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Grade 10 : ATP 2015 Page 1 of 3 GAUTENG PROVINCE MATHEMATICS – ANNUAL TEACHING PLAN – GRADE 10 2015 DATE TOPIC CONTENT TERM 1 Algebraic expressions • (3 days) • 19/1 – 23/1 Algebraic expressions • • • 26/1 – 30/1 Algebraic expressions • • 02/2 – 06/2 ASSESSMENT DATE Completed % Compl eted 2 TASKS FOR TERM 1 • 14/1 – 16/1 F Algebraic expressions Understand that real numbers can be rational or irrational. Establish between which two integers a given simple surd lies. Round real numbers to an appropriate degree of accuracy. Multiplication of a binomial by a trinomial. Factorisation: Difference of two squares Common factors (revision of grade 9) Factorisation: Trinomials Grouping in pairs. Sum and difference of two cubes. Algebraic fractions: Denominator with monomial, binomial and trinomial terms. (limited to sum & difference of cubes) Algebraic fractions: Denominator with monomial, binomial and trinomial terms. (limited to sum & difference of cubes) 3% 6% 9% F TEST 12% SBA marks: 10 09/2 – 13/2 Exponents • Revise laws of exponents where x,y> 0 and m,n∈Z • Use the laws of exponents to simplify expressions and solve equations, accepting that the rules also hold 15% for m,n∈Q • 16/2 – 20/2 • • Number patterns 02/3 - 06/3 Equations 09/3 – 13/3 Equations 16/3 – 20/3 Equations and Inequalities 23/3 – 25/3 (3 days) TERM 2 • • • • • • • • • Euclidean Geometry Euclidean Geometry • • 20/4 - 24/4 Trigonometry • • 27/4 – 01/5 (3 days) Exponential equations Investigate number patterns leading to those where there is a constant difference between consecutive terms, and the general term is therefore linear. WITHOUT USING A FORMULA Linear equations Quadratic equations (by factorisation) Literal equations (changing the subject of the formula) Simultaneous linear equations in two unknowns Solve linear inequalities (show solutions graphically). Solve linear inequalities (show solutions graphically). Interval notation must be known. Word problems involving linear, quadratic or simultaneous linear equations. Revise basic results established in earlier grades. Lines, angles, congruency, similarity 21% 24% 27% F TEST 30% SBA marks: 10 33% 2 TASKS FOR TERM 2 • 13/4 – 17/4 18% for m,n∈Q Exponents 23/2 - 27/2 Use the laws of exponents to simplify expressions andsolve equations, accepting that the rules also hold Trigonometry • Investigate line segments joining the midpoints of two sides of a triangle. Investigate and make conjectures about the properties of the sides, angles, diagonals and areas of special quadrilaterals. Definitions of the trigonometric ratios sin θ, cosθ and tan θ in a right-angled triangles. Extend the definitions of sin θ, cosθ and tan θ to 00 ≤ θ ≤ 3600. Extend the definitions of sin θ, cosθ and tan θ to 00 ≤ θ ≤ 3600. Define the reciprocals of the trig ratios cosecθ, secθ and cotθ using right-angled triangles 36% MATHS WEEK 39% 42% Grade 10 : ATP 2015 • 04/5 – 08/5 Trigonometry • Derive and use values of the trigonometric ratios (without using a calculator for the special angles θ ∈ {0 0;300;450;600;900} Solve simple trig equations for θ ∈ {0 0;900} Page 2 of 3 F ASSIGNMENT/ TEST 45% SBA marks: 10 11/5 – 15/5 Functions 18/5 - 22/5 Functions 25/5 – 29/5 Functions 01/6 - 05/6 Trig Functions 08/6 – 12/6 JUNE EXAMS 15/6 – 19/6 (3 days) JUNE EXAMS 22/6 – 26/6 JUNE EXAMS DATE TOPIC • Relationships and conversions between variables: numerical, graphical, verbal and symbolical • Difference between a relation and a function • Investigate basic graphs to discover shape, domain, range, and intercepts with axes, turning points and axes of symmetry. • Investigate the effect of a and q on each graph • Straight line: y = a(x) + q • Parabola: y = a(x)2 +q • Hyperbola: • Exponential graph: y = a.bx + q ; b > 0 • Finding equations of functions • Interpretation of functions • Trig graphs [a sin x+ q,a cosx + q, a tan x+ q ] • Basic graphs and the effect of a and q on the graphs CONTENT TERM 3 Euclidean Geometry 27/7 – 31/7 Euclidean Geometry 03/8 - 07/8 Functions (4 days) 17/8 – 21/8 Analytical Geometry Analytical Geometry • • • • • • • • • • • • 24/8 –28/8 Finance, growth and decay 31/8 – 04/9 Finance, growth and decay • • 07/9 - 11/9 Statistics 14/9 – 18/9 Statistics • • • • • • • • • • 21/9 – 25/9 (3 days) 51% 54% 57% F JUNE EXAM SBA marks: 30 F ASSESSMENT DATE COMPLED % Compl eted 2 TASKS FOR TERM 3 20/7 – 24/7 10/8 -14/8 48% Kite, parallelogram, rectangle, rhombus, square and trapezium. Prove conjectures. Solve problems and prove riders using the properties of parallel lines, triangles and quadrilaterals. Interpretation of functions Distance between two points Gradient of the line segment jointing the points (from that identify parallel and perpendicular lines) Gradient of the line segment jointing the points (from that identify parallel and perpendicular lines) Co-ordinates of the mid-point of the line segment joining the points Simple and compound growth formula to solve problems Annual interest, hire purchase, inflation, population growth and other real life problems. Annual interest, hire purchase, inflation, population growth and other real life problems Fluctuating foreign exchange rates Collect, organise and interpret univariate numerical data in order to determine: measures of central tendency(mean, median, mode) five number summary; box and whisker diagrams; and measures of dispersion (range, percentiles, quartiles) Collect, organise and interpret univariate numerical data in order to determine: measures of central tendency(mean, median, mode) five number summary; box and whisker diagrams; and measures of dispersion (range, percentiles, quartiles) Revision of trig Problems in two dimensions 60% 63% 66% 69% F TEST 72% SBA marks: 10 75% 78% 81% 84% F PROJECT/ INVESTIGATION 2D Trig SBA marks: 20 87% Grade 10 : ATP 2D Trig 28/9 -02/10 2015 • Problems in two dimensions • Solve problems and prove riders using the properties of parallel lines, triangles and quadrilaterals. and/or Geometry Page 3 of 3 90% TERM 4 2 TASKS FOR TERM 4 • • 12/10 –16/10 Measurement • • • 19/10 - 23/10 Probability • 26/10 –30/10 Probability • • Revise area of circles, quadrilaterals and triangles. Revise the volume and surface areas of right-prisms and cylinders. Study the effect on volume and surface area when multiplying any dimension by a constant factor k. Calculate the volume and surface areas of spheres, right pyramids and right cones. Compare the relative frequency of an experimental outcome with the theoretical probability of the outcome. Venn diagrams as an aid to solving probability problems. Mutually exclusive events and complementary events. The identity for any two events A and B: ܲ()ܣ( ܲ = )ܤݎܣ+ ܲ( )ܤ− ܲ( ܣand )ܤ 02/11 - 06/11 Revision • Exposure to exam type questions 09/11 –13/11 Revision • Exposure to exam type questions 16/11 - 20/11 FINAL EXAMINATIONS 23/11 -27/11 FINAL EXAMINATIONS 30/11 - 04/12 FINAL EXAMINATIONS % Compl eted 93% 96% F TEST 100% SBA marks: 10 25 % SBA 75 % Final exam