Gr 10 Maths ATP 2023-24.pdf

2023/24 ANNUAL TEACHING PLANS: MATHEMATICS: GRADE 10 2023/24 ANNUAL TEACHING PLANS: MATHEMATICS: GRADE 10 (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 Algebraic expressions Exponents, equations and inequalities Trigonometry DATE COMPLETED SBA Investigation or project & test (content of Term 1) 2023/24 ANNUAL TEACHING PLANS: MATHEMATICS: GRADE 10 (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 10 (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 (2D) Statistics Probability Finance and growth DATE COMPLETED SBA Test Test 2023/24 ANNUAL TEACHING PLANS: MATHEMATICS: GRADE 10 (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 Measurement Number patterns Revise Algebra Revise Revise functions Examination Admin PAPER 1 Trigonometry & Algebra 30 Geometry Number patterns 15 DATE Finance, growth 10 COMPLETED Functions and graphs 30 SBA Test Probability 15 TOTAL NUMBER OF SBA TASKS 7 PAPER 2 TERM 1 INVESTIGATION/PROJECT (15%) AND TEST (14%) Statistics 15 TERM 2 ASSIGNMENT (15%) AND MID-YEAR EXAM (14%) Analytical Geometry 15 TERM 3 TEST (14%) AND TEST (14%) Trigonometry 40 TERM 4 TEST (14%) Euclidean Geometry & 30 measurement Downloaded from hlayiso.com 1

2023/24 ANNUAL TEACHING PLANS: MATHEMATICS: GRADE 10 2023/24 ANNUAL TEACHING PLANS: MATHEMATICS: GRADE 10 (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 ALGEBRAIC EXPRESSIONS EXPONENTS, EQUATIONS AND INEQUALITIES TRIGONOMETRY 1. Understand that real numbers can be rational or irrational 1. Revise laws of exponents learnt in Grade 9 where 𝒙, 𝒚 > 𝟎; 𝒎, 𝒏 ∈ ℤ : 1. Define the trigonometric ratios sin 𝜃, cos 𝜃 and tan 𝜃 2. Establish between which two integers a given simple surd lies Using the right – angled triangle 3. Round real numbers to an appropriate degree of accuracy • xm  x n = x m+n Extend the definitions of sin 𝜃, cos 𝜃 and tan 𝜃 for 0° ≤ 𝜃 ≤ 360° 2. 4. Multiplication of a binomial by a trinomial • x m  x n = x m−n 3. Define the reciprocal of the trigonometric ratios cosec 𝜃, sec 𝜃 and cot 𝜃, using the right- 5. Factorisation to include types taught in Grade 9 and: angled triangles (these three reciprocals should be examined in Grade 10 only) (x ) = x n • Trinomials • m mn 4. Derive values of the trigonometric ratios for the special cases (without using a calculator) • Grouping in pairs 𝜃 ∈ {0°, 30°, 45°, 60°, 90°} x m  y m = ( xy ) Solve two-dimensional problems involving right-angled triangle m 5. • Sum and difference of two cubes • 6. Solve simple trigonometric equations for angles between 0° and 90° 6. Simplifying, adding and subtracting algebraic fractions using factorisation with Also, by definition: 7. Use a diagram to determine the numerical values of ratios for angles from 0° to 360° denominators of cubes (limited to sum and difference of cubes) 1 𝑥 −𝑛 = , 𝑥 ≠ 0 and 𝑥 0 = 1,𝑥 ≠ 0 𝑥𝑛 2.Use the laws of exponents to simplify expressions and solve equations, accepting that the rules also hold for m, n  Q 3. 3.1. Revise the solution of linear equations 3.2. Solve quadratic equations (by factorisation) 3.3. Solve simultaneous linear equations in two unknowns 3.4. Solve word problems involving linear, quadratic or simultaneous linear equations 3.5. Solve literal equations (changing the subject of a formula) 3.6. Solve linear inequalities (and show solution graphically) Interval notation must be known DATE COMPLETED SBA Investigation or project Test (content of Term 1) Downloaded from hlayiso.com 2

