quadratic algebraically or graphically. 3. Determine the angle of inclination of a line 3. Convert exponential expressions 4. Manipulating formulae (change subject of the formulae) tologarithmic form 5. Word problems 4. Laws of logarithms: • 𝑙𝑜𝑔𝑎 𝑥 𝑦 = 𝑙𝑜𝑔𝑎 𝑥 + 𝑙𝑜𝑔𝑎 𝑦 𝑥 • 𝑙𝑜𝑔𝑎 = 𝑙𝑜𝑔𝑎 𝑥 − 𝑙𝑜𝑔𝑎 𝑦 𝑦 • 𝑙𝑜𝑔𝑎 𝑥 𝑛 = 𝑛 𝑙𝑜𝑔𝑎 𝑥 𝑙𝑜𝑔 𝑏 • 𝑙𝑜𝑔𝑎 𝑏 = 𝑐 𝑙𝑜𝑔𝑐 𝑎 5. Combine logarithmic laws to simplify expressions 6. Solve logarithmic equations PAT & SBA ASSIGNMENT & TEST Downloaded from hlayiso.com 1

2023/24 ANNUAL TEACHING PLANS: TECHNICAL MATHEMATICS: GRADE 11 2023/24 ANNUAL TEACHING PLANS: TECHNICAL MATHEMATICS: GRADE 11 (TERM 2) TERM 2 WEEK 1 WEEK 2 WEEK 3 WEEK 4 WEEK 5 WEEK 6 WEEK 7 WEEK 8 WEEK 9 WEEK 10 WEEK 11 DATE COMPLETED CAPS TOPICS NATURE OF ROOTS EUCLIDEAN GEOMETRY FUNCTIONS AND GRAPHS REVISION/ASSESSMENT TOPICS/CONCEPTS, Determine the Accept results established in earlier grades as axioms 1. Revise the effect of the parameters a and q on the graphs. 𝑎, 𝑞 ∈ ℝ SKILLS AND nature of roots and Then investigate and apply the theorems of the geometry of circles: Investigate the effect of p on the graphs of the functions defined by: VALUES the conditions for • The line drawn from the centre of a circle perpendicular to a chord • 𝑦 = 𝑓(𝑥) = 𝑎(𝑥 + 𝑝)2 + 𝑞 which the roots are bisects the chord real, non-real, • 𝑦 = 𝑓(𝑥) = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 • The perpendicular bisector of a chord passes through the centre of the 𝑎 equal, unequal, • 𝑦= +𝑞 circle 𝑥 rational, and • The angle subtended by an arc at the centre of a circle is double the • 𝑦 = 𝑎. 𝑓(𝑥) = 𝑎. . 𝑏 𝑥 + 𝑞 , 𝑏 > 0 and 𝑏 ≠ 1 irrational through the value of size of the angle subtended by the same arc at the circle (on the 2. 𝑥 2 + 𝑦 2 = 𝑟 2 same side of the chord as the centre) • 𝑦 = ±√𝑟 2 − 𝑥 2 𝛥 = 𝑏 2 − 4𝑎𝑐 • Angles subtended by a chord of the circle, on the same side of the • 𝑦 = +√𝑟 2 − 𝑥 2 chord, are equal • The opposite angles of a cyclic quadrilateral are supplementary • 𝑦 = −√𝑟 2 − 𝑥 2 • Exterior angle of cyclic quad. is equal to opposite interior angle 3. Determine the equation from given critical points • Two tangents drawn to a circle from the same point outside the circle 4. Interpretation from given graphs are equal in length • Radius is perpendicular to the tangent • The angle between the tangent to a circle and the chord drawn from the point of contact is equal to the angle in the alternate segment Note: No formal proofs of these theorems will be examined, only applications in riders PAT & SBA PAT 1 & TEST / JUNE EXAMINATION Downloaded from hlayiso.com 2

