Gr 11 Maths ATP 2023 24

2023/24 ANNUAL TEACHING PLANS: MATHEMATICS: GRADE 11 2023/24 ANNUAL TEACHING PLANS: 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 TOPICS Exponents and surds Equations and inequalities Trigonometry (reduction formulae, trig equations & general solutions) DATE COMPLETED SBA Investigation or project & test (content of Term 1) 2023/24 ANNUAL TEACHING PLANS: 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 TOPICS Euclidean Geometry Analytical Geometry Functions (including trigonometric functions) DATE COMPLETED SBA Assignment & mid-year exam 2023/24 ANNUAL TEACHING PLANS: 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 TOPICS Trigonometry (sine, cosine and area rules) Statistics Probability Finance, growth and decay DATE COMPLETED SBA Test Test 2023/24 ANNUAL TEACHING PLANS: MATHEMATICS: GRADE 11 (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 Revision of Revision of PAPER 1 150 marks 3 hours TOPICS Number patterns Revision of measurement Examination Algebra Trigonometry Algebraic Expressions, equations 45 DATE and inequalities COMPLETED Number patterns 25 SBA Test Finance, growth and decay 15 Functions and graphs 45 Probability 20 TOTAL NUMBER OF SBA TASKS 7 PAPER 2 150 marks 3 hours TERM 1 INVESTIGATION/PROJECT (15%) AND TEST (14%) Statistics 20 TERM 2 ASSIGNMENT (15%) AND MID-YEAR EXAM (14%) Analytical Geometry 30 TERM 3 TEST (14%) AND TEST (14%) Trigonometry 50 TERM 4 TEST (14%) Euclidean Geometry 50 Downloaded from hlayiso.com 1

2023/24 ANNUAL TEACHING PLANS: MATHEMATICS: GRADE 11 2023/24 ANNUAL TEACHING PLANS: 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 TOPICS EXPONENTS AND SURDS EQUATIONS AND INEQUALITIES TRIGONOMETRY (REDUCTION FORMULAE, TRIG EQUATIONS & GENERAL SOLUTIONS) 1. Complete the square 1. Derive and use the identities: tan  = sin  , 𝜃 ≠ 𝑘. 90° , 𝑘 an odd integer, and sin2 𝜃 + cos 2 𝜃 = 1 1. Simplify expressions and solve equations using the 2. Solve quadratic equations (by factorisation and by using the quadratic formula) cos  laws of exponents for rational 3. Solve quadratic inequalities in one unknown (interpret solutions graphically). NB: It is 2. Derive and use reduction formulae to simplify the following expressions: 𝑝 𝑞 recommended that the solving of equations in two unknowns is important to be used 2.1. sin(90° ± 𝜃) , cos (90° ± 𝜃), exponents were, 𝑥 𝑞 = √𝑥 𝑝 ; in other equations like hyperbola-straight line as this is normal in the case of graphs 𝑥 > 0 ,𝑞 > 0 2.2. sin(180° ± 𝜃) , cos (180° ± 𝜃) and tan (180° ± 𝜃), 4. Equations in two unknowns, one of which is linear and the other quadratic 2. Add, subtract, multiply and 2.3. sin(360° ± 𝜃) , cos (360° ± 𝜃) and tan (360° ± 𝜃), divide simple surds 5. Nature of roots 2.4. sin(−𝜃) , cos (−𝜃) and tan (−𝜃), 3. Solve simple equations 3. Determine for which values of a variable an identity holds involving surds 4. Determine the general solutions of trigonometric equations. Also, determine solutions in specific intervals DATE COMPLETED SBA Investigation or project & Test (content of Term 1) Downloaded from hlayiso.com 2

