GRADE 11 sba ADMINISTRATION dOCUMENTS
FET MATHEMATICS GRADE 11
SBA ADMINISTRATION DOCUMENTS
2019
ASPECT ANNUAL TEACHING PLAN COMMON TESTS & EXAMINATION SCOPES SBA MODERATION TOOL PROGRAM OF ASSESSMENT CONSOLIDATION SHEET LEARNER DECLARATION COGNITIVE LEVEL GRID LEARNER TRACKING FORM DIAGNOSTIC ANALYSIS GRID
PAGE NO. 1 7
8 21 22 23 24 25 27
COMPILED BY KZN FET MATHEMATICS ADVISORS
KZN DEPARTMENT OF EDUCATION MATHEMATICS ANNUAL TEACHING PLAN
GRADE 11 ? 2019
NAME OF SCHOOL: ................................................ NAME OF TEACHER: ..............................................
DATES
09/1 ? 16/1 (6 days)
17/1 ? 18/1 (2 days)
21/ 1? 22/1 (2 days)
23/1 ? 25/1 (3 days)
28/1 ? 31/1 (4 days)
01/2 ? 07/2 (5 days)
08/2 ? 15/2 (6 days)
TERM 1
TOPIC
EXPONENTS AND SURDS
CURRICULUM STATEMENT
? Simplify expressions using the laws of exponents for rational
p
exponents where x q q x p ; x 0; q 0. ? Solve equations using the laws of exponents for rational exponents
p
where x q q x p ; x 0; q 0.
ASSESSMENT
F/IF
DATE STARTED
DATE COMPLETED
EXPONENTS AND SURDS EXPONENTS AND SURDS
EQUATIONS
? Add, Subtract, Multiply and Divide Simple Surds.
? Solve simple equations involving surds. ? Revision of factorization. ? Quadratic equations (by factorisation). ? Complete the square.
EQUATIONS AND ? Quadratic equations (by using the quadratic formula). INEQUALITIES ? Quadratic inequalities in one unknown (Interpret solutions graphically).
SIMULTANEOUS ? Equations in two unknowns, one of which is linear and the other
EQUATIONS &
quadratic.
NATURE OF ROOTS
? Nature of roots.
INVESTIGA-
TION SBA weighting:
F
15
EUCLIDEAN GEOMETRY
? Revision of grade 10 geometry (1 day)
? Investigate and prove the following theorems of the geometry of circles, assuming results from earlier grades: The line drawn from the centre of a circle perpendicular to a chord bisects the chord; The perpendicular bisector of a chord passes through the centre of the circle; The angle at the centre of a circle is double the size of the angle at the circle. Angles subtended by a chord of the circle, on the same side of the chord, are equal.
HOD: SIGNATURE
and DATE
% COMPLETED
5% 6% 7% 9% 12% 16%
21%
Page 1 of 28
DATES 18/2 ? 19/2
(2 days)
20/2 ? 22/2 (3 days)
25/2 ? 27/2 (3 days)
28/2 ? 15/3 (12 days)
TOPIC EUCLIDEAN GEOMETRY
EUCLIDEAN GEOMETRY
EUCLIDEAN GEOMETRY
TRIGONOMETRIC
IDENTITIES and
REDUCTION FORMULAE
MARCH TEST
TERM 1 (continued) CURRICULUM STATEMENT
ASSESSMENT
F/IF
DATE STARTED
DATE COMPLE
TED
HOD: SIGNATURE
and DATE
? Solve circle geometry problems, providing reasons for statements.
? Accept results established in earlier grades as axioms and that a tangent to a circle is perpendicular to the radius, drawn to the point of contact. Then investigate and prove the following theorems of the geometry of circles:
The opposite angles of a cyclic quadrilateral are supplementary;
Two tangents drawn to a circle from the same point outside the circle are equal in length;
The angle between the tangent to a circle and the chord drawn from the point of contact is equal to the angle in the alternate segment.
? Solve circle geometry problems, providing reasons for statements.
The proofs of the four theorems printed in bold above can be asked in examinations.
(See Gr. 11 Examination Guidelines page 7.)
? Derive and use the identities:
tan sin ; k.90 , k an odd integer; cos
sin2 cos2 1.
? Determine for which values of a variable an identity holds.
