| Sekhukhune Science & Technology Foundation



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Department of Education

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MATHEMATICS

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2018

|TERM 1 |

|WEEK | Topic |CURRICULUM STATEMENT |ASSESSMENT |

|Week 1-3 |Number patterns, Sequences |1. Number patterns, including arithmetic and geometric sequences and series | |

|17 Jan – 02 Feb 2018 |and Series |2. Sigma notation | |

| | |3. Derivation and application of the formulae for the sum of arithmetic and geometric | |

| | |series: | |

| | |3.1 [pic]; [pic] |Exercises |

| | |3.2 [pic]; and | |

| | |3.3 [pic] | |

| | | | |

| | | | |

| | | |Short Test |

|Week 4-6 |Functions: Formal definition;|1. Definition of a function. |Exercises |

|05 - 23 Feb 2018 |Inverse |2. General concept of the inverse of a function and how the domain of the function may | |

| | |need to be restricted (in order to obtain a one-to-one function) to ensure that the inverse |Control Test 1 |

| | |is a function. | |

| | |3. Determine and sketch graphs of the inverses of the functions defined by Focus on the | |

| | |following characteristics: | |

| | |domain and range, intercepts with the axes, turning points, minima, maxima, |Investigation/ project |

| | |asymptotes (horizontal and vertical), shape and symmetry, average gradient (average | |

| | |rate of change), intervals on which the function increases /decreases. | |

|Week 7 |Functions: Exponential and |1. Revision of the exponential function and the |Exercises |

|26 Feb – 02 March 2018|Logarithmic |exponential laws and graph of the function | |

| | |defined by [pic] where [pic]and [pic] | |

| | |2. Understand the definition of a logarithm: [pic] | |

| | |3. The graph of the function define [pic]for both the cases 0 < b < 1 and b > 1. | |

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|TIME | |CONTENT |ASSESSMENT |

|Week 8 - 9 |Finance and Decay |1. Solve problems involving present value and future value annuities. |Exercises |

|05 – 16 March 2018 |(Logarithmic laws) |2. Make use of logarithms to calculate the value of n , the time period, in the equations | |

| | |[pic] | |

| | |3. Critically analyse investment and loan options and make informed decisions as to best |Assignment 1 |

| | |option(s) (including pyramid). | |

|Week 10 -11 |Trigonometry |Compound angle identities: |Exercises |

|19 – 28 March 2018 | |[pic] | |

| | |[pic] | |

| | |[pic] | |

| | |[pic] | |

| | |[pic] | |

| | |[pic] | |

| | |Solve Problems in two and three dimensions | |

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|TERM 2 |

|WEEKS |TOPIC |CURRICULUM STATEMENT |ASSESSMENT |

|Week 1 |Functions: Polynomials |Factorise third-degree polynomials. Apply the Remainder and Factor Theorems to |Exercises |

|10 - 13 April 2018 | |polynomials of degree at most 3 (no proofs required). | |

| | | | |

|Week 2 - 5 |Differential Calculus |1. An intuitive understanding of the limit concept, in the context of approximating the rate | |

|16 April – 11 May | |of change or gradient of a function at a point. | |

|2018 | |2. Use limits to define the derivative of a function f at any x : | |

| | |[pic] | |

| | |Generalise to find the derivative of f at any point x in the domain of f , i.e., define the derivative function f '(x) of the | |

| | |function f (x) . Understand intuitively that f '(a) is the gradient of the tangent to the graph of f at the point with x -coordinate| |

| | |a. | |

| | | | |

| | |3. Using the definition (first principle), find the derivative, f '(x) for a, b and c constants: | |

| | |3.1 [pic] | |

| | |3.2 [pic]; | |

| | |3.3 [pic] and | |

| | |3.4 f (x) = c. | |

| | | | |

| | |4. Use the formula (for any real number n) together with the rules | |

| | |4.1 [pic]and | |

| | |4.2 [pic]a constant) | |

| | | | |

| | |5. Find equations of tangents to graphs of functions. | |

| | | | |

| | |6. Introduce the second derivative of f (x) and how it determines the concavity of a | |

| | |function. | |

| | |7. Sketch graphs of cubic polynomial functions using differentiation to determine the | |

| | |Coordinate of stationary points, and points of inflection (where concavity changes). | |

| | |Also, determine the x -intercepts of the graph using the factor theorem and othe | |

| | |techniques. | |

| | |8. Solve practical problems concerning optimisation and rate of change, including | |