2023/24 ANNUAL TEACHING PLANS: MATHEMATICS: GRADE 11 2023/24 ANNUAL TEACHING PLANS: 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 TOPICS EUCLIDEAN GEOMETRY ANALYTICAL GEOMETRY FUNCTIONS (INCLUDING TRIGONOMETRIC FUNCTIONS) 1. Accept results established in earlier grades as axioms that a tangent to a circle is 1. Revise, 1. Revise the effect of the parameters 𝑎 and q and investigate the effect of p on the graphs of the functions defined by: perpendicular to the radius drawn to the point of contact • Distance between the two points 1.1. 𝑦 = 𝑓(𝑥) = 𝑎(𝑥 + 𝑝)2 + 𝑞 • Gradient of the line segment connecting the 2. Then investigate and prove the theorems of the geometry of circles: two points (and from that identify parallel 𝑎 1.2. 𝑦 = 𝑓(𝑥) = +𝑞 • The line drawn from the centre of a circle perpendicular to a chord bisects the and perpendicular lines) 𝑥+𝑝 chord • Coordinates of the mid-point of the line • The line drawn from the centre of a circle to the midpoint of a chord is segment joining the two points 1.3. 𝑦 = 𝑓(𝑥) = 𝑎. 𝑏 𝑥+𝑝 + 𝑞 where 𝑏 > 0, 𝑏 ≠ 1 perpendicular to the chord 2. Derive and apply: • The perpendicular bisector of a chord passes through the centre of the circle • The equation of a line through two given 2. Investigate numerically the average gradient between two points on a curve and develop an intuitive understanding of the points concept of the gradient of a curve at a point • The angle subtended by an arc at the centre of a circle is double the size of the • The equation of a line through one point angle subtended by the same arc at the circle (on the same side of the chord as and parallel or perpendicular to a given line 3. Point by point plotting of basic graphs defined by 𝑦 = sin 𝜃 , 𝑦 = cos 𝜃 and 𝑦 = tan 𝜃 for 𝜃 ∈ [−360° , 360° ] the centre) • The inclination (θ) of a line, where 𝑚 = • Angles subtended by a chord of the circle, on the same side of the chord, are tan 𝜃 is the gradient of the line (0° ≤ equal 4. Investigate the effect of the parameter k on the graphs of the functions defined by, 𝜃 ≤ 180° ) • The opposite angles of a cyclic quadrilateral are supplementary 𝑦 = sin(𝑘𝑥) , 𝑦 = cos(𝑘𝑥) and 𝑦 = tan(𝑘𝑥) • Two tangents drawn to a circle from the same point outside the circle are equal in length 5. Investigate the effect of the parameter 𝑝 on the graphs of the functions defined by, • The angle between the tangent to a circle and the chord drawn from the point of 𝑦 = sin(𝑥 + 𝑝) , 𝑦 = cos(𝑥 + 𝑝) and 𝑦 = tan(𝑥 + 𝑝) contact is equal to the angle in the alternate segment Use the above theorems and their converses, where they exist, to solve riders 6. Draw sketch graphs defined by: 𝑦 = 𝑎 sin 𝑘(𝑥 + 𝑝) , 𝑦 = 𝑎 cos 𝑘(𝑥 + 𝑝) and 𝑦 = 𝑎 tan 𝑘(𝑥 + 𝑝) at most two parameters at a time DATE COMPLETED SBA Assignment & mid-year exam Downloaded from hlayiso.com 3

