# Grade 11 ATP Mathematics Jan 2022 ```ANNUAL TEACHING PLAN (ATP) / JAARLIKSE ONDERRRING PLAN (JOP) 2022
12 January 2022
SCHOOL / SKOOL ………………………………………………………………..
SUBJECT / VAK : MATHEMATICS / WISKUNDE
TEACHER / ONDERWYSER : ……………………………………………………….
Week
1
Date planned/
Datum beplan
12 – 14 Jan
Topics planned for the week/
Onderwerpebeplan vir die week
Resources/ Assessment /
Hulpmiddels Assessering
Date completed/
Datum afgehandel
SURDS AND EXPONENTS
1. Simplify expressions and solve equations using the laws of exponents for
p
rational exponents where x q 
q
x p ; x  0; q  0
2
17 – 21 Jan
SURDS AND EXPONENTS
2. Add, subtract, multiply and divide simple surds.
3. Solve simple equations involving surds.
3
24 – 28 Jan
4
31 Jan – 04 Feb
5
07 – 11 Feb
EQUATIONS AND INEQUALITIES
1.Theory of numbers
2. Complete the square.
formula), including k-method, fractions and with radical sign (squaring both
sides).
EQUATIONS AND INEQUALITIES
4. Quadratic inequalities in one unknown (Interpret solutions graphically).
5. Equations in two unknowns.
NATURE OF THE ROOTS
Nature of the roots.
6
14 – 18 Feb
Investigation
EUCLIDEAN GEOMETRY
 Revision of Grade 8, 9 and 10 Euclidean Geometry
1. The line drawn from the centre of a circle perpendicular to a chord bisects the
chord; Proof is Examinable
2.The perpendicular bisector of a chord passes through the centre of the circle;
Use the above theorems and their converses, where they exist, to solve riders.
1
Week
7
Date planned/
Datum beplan
21 – 25 Feb
8
28Feb – 4 March
Topics planned for the week/
Onderwerpebeplan vir die week
EUCLIDEAN GEOMETRY
1. The angle subtended by an arc at the centre of a circle is double the size of the
angle subtended by the same arc at the circle
(on the same side of the chord as the centre);
Proof is Examinable
2. Angles subtended by a chord of the circle, on the same side of the chord, are
equal;
Use the above theorems and their converses, where they exist, to solve riders.
Resources/ Assessment /
Hulpmiddels Assessering
Date completed/
Datum afgehandel
EUCLIDEAN GEOMETRY
1. The opposite angles of a cyclic quadrilateral are supplementary Proof is Examinable
2. Exterior angle of acyclic quadrilateral equals to interior opposite angle
9
07 – 11 March
10
14 – 17 March
(4 days)
11
EUCLIDEAN GEOMETRY
1. Radius is perpendicular to tangent at the point of contact.
2. Two tangents drawn to a circle from the same point outside the circle are equal in
length;
3. 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. Proof is Examinable
Use the above theorems and their converses, where they exist, to solve riders.
Test
End of term Test
18 March– 4Apr
HOLIDAYS
05 – 08 April
TRIGONOMETRY
(4 days)
sin 
0
1. Derive and use the identities tan  
,   k .90 , k an odd integer;
cos
and sin
.
2.
12
11 – 14 April
(4 days)
2
2
  cos   1
Derive and use reduction formulae to simplify the following expressions:
 sin (90&deg;   ), cos (90&deg;   )
 sin (180&deg;   ), cos (180&deg;   ), tan (180&deg;   )
 sin (360&deg;   ), cos (360&deg;   ), tan (360&deg;   )
sin(-  ), cos(-  ), tan(-  )
TRIGONOMETRY
1. Special Angles
2. Solving right angled triangles
3. Determine the general solutions of trigonometric equations. Also, determine solutions in
specific intervals
2
Week
13
Date planned/
Datum beplan
19 – 22 April
(4 days)
Topics planned for the week/
Onderwerpebeplan vir die week
Resources/ Assessment /
Hulpmiddels Assessering
Date completed/
Datum afgehandel
ANALYTICAL GEOMETRY
(a) Co- ordinates of the midpoint of a line segment
(b) The distance between two points
(c) The gradient of line joining the points
14
25 – 29 April
(4 days)
ANALYTICAL GEOMETRY
1 Conditions for collinear points, parallel and perpendicular lines.
2 Use analytical Geometry to solve triangles and quadrilaterals.
3 Equation of a line through two given points.
4 the inclination
( )
of a line where m  tan  is the gradient of the line.
(0 0    180 0 )
15
03 – 06 May
(4 days)
NUMBER PATTERNS:


16
Investigate number patterns leading to those where there is a constant second difference
between consecutive terms, and the general term is therefore quadratic.
09 – 13 May
ALGEBRAIC FUNCTIONS
1. Revise the effect of the parameters a and q and investigate the effect of p on the graphs of
the functions defined by:
y  f ( x)  ax  q
2
1.2 y  f ( x)  ax  q
1.1
Investigate the effect of p and q on the graphs of the functions defined by:
2
1.3.1 y  f ( x )  a ( x  p )  q
1.3.2 y  f ( x )  a ( x  x1 )( x  x 2 )
2
1.3.3 y  f ( x )  ax  bx  c
2. Investigate numerically the average gradient between two points on a curve and
develop an intuitive understanding of the concept of the gradient of a curve at a point.