2023/24 ANNUAL TEACHING PLANS: TECHNICAL MATHEMATICS: GRADE 11 2023/24 ANNUAL TEACHING PLANS: TECHNICAL MATHEMATICS: GRADE 11 (TERM 3) TERM 3 WEEK 1 WEEK 2 WEEK 3 WEEK 4 WEEK 5 WEEK 6 WEEK 7 WEEK 8 WEEK 9 WEEK 10 WEEK 11 DATE COMPLETED CAPS TOPICS TRIGONOMETRY CIRCLES, ANGLES AND ANGULAR MOVEMENT FINANCE, GROWTH AND DECAY REVISION/ASSESSMENT TOPICS/CONCEPTS, 1. Revise the trig ratios in the solving of right-angle triangle in all 4 quadrants (Grade 10). 1. Circle: 1. Use simple and compound growth/decay SKILLS, AND 2. Apply the sine, cosine, and area rules. (No proofs of these rules) formulae: • x + y = r with centre (0; 0) 2 2 2 VALUES 3. Solve problems in two dimensions using the sine, cosine, and area rules (no variables) • 𝐴 = 𝑃(1 ± 𝑖𝑛) 2. Degrees and radians: 4. Draw the graphs of the functions defined by: • 𝐴 = 𝑃(1 ± 𝑖)𝑛 • 𝜋𝑟𝑎𝑑 = 180° • 𝑦 = 𝑎𝑠𝑖𝑛𝑥 + 𝑞 to solve problems (including interest, hire 3. Angles and arcs: purchase, inflation, population growth and • 𝑦 = 𝑎𝑐𝑜𝑠𝑥 + 𝑞 • Arc length: 𝑠 = 𝑟𝜃 other real-life problems) • 𝑦 = 𝑎𝑡𝑎𝑛𝑥 4. Sectors and segments: 2. The effect of different periods of • 𝑦 = sin(𝑎𝑥) 𝑟𝑠 𝑟 2𝜃 compounding growth and decay • Area of sector = = • 𝑦 = 𝑐𝑜𝑠(𝑎𝑥) 2 2 3. Effective and nominal interest rate 5. Draw the graphs of the functions defined by and determine the effect of 𝑝 on: Area of segment = Area of sector − Area of triangle • 4. Calculating n using logs r 2 1 2 • 𝑦 = 𝑠𝑖𝑛(𝑥 + 𝑝) = − r sin  5. Timelines 2 2 • 𝑦 = 𝑐𝑜𝑠(𝑥 + 𝑝) • 4ℎ2 − 4𝑑ℎ + 𝑥 2 = 0 6. Determine the effect of 𝑝 on 𝑦 = 𝑡𝑎𝑛(𝑥 + 𝑝) 5. Angular and circumferential velocity: 7. Rotating vectors: developing the sine and cosine curve • 𝜔 = 2𝜋𝑛 = 360°𝑛 8. Trigonometric equations for 𝜃 ∈ [0°; 360°] • 𝜐 = 𝜋𝐷𝑛 9. Reduction formulae: • 𝜐 = 𝜔𝑟 • 180° ± 𝜃 • 360° ± 𝜃 10. Introduce and apply identities 𝑠𝑖𝑛𝜃 • 𝑡𝑎𝑛𝜃 = 𝑐𝑜𝑠𝜃 • sin2 𝜃 + cos 2 𝜃 = 1 • 1 + tan2 𝜃 = sec 2 𝜃 • 1 + cot 2 𝜃 = 𝑐𝑜𝑠𝑒𝑐 2 𝜃 PAT & SBA PAT 2 & TEST Downloaded from hlayiso.com 3

2023/24 ANNUAL TEACHING PLANS: TECHNICAL MATHEMATICS: GRADE 11 2023/24 ANNUAL TEACHING PLANS: TECHNICAL MATHEMATICS: GRADE 11 (TERM 4) TERM 4 WEEK 1 WEEK 2 WEEK 3 WEEKS 4 WEEKS 5 WEEKS 6 WEEKS 7 WEEKS 8 WEEKS 9 WEEKS 10 DATE COMPLETED CAPS TOPICS MENSURATION REVISION & FINAL EXAMINATION TOPICS/CONCEPTS, SKILLS, AND VALUES 1. Determine the area of an irregular figure using mid-ordinate rule 2. Surface area and volume of right prisms, cylinders, pyramids, cones and spheres, and combinations of these geometric objects. (Formulae to be given) 3. The effect on volume and surface area when multiplying any dimension by factor k SBA FINAL EXAMS (PAPER 1 & PAPER 2) EXAMINATION PAPER 1 PAPER 2 TOPIC MARKS TOPIC MARKS Algebra (Number system exponents, logarithms, expressions, equations and inequalities including 90 ± 3 Analytical geometry 25 ± 3 nature of roots) Functions & graphs 45 ± 3 Trigonometry 50 ± 3 Finance, growth, and decay 15 ± 3 Euclidean geometry 40 ± 3 Mensuration and circles, angles, and angular movement 35 ± 3 TOTAL 150 TOTAL 150 Downloaded from hlayiso.com 4