2023/24 ANNUAL TEACHING PLANS: MATHEMATICS: GRADE 11 2023/24 ANNUAL TEACHING PLANS: 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 TRIGONOMETRY (SINE, COSINE AND STATISTICS PROBABILITY FINANCE, GROWTH AND DECAY TOPICS AREA RULES) 1. Prove and apply the sine, cosine and area 1. Revise measures of central 1. Revise the use of probability models to compare the relative frequency of events with the theoretical probability 1. Revise the use of the simple and compound growth rules tendency and dispersion in formulae [𝐴 = 2. Solve problems in two dimensions using ungrouped and grouped data 2. Revise the use of Venn diagrams to solve probability problems, deriving and applying the following for any two events in a sample 𝑃(1 + 𝑖𝑛) and 𝐴 = 𝑃(1 + 𝑖)𝑛 ] to solve the sine, cosine and area rules 2. Revise five number summary space S: problems, including interest, hire purchase, (maximum, minimum and inflation, population growth and other real-life quartiles) and box and whisker • Addition rule 𝑃(𝐴 𝑜𝑟 𝐵) = 𝑃(𝐴) + 𝑃(𝐵) − 𝑃(𝐴 𝑎𝑛𝑑 𝐵), problems diagram 2. Understand the implication of fluctuating foreign 3. Revise histograms exchange rates (e.g., on the petrol price, imports, 4. Frequency polygons • 𝐴 and 𝐵 are mutually exclusive if 𝑃(𝐴 𝑎𝑛𝑑 𝐵) = 0, addition rule for mutually exclusive events 𝐴 and 𝐵 is: 𝑃(𝐴 𝑜𝑟 𝐵) = 𝑃(𝐴) + 𝑃(𝐵) exports, overseas travel) 5. Ogives (cumulative frequency curves) • A and B are complementary if they are, 3. Use simple and compound decay formulae: 6. Variance and standard deviation of ➢ mutually exclusive 𝐴 = 𝑃(1 − 𝑖𝑛) and ungrouped data and 𝐴 = 𝑃(1 − 𝑖)𝑛 7. Symmetric and skewed data ➢ 𝑃(𝐴) + 𝑃(𝐵) = 1 To solve problems (including straight line 8. Identification of outliers Then depreciation and depreciation on a reducing 𝑃(𝐵) = 𝑃(𝑛𝑜𝑡 𝐴) = 1 − 𝑃(𝐴) balance) 4. The effect of different periods of compound growth and decay, including nominal and effective interest 3. Identify dependent and independent events and the product rule for independent events: rates 𝑃(𝐴 𝑎𝑛𝑑 𝐵) = 𝑃(𝐴) × 𝑃(𝐵) 4. The use of Venn diagrams to solve probability problems, deriving and applying formulae for any three events 𝐴, 𝐵 and 𝐶 in a sample space S. 5. Use tree diagrams for the probability of consecutive or simultaneous events, which are not necessarily independent 6. Use Venn diagrams, tree diagrams and contingency tables to solve real-life problems DATE COMPLETED SBA Test Test Downloaded from hlayiso.com 4

2023/24 ANNUAL TEACHING PLANS: MATHEMATICS: GRADE 11 2023/24 ANNUAL TEACHING PLANS: MATHEMATICS: GRADE 11 (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 NUMBER PATTERNS REVISION OF MEASUREMENT REVISION OF REVISION OF EXAMINATION PAPER 1 150 marks 3 hours TOPICS ALGEBRA TRIGONOMETRY Algebraic expressions, equations 45 Patterns: Investigate number patterns 1. Revise the volume and surface areas of right and inequalities leading to those where there is a prisms and cylinders Number patterns 25 constant second difference between 2. Study the effect on volume and surface areas Finance, growth and decay 15 consecutive terms and the general when multiplying any dimension by a constant Functions and graphs 45 term is therefore quadratic factor k Probability 20 3. Calculate volume and surface areas of spheres, right prisms, right cones and combination of those objects (figures) DATE PAPER 2 150 marks 3 hours COMPLETED Statistics 20 SBA Test Analytical Geometry 30 Trigonometry 50 Euclidean Geometry 50 TOTAL NUMBER OF SBA TASKS 7 TERM 1 INVESTIGATION/PROJECT (15%) AND TEST (14%) TERM 2 ASSIGNMENT (15%) AND MID-YEAR EXAM (14%) TERM 3 TEST (14%) AND TEST (14%) TERM 4 TEST (14%) Downloaded from hlayiso.com 5