? Derive and use reduction formulae to simplify the following expressions: sin(90? ? ); cos(90? ? );
sin(180? ? ); cos(180? ? ); tan(180? ? ); sin(360? ? ); cos(360? ? ); tan(360? ? ); and sin(-); cos(-); tan(-).
? Proving trigonometric identities
March Test to cover the work done during Term 1, except: Proving Trigonometric Identities.
MARCH TEST SBA weighting: F
10
% COMPLETED
22%
24%
26%
35%
Page 2 of 28
DATES
02/4 ? 08/4 (5 days)
09/4-15/4 (5 days)
16/4 ? 24/4 (5 days)
25/4 ? 26/4 (2 days)
29/4 ? 02/05 (3 days)
03/5 ? 08/5 (4 days)
09/5 ? 16/5 (5 days)
17/5 ? 22/5 (4 days)
TOPIC TRIG EQUATIONS and GENERAL SOLUTIONS
ANALYTICAL GEOMETRY
ANALYTICAL GEOMETRY
NUMBER PATTERNS NUMBER PATTERNS
FUNCTIONS
FUNCTIONS
FUNCTIONS
TERM 2
CURRICULUM STATEMENT
? Determine the general solution and / or specific solutions (given intervals) of trigonometric equations.
? The equation of a line through two given points. ? The equation of a line through one point and parallel or
perpendicular to a given line. ? Collinear lines. ? The inclination () of a given line, where m tan is the gradient of
the line ( 0 180 ). ? Applications.
? Revise linear number patterns.
? Investigate number patterns leading to those where there is a constant second difference between consecutive terms, and the general term is therefore quadratic.
? Revise the effect of the parameters a and q and investigate the effect of p on the graph of the function defined by
y f x ax p2 q
? Revise the effect of the parameters a and q and investigate the effect of p on the graph of the function defined by
y f x a q
x p ? Revise the effect of the parameters a and q and investigate the effect
of p on the graph of the function defined by
y f x a.bx p q , where b 0 and b 1.
ASSESSMENT
F/IF
DATE STARTED
DATE COMPLE
TED
HOD: SIGNATURE
and DATE
% COMPLETED
39%
43%
47% 48% 50% 53%
57%
ASSIGNMENT
SBA weighting: F
60%
15
Page 3 of 28
DATES
TOPIC
23/5 ? 27/5 (3 days)
FUNCTIONS
28/5 ? 14/6 (14 days)
JUNE EXAMS
TERM 2 (continued)
CURRICULUM STATEMENT
? Investigate numerically the average gradient between two points on a curve.
? Develop an intuitive understanding of the concept of the gradient of a curve at a point.
? Interpretations, applications and practical problems. NB: Integration between Nature of roots and Functions.
June Examination to cover the work done during Terms 1 and 2.
ASSESSMENT
F/IF
DATE STARTED
DATE COMPLE
TED
HOD: SIGNATURE
and DATE
% COMPLETED
62%
JUNE EXAMI-
NATION SBA weighting:
F
30
Page 4 of 28
DATES
09/7 ? 17/7 (7 days)
18/7 ? 24/7 (5 days)
25/7 ? 31/7 (5 days)
01/8 ? 06/8 (4 days)
07/8 ? 12/8 (3 days)
13/8 ? 21/8 (7 days)
22/8 ? 23/8 (2 days)
TERM 3
TOPIC
CURRICULUM STATEMENT ? Point by point plotting of basic graphs defined by y sin ,
ASSESSMENT
F/IF
DATE STARTED
DATE COMPLE
TED
HOD: SIGNATURE
and DATE
TRIGONOMETRIC
FUNCTIONS
TRIGONOMETRY
TRIGONOMETRY
y cos and y tan for 360 ; 360 . ? Investigate the effect of the parameter on the graphs of the functions
defined by y sin kx , y coskx and y tan kx .
? Investigate the effect of the parameter on the graphs of the functions
defined by y sin x p , y cos x p , and y tan x p . ? 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 will be varied.
? Prove and apply the sine, cosine and area rules.
? Solve problems in two dimensions using the sine, cosine and area rules.
MEASUREMENT ? Revision of grade 10 work.
