Gr 12 Maths ATP 2023 24

2023/24 ANNUAL TEACHING PLANS: MATHEMATICS: GRADE 12 2023/24 ANNUAL TEACHING PLANS: 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 Number patterns, sequences and series Functions: Formal definition, inverses, exponential and logarithmic Trigonometry TOPICS DATE COMPLETED SBA Investigation or project & test (content Term 1) 2023/24 ANNUAL TEACHING PLANS: 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 Euclidean Geometry Analytical Geometry Differential Calculus, including polynomials TOPICS DATE COMPLETED SBA Assignment JUNE EXAM/CONTROL TEST 2023/24 ANNUAL TEACHING PLANS: 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 TOPICS Finance, growth and decay (continuation) Statistics Counting and probability Revision DATE COMPLETED SBA Test TRIAL EXAMINATION 2023/24 ANNUAL TEACHING PLANS: MATHEMATICS: GRADE 12 (TERM 4) TERM 4 WEEK 1 WEEK 2 WEEK 3 WEEK 4 WEEK 5 WEEK 6 WEEK 7 WEEK 8 WEEK 9 WEEK 10 EXAM TOPICS Revision Final examination PAPER 1 150 marks 3 hours Algebraic expressions, equations 25 SBA and inequalities Number patterns 25 Functions and graphs 35 Finance, growth and decay 15 Differential Calculus 35 Counting principle and probability 15 PAPER 2 150 marks 3 hours TOTAL NUMBER OF SBA TASKS 6 Statistics 20 TERM 1 INVESTIGATION/PROJECT 15%) AND TEST (15%) Analytical Geometry 40 TERM 2 ASSIGNMENT (15%) AND JUNE EXAM/CONTROL TEST (15%) Trigonometry 40 TERM 3 TEST (15%) AND TRIAL (25%) Euclidean Geometry 50 TERM 4 FINAL EXAMINATION Downloaded from hlayiso.com 1

2023/24 ANNUAL TEACHING PLANS: MATHEMATICS: GRADE 12 2023/24 ANNUAL TEACHING PLANS: 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 TOPICS PATTERNS, SEQUENCES AND SERIES FUNCTIONS TRIGONOMETRY 1. Patterns: Revise number patterns leading to those where there is a constant 1. Definition of a function 1. Compound angle identities: second difference between consecutive terms and the general term is therefore 2. General concept of the inverse of a function and how the domain of the function may sin(   ) = sin  cos   sin  cos  quadratic need to be restricted (in order to obtain a one-to-one function) to ensure that the 2. Number patterns, including arithmetic and geometric sequences and series cos(   ) = cos  cos   sin  sin  inverse is a function 3. Sigma notation 3. Determine and sketch graphs of the inverses of the functions defined by sin 2 = 2 sin  cos  4. Derivation and application of the formulae for the sum of arithmetic and 𝑦 = 𝑎𝑥 + 𝑞, cos 2 = cos  − sin  2 2 geometric series: 𝑛 𝑛 𝑦 = 𝑎𝑥 2 , 4.1 𝑆𝑛 = [2𝑎 + (𝑛 − 1)𝑑], 𝑆𝑛 = (𝑎 + 𝑙) 2 2 𝑦 = 𝑏 𝑥 , 𝑏 > 0, 𝑏≠1 = 2 cos 2  − 1 Focus on the following characteristics: = 1 − 2 sin 2  𝑎(𝑟 𝑛 −1) Domain and range, intercepts with the axes, turning points, minima, maxima, 4.2 𝑆𝑛 = ; (𝑟 ≠ 1), and 𝑟−1 asymptotes (horizontal and vertical), shape and symmetry, average gradient (average 2. Revise the proof of the sine, cosine and area rules rate of change), intervals on which the function increases/decreases 𝑎 3. Solve problems in two and three dimensions applying the sine, cosine and area rules 4.3 𝑆𝑛 = ; (−1 < 𝑟 < 1), (𝑟 ≠ 1) 4. Revision of the exponential function and the exponential laws and graph of the 1−𝑟 function defined by y = b where b  0 and b  0 x 5. Understand the definition of a logarithm: y = log b x  x = b y where b  0 and b  1 6. The graph of the function, 𝑦 = 𝑙𝑜𝑔𝑏 𝑥 for both the cases 0 < 𝑏 < 1 and 𝑏 > 1. DATE COMPLETED SBA Investigation or project & Test (content Term 1) Downloaded from hlayiso.com 2