2023/24 ANNUAL TEACHING PLANS: MATHEMATICS: GRADE 10 2023/24 ANNUAL TEACHING PLANS: MATHEMATICS: GRADE 10 (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 AND GRAPHS (INCLUDING TRIGONOMETRIC FUNCTIONS) 1. Revise basic results established in earlier grades regarding lines, angles 1. Represent quadrilaterals amongst other 1. The concept of a function, where a certain quantity (output value) uniquely depends on another quantity (input value). Work with relationships and triangles, especially the similarity and congruence of triangles geometric figures on a Cartesian co-ordinate between variables using tables, graphs, words and formulae. Convert flexibly between these representations 2. Define the following special quadrilaterals: The kite, parallelogram, rectangle, system. Derive and apply for any two points 2. Note: That the graph defined by y = x should be known from Grade 9 rhombus, square and trapezium. Investigate and make conjectures about the (𝑥1 , 𝑦1 ) and (𝑥2 , 𝑦2 ) the formulae for 1 properties of the sides, angles, diagonals and areas of these quadrilaterals. calculating the: 3. Point by point plotting of basic graphs defined by y = x , 2 y= and y = b x ; b  0 and b  1 to discover shape, domain (input Prove these conjectures • Distance between the two points x • Gradient of the line segment connecting values), range (output values), asymptotes, axes of symmetry, turning points and intercepts on the axes (where applicable) 3. Investigate line segment joining the midpoints of two sides of a triangle 4. Investigate the effect of a and q on the graphs defined by, 4. Solve problems and prove riders using the properties of parallel lines, the two points (and from that identify 1 triangles, quadrilaterals and midpoint theorem parallel and perpendicular lines) 𝑦 = 𝑎. 𝑓(𝑥) + 𝑞, where 𝑓(𝑥) = 𝑥, 𝑓(𝑥) = 𝑥 2 , 𝑓(𝑥) = and 𝑓(𝑥) = 𝑏 𝑥 , 𝑏 > 0, 𝑏 ≠ 1 𝑥 • Coordinates of the mid-point of the line 5. Point by point plotting of basic graphs defined by 𝑦 = 𝑠𝑖𝑛𝜃 , 𝑦 = cos 𝜃 and 𝑦 = 𝑡𝑎𝑛𝜃 for 𝜃 ∈ [0°, 360°] segment joining the two points 6. Study the effect of a and q on the graphs defined by: 𝑦 = 𝑎 sin 𝜃 + 𝑞, 𝑦 = 𝑎 cos 𝜃 + 𝑞, and 𝑦 = 𝑎 tan 𝜃 + 𝑞 where a and q ∈ 𝑄and 𝜃 ∈ [0°, 360°] 7. Sketch graphs, find the equations of given graphs and interpret graphs Note: Sketching of the graphs must be based on the observation of the effect number 3 and number 5 DATE COMPLETED SBA Assignment & mid-year exam Downloaded from hlayiso.com 3

2023/24 ANNUAL TEACHING PLANS: MATHEMATICS: GRADE 10 2023/24 ANNUAL TEACHING PLANS: MATHEMATICS: GRADE 10 (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 (2D) STATISTICS PROBABILITY FINANCE AND GROWTH 1. Solve two-dimensional problems 1. Measures of central tendency in ungrouped data. Calculate the 1. The use of probability models to compare the relative frequency of events with the 1. Use the simple and compound growth formulae involving right- angled triangle mean. Determine the median and the mode theoretical probability [𝐴 = 𝑃(1 + 𝑖𝑛) and 𝐴 = 𝑃(1 + 𝑖)𝑛 ] 2. Measures of central tendency in grouped data: Calculation of mean to solve problems, including interest, hire purchase, inflation, 2. Problems in two dimensional estimate of grouped data and identification of modal interval and population growth and other real-life problems 2. The use of Venn diagrams to solve probability problems, deriving and applying the interval in which the median lies following for any two events in a sample space S: 3. Range as a measure of dispersion and extension to include Understand the implication of fluctuating foreign exchange rates (e.g., percentiles, quartiles, inter-quartile and semi-inter-quartile range • 𝑃(𝐴 𝑜𝑟 𝐵) = 𝑃(𝐴) + 𝑃(𝐵) − 𝑃( 𝐴 𝑎𝑛𝑑 𝐵) on the petrol price, imports, exports, overseas travel) 4. Five number summary (maximum, minimum and quartiles) and box and whisker diagram • A and B are mutually exclusive if 𝑃(𝐴 𝑎𝑛𝑑 𝐵) = 0, 5. Use the statistical summaries (measures of central tendency and • A and B are complementary if they are, dispersion), and graphs to analyse and make meaningful comments ➢ mutually exclusive and 𝑃(𝐴) + 𝑃(𝐵) = 1 on the context associated with the given data Then 6. Histogram 𝑃(𝐵) = 𝑃(𝑛𝑜𝑡 𝐴) = 1 − 𝑃(𝐴) DATE COMPLETED SBA Test Test Downloaded from hlayiso.com 4

2023/24 ANNUAL TEACHING PLANS: MATHEMATICS: GRADE 10 2023/24 ANNUAL TEACHING PLANS: MATHEMATICS: GRADE 10 (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 MEASUREMENT NUMBER PATTERNS REVISE REVISE REVISE EXAMINATION ADMIN PAPER 1 ALGEBRA TRIGONOMETRY FUNCTIONS Algebra 30 & GEOMETRY Number patterns 15 1. Revise the volume and surface areas Patterns: Investigate number Finance, growth 10 of right-prisms and cylinders patterns leading to those Functions and graphs 30 2. Study the effect on volume and where there is a constant Probability 15 surface area when multiplying any difference between dimension by a constant factor k consecutive terms, and the 3. Calculate the volume and surface general term (without using a areas of spheres, right pyramids, formula – see content right cones and combination of those overview) is therefore linear objects (figures) DATE PAPER 2 COMPLETED Statistics 15 SBA TEST Analytical Geometry 15 Trigonometry 40 TOTAL NUMBER OF SBA TASKS 7 Euclidean Geometry & 30 TERM 1 INVESTIGATION/PROJECT (15%) AND TEST (14%) Measurement 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