STATISTICS STATISTICS PROBABILITY
? Histograms ? Frequency polygons
? Variance and standard deviation of ungrouped data ? Ogives (cumulative frequency curves). ? Symmetric and skewed data. ? Identification of outliers
? Revise the addition rules for mutually exclusive events: P(A or B) = P(A) + P(B); the complementary rule, P(not A) = 1 - P(A); and the identity P(A or B) = P(A) + P(B) - P(A and B).
TERM 3 TEST SBA weighting: F
10
% COMPLETED
67%
71% 75% 78% 80% 86%
88%
Page 5 of 28
DATES
26/8 ? 2/9 (6 days)
03/9 ? 20/9 (14 days)
TOPIC
Probablilty
REVISION and SEPT.
TEST
TERM 3 (continued)
CURRICULUM STATEMENT
ASSESSMENT
F/IF
DATE STARTED
DATE COMPLE
TED
HOD: SIGNATURE
and DATE
Identify dependent and independent events and the product rule for
independent events: P(A and B) = P(A) ? P(B).
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.
Use tree diagrams for the probability of consecutive or simultaneous
events which are not necessarily independent.
Use contingency tables to solve probability problems.
September Test to cover the work done during Term 3.
SEPT. TEST SBA weighting: F
10
% COMPLETED
92%
DATES
01/10?04/10 (4 days)
07/10 ? 11/10 (5 days)
14/10 ? 04/12 (38 days)
TOPIC
FINANCE, GROWTH AND DECAY FINANCE, GROWTH AND DECAY
REVISION and NOV.
EXAM
TERM 4
CURRICULUM STATEMENT
ASSESSMENT
F/IF
DATE STARTED
? Use simple and compound decay formulae, = (1 - ) and = (1 - ), to solve problems (including straight line depreciation and
depreciation on a reducing balance).
? Different periods of compound growth and decay. ? Effective and nominal interest rates..
TERM 3 TEST SBA weighting:
10
November Examination to cover all the work done during Terms 1, 2, 3 and 4.
NOVEMBER EXAMINA-
TION
F
DATE COMPLE
TED
HOD: SIGNATURE
and DATE
% COMPLETED
95%
100%
Page 6 of 28
GR. 11 MATHEMATICS 2019 TEST and EXAMINATION SCOPE/GUIDELINES
TERM 1
TERM 2
TERM 3
TERM 4
MARCH TEST
JUNE EXAMINATION PAPER 1:
SEPTEMBER TEST
NOVEMBER EXAMINATION PAPER 1:
DURATION:
1? hours
DURATION:
2 hours
DURATION:
1? hours
DURATION:
3 hours
TOTAL MARKS:
75
TOTAL MARKS:
100
TOTAL MARKS:
75
This test will consist of the following sections:
This examination paper will consist of the This test will consist of the following
following sections:
sections:
Exponents and surds
12?3 marks Exponents and surds
15?3 marks Probability
20?3 marks
Equations and inequalities
Euclidean Geometry (Including the Examinable Proofs of Theorems)
Trigonometry (Excluding Proving Identities)
18?3 marks Equations and inequalities 30?3 marks Number patterns 15?3 marks Functions and graphs
PAPER 2:
25?3 marks Statistics
20?3 marks
25?3 marks Measurement
7?3 marks
35?3 marks
Proof and Application of Sine, Cosine and Area Rules (2D problems) Graphs of Trigonometric Functions
7?3 marks 15?3 marks
TOTAL MARKS:
150
This examination paper will consist of the
following sections:
Algebra, equations and inequalities
45?3 marks
Number patterns
20?3 marks
Finance, growth and decay 15?3 marks
Functions and graphs
45?3 marks
Probability
PAPER 2:
25?3 marks
DURATION:
2 hours
DURATION:
3 hours
TOTAL MARKS:
100
This examination paper will consist of the following sections:
Analytical Geometry
30?3 marks
TOTAL MARKS:
150
This examination paper will consist of the following sections:
Statistics
20?3 marks
Trigonometry
35?3 marks
Analytical Geometry
30?3 marks
Euclidean Geometry
35?3 marks
Completion date of the last topic for the March Common Test: 08/03/2019
Completion date of the last topic for Completion date of the last topic for the June Examination: 27/05/2019 the Sept. Common Test: 02/09/2019
Trigonometry
60?3 marks
Euclidean Geometry and Measurement
40?3 marks
Completion date of the last topic for
the Nov. Examination: 11/10/2019
Page 7 of 28
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