2023/24 ANNUAL TEACHING PLANS: MATHEMATICS: GRADE 12 2023/24 ANNUAL TEACHING PLANS: 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 TOPICS EUCLIDEAN GEOMETRY ANALYTICAL GEOMETRY DIFFERENTIAL CALCULUS, INCLUDING POLYNOMIALS JUNE EXAMINATION/CONTROL TEST 1. Revise earlier work on the necessary and 1. Revise the following, including Grade 10 concepts: 1. Factorise third-degree polynomials. Apply the remainder and factor theorems to sufficient conditions for polygons to be similar • The equation of a line through two given points polynomials of degree at most 3 (no proofs required) 2. Prove (accepting results established in earlier • The equation of a line through one point and parallel 2. An intuitive understanding of the limit concept, in the context of approximating the grades): or perpendicular to a given line rate of change or gradient of a function at a point • That a line drawn parallel to one side of a • The inclination (θ) of a line, where 3. Use limits to define the derivative of a function f at any 𝑥: triangle divides the other two sides 𝑚 = tan 𝜃 is the gradient of the line f ( x + h) − f ( x ) proportionally (and the Mid-point Theorem as (0° ≤ 𝜃 ≤ 180° ) f ( x) = lim h →0 h a special case of the converse of this Generalise to find the derivative of f at any point x in the domain of f i.e., define the theorem) 2. Apply the equation derivative function f '(x) of the function f (x) Understand intuitively that f '(a) is the • That equiangular triangles are similar (𝑥 − 𝑎)2 + (𝑦 − 𝑏)2 = 𝑟 2 gradient of the tangent to the graph of f at the point with x -coordinate a • That triangles with sides in proportion are that defines a circle with radius r and centre (a , b). 4. Using the definition (first principle), determine the derivative, f '(x) where a, b and c are similar 3. Determine the equation of a tangent to a given circle constants: • The Pythagorean Theorem by similar triangles 4.1 f ( x) = ax 2 + bx + c , 4.2 f ( x) = ax3 , 4.3 f ( x ) = a and x 4.4 f (x) = c 𝑑 5. Use the formula, (𝑎𝑥 𝑛 ) = 𝑎𝑛𝑥 𝑛−1 𝑑𝑥 (for any real number n) together with the rules 5.1 d d d [ f ( x)  g ( x)] = [ f ( x)]  [ g ( x)] dx dx dx and 5.2 d d [ kf ( x)] = k [ f ( x)], ( k a constant) dx dx 6. Determine equations of tangents to graphs of functions 7. Introduce the second derivative 𝑑 𝑓 ′′ (𝑥) = (𝑓 ′ (𝑥)) of f (x) 𝑑𝑥 and how it determines the concavity of a function 8. Sketch graphs of cubic polynomial functions using differentiation to determine the coordinates of stationary points, and points of inflection (where concavity changes). Also, determine the x -intercepts of the graph using the factor theorem and other techniques 9. Solve practical problems concerning optimisation and rate of change, including calculus of motion DATE COMPLETED SBA Assignment JUNE EXAM/CONTROL TEST Downloaded from hlayiso.com 3

2023/24 ANNUAL TEACHING PLANS: MATHEMATICS: GRADE 12 2023/24 ANNUAL TEACHING PLANS: 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 TOPICS FINANCE, GROWTH AND DECAY STATISTICS COUNTING AND PROBABILITY REVISION TRIAL EXAMINATION 1. Revise and use simple and compound growth and 1. Revise: 1. Revise, decay formulae: • Histograms • The identity: 𝐴 = 𝑃(1 ± 𝑖𝑛) and 𝐴 = 𝑃(1 ± 𝑖)𝑛 • Frequency polygons P(A or B) = P(A) + P(B) − P(A and B) • Ogives (cumulative frequency curves) • The addition rule for mutually exclusive events: to solve problems (including straight line, depreciation • Variance and standard deviation of ungrouped data P(A or B) = P(A) + P(B) and depreciation on a reducing balance) • Symmetric and skewed data • The complementary rule: 2. Solve problems involving present value and future value • Identification of outliers P(not A) = 1 − P(A) annuities 2. Use statistical summaries, scatterplots, regression (in • Identifying dependent and independent events and, 3. Make use of logarithms to calculate the value of n, the particular the least squares regression line) and • The product rule for independent events: time period, in the equations correlation to analyse and make meaningful comments on P(A and B) = P(A) × P(B) the context associated with given bivariate data, including • The use of Venn diagrams to solve probability interpolation, extrapolation and discussions on skewness problems, deriving and applying formulae for any 𝐴 = 𝑃(1 + 𝑖)𝑛 𝑜𝑟 𝐴 = 𝑃(1 − 𝑖)𝑛 . three events A, B and C in a sample space S • The use of tree diagrams for the probability of 4. Critically analyse investment and loan options and make consecutive or simultaneous events, which are not informed decisions as to best option(s) (including necessarily independent pyramid) 2. Apply the fundamental counting principle to solve probability problems 3. Probability problems using Venn diagrams, tree diagrams, two-way contingency tables and other techniques (like the Fundamental Counting Principle) to solve probability problems (where events are not necessarily independent) DATE COMPLETED SBA Test TRIAL EXAMINATION Downloaded from hlayiso.com 4

2023/24 ANNUAL TEACHING PLANS: MATHEMATICS: GRADE 12 2023/24 ANNUAL TEACHING PLANS: MATHEMATICS: GRADE 12 (TERM 4) TERM 4 WEEK 1 WEEK 2 WEEK 3 WEEK 4 WEEK 5 WEEK 6 WEEK 7 WEEK 8 WEEK 9 WEEK 10 EXAM TOPICS REVISION FINAL EXAMINATION PAPER 1 150 MARKS 3 HOURS MARKS Algebraic expressions, equations 25 and inequalities Number patterns 25 Functions and graphs 35 Finance, growth and decay 15 Differential Calculus 35 Counting principle and probability 15 TOTAL NUMBER OF SBA TASKS 6 PAPER 2 150 marks 3 hours Marks TERM 1 INVESTIGATION/PROJECT 15%) AND TEST (15%) Statistics 20 TERM 2 ASSIGNMENT (15%), JUNE EXAM/CONTROL TEST (15%) Analytical Geometry 40 TERM 3 TEST (15%) AND TRIAL (25%) Euclidean Geometry 40 TERM 4 FINAL EXAMINATION Trigonometry 50 Downloaded from hlayiso.com 5