| | |calculus of motion. | |

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| | | |Controlled Test 2 |

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|Week 6 – 7 |Analytical Geometry |1. The equation that defines a circle with radius r and centre (a;b) . | |

|14 – 25 May 2018 | |2. Determination of the equation of a tangent to a given circle. | |

| | | |Exercises |

|Week 8 -11 |Mid-year Exam | |Mid year Examination |

|28 May – 22 June | | | |

|2018 | | | |

|TERM 3 |

|WEEK |TOPIC |CURRICULUM STATEMENT |ASSESSMENT |

|Week 1 -2 |Euclidean Geometry |1. Revise earlier work on the necessary and sufficient conditions for polygons to be | |

|17 – 27 July 2018 | |similar. | |

| | |2. Prove (accepting results established in earlier grades): |Exercises |

| | |• that a line drawn parallel to one side of a triangle divides the other two sides | |

| | |proportionally (and the Mid-point Theorem as a special case of this theorem) ; | |

| | |• that equiangular triangles are similar; | |

| | |• that triangles with sides in proportion are similar; and | |

| | |• the Pythagorean Theorem by similar triangles. | |

|Week 3 - 4 |Statistics |1. Revise symmetric and skewed data. | |

|30 July – 08 Aug 2018| |2. Use statistical summaries, scatterplots, regression (in particular the least squares |Exercises |

| | |regression line) and correlation to analyse and make meaningful comments on the | |

| | |context associated with given bivariate data, including interpolation, extrapolation | |

| | |and discussions on skewness. | |

|Week 5 – 6 |Counting and Probability |1. Revise: |Preparatory examinations |

|13 - 24 Aug 2018 | |• dependent and independent events; | |

| | |• the product rule for independent events: P(A and B) = P(A) × P(B). | |

| | |• the sum rule for mutually exclusive events A and B: P(A or B) = P(A) + P(B) | |

| | |• the identity: P(A or B) = P(A) + P(B) – P(A and B) | |

| | |• the complementary rule: P( not A) = 1 – P(A) |Controlled Test No 3 |

| | |2. Probability problems using Venn diagrams, tree diagrams, two-way contingency tables | |

| | |and other techniques to solve probability problems (where events are not necessarily | |

| | |independent). | |

| | |3. Apply the fundamental counting principle to solve probability problems. | |

|Week 7 - 11 |Revision and Trial | |TRIAL EXAMINATION |

|27 Aug – 28 Sep 2018|Examination | | |

|TERM 4 |

|Week 1-8 |Revision and Final | | |

|09 Oct – 30 Nov 2018 |Examination | | |

ANNUAL ASSESSMENT PLAN: Mathematics Grade 12

| |TERM 1 |TERM 2 |TERM 3 |

|Formal Assessment Task |TEST 1 |TEST 2 |TEST 3 |

|Topics |Number Patterns Sequences and Series. |Trigonometry, Polynomial Functions and Differential Calculus, |Euclidean Geometry, Statistics, Counting and |

| |Algebraic Functions and Inverses of functions excluding | |Probability. (Grade 11 work based on these |

| |logarithmic functions. | |topics is Included) |

| |(Grade 11 work based on these topics is Included) | | |

|Date | 15 February |17 May |23 August |

|Formal Assessment |INVESTIGATION / PROJECT |MID-YEAR EXAMINATION |TRIAL EXAMINATION |

|Topics |Number Patterns Sequences and Series. |PAPER 1 | |

| |Algebraic Functions and Inverses of functions Including |Algebra and Equations, Number patterns, Sequences and Series, Algebraic Functions and |P1 and P2 Grade 10 – 12 Mathematics content. |

| |logarithmic functions. |inverses Including logarithmic functions and Differential Calculus and its | |

| | |application, Finance, growth and decay, Probability (Grade 10 &11 work) | |

| | |PAPER 2 | |

| | |Trigonometry (Compound angle Identities, Height and Distance i.e. Application of sine,| |

| | |cosine and area rules), Analytical Geometry Data Handling (Grade 10 &11 work) | |

| | |Euclidean Geometry (Grade 10 &11 work). | |

| | |(Grade 11 work based on these topics is Included) | |

|Date |Submission date: 22 February | | |

| | | | |

|Formal Assessment Task |ASSIGNMENT | | |

| |Finance, growth and decay, Trigonometry | | |

|NB: In the Annual Assessment Plan dates are suggested and may be altered by districts. |

|Analysis per topic should be done after each formal assessment task to check the topics which learners do not perform well hence need remedial actions. |

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