Exponents and surds
Simplify expressions and solve equations using the laws of exponents for rational exponents. Add, subtract, multiply and divide simple surds, and solve simple equations involving surds.
Grade 11 Mathematics
Annual Teaching Plan (Terms 1-4)
The Grade 11 Mathematics CAPS syllabus for South Africa follows the annual teaching plan across Terms 1-4. Use the term topics below as a study checklist, then practise with Grade 11 Mathematics past papers for exam preparation.
How to study using this page: Revise term topics attempt past papers mark with memos.
Term 1 topics
Weeks 1-11
Assessment: Investigation or project & test (content of Term 1).
Equations and inequalities
Complete the square, solve quadratic equations (by factorisation and by using the quadratic formula), and solve quadratic inequalities in one unknown (interpret solutions graphically). Work with equations in two unknowns where one is linear and the other quadratic, and study the nature of roots.
Trigonometry (reduction formulae, trig equations & general solutions)
Derive and use identities, including sin2 a + cos2 a = 1, and derive and use reduction formulae for sin(90 degrees +/- a), cos(90 degrees +/- a), sin(180 degrees +/- a), cos(180 degrees +/- a), tan(180 degrees +/- a), sin(360 degrees +/- a), cos(360 degrees +/- a), tan(360 degrees +/- a), and sin(-a), cos(-a), tan(-a). Determine for which values of a variable an identity holds, and determine general solutions of trigonometric equations (including solutions in specific intervals).
Exponents and surds
Simplify expressions and solve equations using the laws of exponents for rational exponents. Add, subtract, multiply and divide simple surds, and solve simple equations involving surds.
Equations and inequalities
Complete the square, solve quadratic equations (by factorisation and by using the quadratic formula), and solve quadratic inequalities in one unknown (interpret solutions graphically). Work with equations in two unknowns where one is linear and the other quadratic, and study the nature of roots.
Trigonometry (reduction formulae, trig equations & general solutions)
Derive and use identities, including sin2 a + cos2 a = 1, and derive and use reduction formulae for sin(90 degrees +/- a), cos(90 degrees +/- a), sin(180 degrees +/- a), cos(180 degrees +/- a), tan(180 degrees +/- a), sin(360 degrees +/- a), cos(360 degrees +/- a), tan(360 degrees +/- a), and sin(-a), cos(-a), tan(-a). Determine for which values of a variable an identity holds, and determine general solutions of trigonometric equations (including solutions in specific intervals).
Term 2 topics
Weeks 1-11
Assessment: Assignment & mid-year exam.
Euclidean Geometry
Use earlier results as axioms, including that a tangent to a circle is perpendicular to the radius at the point of contact. Investigate and prove circle geometry theorems (and use them and their converses, where they exist, to solve riders), including: the centre-perpendicular-to-chord results, angles subtended by an arc, equal angles in the same segment, cyclic quadrilaterals, equal tangents from an external point, and the tangent-chord theorem (alternate segment).
Analytical Geometry
Revise distance between two points, gradient (including identifying parallel and perpendicular lines), and midpoint. Derive and apply the equation of a line through two points, the equation of a line through one point parallel or perpendicular to a given line, and the inclination (theta) of a line where m = tan theta (0 degrees <= theta <= 180 degrees).
Functions (including trigonometric functions)
Revise the effect of parameters a and q and investigate the effect of p on graphs defined by y = a(x + p)^2 + q, y = a/(x + p) + q, and y = a.b^(x+p) + q where b > 0 and b != 1. Investigate average gradient between two points on a curve and the gradient of a curve at a point. Plot basic graphs y = sin theta, y = cos theta and y = tan theta for theta in [-360 degrees, 360 degrees], and investigate the effect of parameters k and p on trigonometric graphs. Draw sketch graphs 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).
Euclidean Geometry
Use earlier results as axioms, including that a tangent to a circle is perpendicular to the radius at the point of contact. Investigate and prove circle geometry theorems (and use them and their converses, where they exist, to solve riders), including: the centre-perpendicular-to-chord results, angles subtended by an arc, equal angles in the same segment, cyclic quadrilaterals, equal tangents from an external point, and the tangent-chord theorem (alternate segment).
Analytical Geometry
Revise distance between two points, gradient (including identifying parallel and perpendicular lines), and midpoint. Derive and apply the equation of a line through two points, the equation of a line through one point parallel or perpendicular to a given line, and the inclination (theta) of a line where m = tan theta (0 degrees <= theta <= 180 degrees).
Functions (including trigonometric functions)
Revise the effect of parameters a and q and investigate the effect of p on graphs defined by y = a(x + p)^2 + q, y = a/(x + p) + q, and y = a.b^(x+p) + q where b > 0 and b != 1. Investigate average gradient between two points on a curve and the gradient of a curve at a point. Plot basic graphs y = sin theta, y = cos theta and y = tan theta for theta in [-360 degrees, 360 degrees], and investigate the effect of parameters k and p on trigonometric graphs. Draw sketch graphs 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).
