Gr 12 Tech Math ATP 2023 24

2023/24 ANNUAL TEACHING PLANS: TECHNICAL MATHEMATICS: GRADE 12 2023/24 ANNUAL TEACHING PLANS: TECHNICAL MATHEMATICS: GRADE 12 (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 COMPLEX NUMBERS ANALYTICAL GEOMETRY POLYNOMIALS DIFFERENTIAL CALCULUS CONSOLIDATION AND ASSESSMENT TOPICS/CONCEPTS, 1. Define a complex number, ℂ, z = a + bi Use a two-dimensional Cartesian co-ordinate 1. Revise the 1. An intuitive understanding of the limit concept, in the context of approximating the rate ofchange SKILLS AND VALUES 2. Simplify by add, subtract, divide, multiply and system to determine: function notation or gradient of a function at a point. simplify imaginary numbers and complex • The equation of a circle, x 2 + y 2 = r 2 , with and define f (x + h) − f (x) numbers polynomials in 2. Determine the average gradient of a curve between two points. m = radius r and centre at the origin ( 0; 0 ) one variable h 3. Represent complex numbers in the Argand 3. Determine the gradient of a tangent to a graph, which is also the gradient of the graph at that diagram, • The equation of a tangent to a circle at a 2. Revise factorising given point on the circle point. 4. Argument of z of quadratic • The equation of a circle of a tangent and a polynomials Introduce the limit-principle by shifting the secant until it becomes a tangent 5. Trigonometric (polar) & rectangular form of 4. By using first principle: given circle 3. Define the complex numbers • Point/s of intersection of a circle and a Remainder f (x + h) − f (x) 6. Solve equations involving complex numbers straight line. theorem and f ' (x) = lim for with two variables h→0 h • Plotting of the graph of ellipse in the form apply it where a • f ( x) = k third-degree x2 y 2 • f ( x) = ax + =1 polynomial is a 2 b2 divided by a linear • f ( x) = ax + b binomial d 5. Use the rule (ax ) = anx n −1 for n  n 4. Define the Factor dx theorem and 6. Find equations of tangents to graphs of functions apply it where a 7. Sketch graphs of cubic polynomial functions using differentiation to determine the co-ordinate of third-degree stationary points. Also, determine the x - intercepts of the graph using the factor theorem and polynomial is other techniques divided by a linear binomial 8. Solve practical problems concerning optimization and rates of change, including calculus of motion 5. Factorise third degree polynomials (No proofs are required. Long division method can also be use) SBA PAT 1 & TEST Downloaded from hlayiso.com 1

2023/24 ANNUAL TEACHING PLANS: TECHNICAL MATHEMATICS: GRADE 12 2023/24 ANNUAL TEACHING PLANS: TECHNICAL MATHEMATICS: GRADE 12 (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 INTEGRATION TRIGONOMETRY EUCLIDEAN GEOMETRY CONSOLIDATION TOPICS 1. Understand the basic concept. 1. Revision of Gr. 11 Trigonometry 1. Revision Gr. 11 Euclidean Geometry NB: All topics taught in Gr. 10 & 11 will be /CONCEPTS, 2. Apply standard forms of integrals as a converse of differentiation 2. Revise the basic trigonometric ratios and 2. Revise earlier work on the necessary and sufficient conditions for polygons to be similar and assessed in June Examination SKILLS AND 3. Integrate the following functions: apply them to solve right angled triangles congruent VALUES 3. Sine, Cosine and Area rules 3. Introduce and apply the following theorems: • kxn k 4. Solving problems in 2 dimensions • That equiangular triangles are similar • • Measurements must always be given for • That triangles with sides in proportion are similar x angles and lengths of sides • That a line drawn parallel to one side of a triangle divided the other two sided proportionally • ka nx 4. Integrate polynomials 5 Applying integration to determine the magnitude of an area included by: • a curve and the x-axis • curve by a curve • the x-axis and the ordinates x = a and x = b , where a, b  Z PAT & SBA PAT 2 & ASSIGNMENT & JUNE EXAM Downloaded from hlayiso.com 2

2023/24 ANNUAL TEACHING PLANS: TECHNICAL MATHEMATICS: GRADE 12 2023/24 ANNUAL TEACHING PLANS: TECHNICAL MATHEMATICS: GRADE 12 (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 CONSOLIDATION TRIAL EXAMS TOPICS/CONCEPTS, Solving problems in 2 and 3 dimensions SKILLS AND VALUES • Measurements must always be given for angles and lengths of sides PAT & SBA PAT 3 & TEST & TRIAL EXAM (PAPER 1 AND PAPER 2) Downloaded from hlayiso.com 3

2023/24 ANNUAL TEACHING PLANS: TECHNICAL MATHEMATICS: GRADE 12 2023/24 ANNUAL TEACHING PLANS: TECHNICAL MATHEMATICS: GRADE 12 (TERM 4) TERM 4 WEEK 1 WEEK 2 WEEK 3 WEEK 5 WEEK 6 WEEK 7 WEEK 8 WEEK 9 WEEK 10 DATE COMPLETED CAPS TOPICS REVISION FINAL EXAMS TOPICS/CONCEPTS, SKILLS AND VALUES SBA FINAL EXAMINATION (PAPER 1 AND PAPER 2) EXAMINATION PAPER 1 PAPER 2 TOPIC MARKS TOPIC MARKS Algebra (Number system, exponents logarithms, expressions, equations and inequalities including 50 ± 3 Analytical geometry 25 ± 3 nature of roots) Functions & graphs 35 ± 3 Trigonometry 50 ± 3 Finance, growth, and decay 15 ± 3 Euclidean geometry 40 ± 3 Differential calculus and Integration 50 ± 3 Mensuration and circles, angles, and angular movement 35 ± 3 TOTAL 150 TOTAL 150 Downloaded from hlayiso.com 4