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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