Term 3 topics
Weeks 1-11
Assessment: Test; test.
Trigonometry (sine, cosine and area rules)
Prove and apply the sine, cosine and area rules, and solve problems in two dimensions using the sine, cosine and area rules.
Statistics
Revise measures of central tendency and dispersion in ungrouped and grouped data, five number summary (maximum, minimum and quartiles) and box and whisker diagram, histograms, frequency polygons, and ogives (cumulative frequency curves). Work with variance and standard deviation of ungrouped data, and interpret symmetric and skewed data and identification of outliers.
Probability
Revise probability models comparing relative frequency with theoretical probability. Use Venn diagrams to solve probability problems, including the addition rule for any two events in a sample space S, mutually exclusive events, complementary events, and identifying dependent and independent events with the product rule for independent events. Use Venn diagrams for three events in a sample space S, and use tree diagrams and contingency tables to solve real-life probability problems (including events that are not necessarily independent).
Finance, growth and decay
Revise simple and compound growth formulae to solve real-life problems (including interest, hire purchase, inflation and population growth). Understand implications of fluctuating foreign exchange rates. Use simple and compound decay formulae to solve problems (including straight line depreciation and depreciation on a reducing balance). Study the effect of different periods of compound growth and decay, including nominal and effective interest rates.
Trigonometry (sine, cosine and area rules)
Prove and apply the sine, cosine and area rules, and solve problems in two dimensions using the sine, cosine and area rules.
Statistics
Revise measures of central tendency and dispersion in ungrouped and grouped data, five number summary (maximum, minimum and quartiles) and box and whisker diagram, histograms, frequency polygons, and ogives (cumulative frequency curves). Work with variance and standard deviation of ungrouped data, and interpret symmetric and skewed data and identification of outliers.
Probability
Revise probability models comparing relative frequency with theoretical probability. Use Venn diagrams to solve probability problems, including the addition rule for any two events in a sample space S, mutually exclusive events, complementary events, and identifying dependent and independent events with the product rule for independent events. Use Venn diagrams for three events in a sample space S, and use tree diagrams and contingency tables to solve real-life probability problems (including events that are not necessarily independent).
Finance, growth and decay
Revise simple and compound growth formulae to solve real-life problems (including interest, hire purchase, inflation and population growth). Understand implications of fluctuating foreign exchange rates. Use simple and compound decay formulae to solve problems (including straight line depreciation and depreciation on a reducing balance). Study the effect of different periods of compound growth and decay, including nominal and effective interest rates.
Term 4 revision focus
Weeks 1-10 plus examination
Assessment: Test; final examination.
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%).
Number patterns
Exam relevance: Appears in Paper 1 (25 marks).
Patterns: Investigate number patterns leading to those where there is a constant second difference between consecutive terms and the general term is therefore quadratic.
Revision of measurement
Revise the volume and surface areas of right prisms and cylinders. Study the effect on volume and surface areas when multiplying any dimension by a constant factor k. Calculate volume and surface areas of spheres, right prisms, right cones and combination of those objects (figures).
Revision of Algebra
Exam relevance: Algebraic expressions, equations and inequalities appear in Paper 1 (45 marks).
[unclear]
Revision of Trigonometry
Exam relevance: Trigonometry appears in Paper 2 (50 marks).
[unclear]
Examination
Exam relevance: Paper 1 marks: Algebraic expressions, equations and inequalities (45); Number patterns (25); Finance, growth and decay (15); Functions and graphs (45); Probability (20). Paper 2 marks: Statistics (20); Analytical Geometry (30); Trigonometry (50); Euclidean Geometry (50).
Paper 1: 150 marks, 3 hours. Paper 2: 150 marks, 3 hours.
Number patterns
Exam relevance: Appears in Paper 1 (25 marks).
Patterns: Investigate number patterns leading to those where there is a constant second difference between consecutive terms and the general term is therefore quadratic.
Revision of measurement
Revise the volume and surface areas of right prisms and cylinders. Study the effect on volume and surface areas when multiplying any dimension by a constant factor k. Calculate volume and surface areas of spheres, right prisms, right cones and combination of those objects (figures).
Revision of Algebra
Exam relevance: Algebraic expressions, equations and inequalities appear in Paper 1 (45 marks).
[unclear]
Revision of Trigonometry
Exam relevance: Trigonometry appears in Paper 2 (50 marks).
[unclear]
Examination
Exam relevance: Paper 1 marks: Algebraic expressions, equations and inequalities (45); Number patterns (25); Finance, growth and decay (15); Functions and graphs (45); Probability (20). Paper 2 marks: Statistics (20); Analytical Geometry (30); Trigonometry (50); Euclidean Geometry (50).
Paper 1: 150 marks, 3 hours. Paper 2: 150 marks, 3 hours.