3
Week
17
Date planned/
Datum beplan
16 – 20 May
Topics planned for the week/
Onderwerpebeplan vir die week
23 – 27 May
Date completed/
Datum afgehandel
ALGEBRAIC FUNCTIONS
Revise the effect of the parameters a and q and investigate the effect of p on the graphs of
the functions defined by:
1.1.
18
Resources/ Assessment /
Hulpmiddels Assessering
y  f ( x) 
a
q
x p
2. Investigate numerically the average gradient between two points on a curve and
develop an intuitive understanding of the concept of the gradient of a curve at a point.
ALGEBRAIC FUNCTIONS
x p
1.2. y  f ( x )  a.b
 q where b&gt;0, b≠1
2. Investigate numerically the average gradient between two points on a curve and
develop an intuitive understanding of the concept of the gradient of a curve at a point.
19
30 May – 03 June TRIGONOMETRIC FUNCTIONS
1. Point by point plotting of basic graphs defined by ,
Assignment
y  sin  , y  cos
and y  tan  for   [−360&deg;;360&deg;]
2. Investigate the effect of the parameter k on the graphs of the functions defined by
y  sin( kx ) , y  cos(kx) and y  tan(kx)
4. Investigate the effect of the parameter p on the graphs of the functions defined
by y = sin(x + p), y = cos(x + p), and y = tan(x + p),
5. Draw sketch graphs defined by: y  a sin k ( x  p) , y  a cos k ( x  p)
y  a tan k ( x  p ) at most TWO parameters at a time.
20
06 – 10 June
TRIGONOMETRIC FUNCTIONS
Interpretation of the combination of the above graphs when they are drawn on
same set of axes.
21
22
13 – 15 June
(3 days)
20 – 24 June
the
MID-YEAR EXAMINATION
MID-YEAR EXAMINATION
25 June – 18 July
HOLIDAYS
23
24
19 – 22 July
(4 days)
TRIGONOMETRIC FORMULAE
1. Prove and apply the sine and cosine rules
2. Solve problems in Two Dimensions using the sine and cosine rules.
25 – 29 July
TRIGONOMETRIC FORMULAE
1. Prove and apply area rule.
2. Solve problems in Two Dimensions using the sine, cosine and area rules.
4
Week
25
Date planned/
Datum beplan
01 – 05 Aug
Topics planned for the week/
Onderwerpebeplan vir die week
Resources/ Assessment /
Hulpmiddels Assessering
Date completed/
Datum afgehandel
MEASUREMENT
 Revise volume and surface areas of right-prisms and cylinders
 Study the effect on volume and surface area when multiplying any dimension
by constant factor k
26
10 – 12 Aug
(3 days)
MEASUREMENT
 Calculate the volume and surface areas of spheres, right pyramids, right.cones
and combination of those objects (figures).
27
15 – 19 Aug
STATISTICS
(a) Revise Measures of central tendency (mean, median, mode) in grouped data.
(b) Measure of central tendency in grouped data (calculation of mean estimate,
identify modal interval)
(c) Range, percentiles, quartiles, interquartile and semi-interquartile range.
(d) Five number summary, Box and Whisker diagrams
28
22 – 26 Aug
STATISTICS
1. Histograms
2. Frequency polygons
3. O gives (cumulative frequency curves)
Sketching and interpretation
29
29 Aug – 02 Sept STATISTICS
Test
4. Variance and standard deviation of ungrouped data
5. Symmetric and skewed data (box and whisker diagram and other methods)
6. Identification of outliers
30
05 – 09 Sept
PROBABILITY
(a) Probability – Definition, and compare with relative frequency
(b) Venn diagrams
1.
Revise the addition rule for mutually exclusive events:
(
)= + ( ),
The complementary rule:
(
)=1− ( ) and
The identity:
P(A or B) = P(A) + P(B) – P(A and B)
5
Week
31
32
33
Date planned/
Datum beplan
12 – 16 Sept
Topics planned for the week/
Onderwerpebeplan vir die week
Resources/ Assessment /
Hulpmiddels Assessering
Date completed/
Datum afgehandel
PROBABILITY
1. Identify dependent and independent events and the product rule for independent
events:
(
)= ( )&times; ( ).
2. The use of Venn diagrams and /or Contingency tables to solve probability
problems, deriving and applying formulae for any three events A, B and C in a
sample space, S.
3. Use tree diagrams for the probability of consecutive or simultaneous events which
are not necessarily independent.
REVISION
End of term test
34
19 – 23 Sept
26 – 30 Sept
01 – 10 Oct
11 – 14 Oct
35
17 – 21Oct
FINANCE
3. Use simple and compound decay formulae:
A = P(1 - in) and
A = P(1- i)n
to solve problems (including straight line depreciation and depreciation on a reducing balance)
. 4. The effect of different periods of compound growth and decay, including nominal and
effective interest rates.
36
37
38
39
40
41
42
43
24 – 28 Oct
31 Oct – 04 Nov
07 – 11 Nov
14 – 18 Nov
21 – 25 Nov
28 Nov – 2 Dec
05 – 09 Dec
12 – 14 Dec
Revision
Revision
FINAL EXAMINATION
FINAL EXAMINATION
FINAL EXAMINATION
FINAL EXAMINATION
Test
HOLIDAYS
FINANCE AND DECAY
1. Use the simple and compound growth formulae to solve problems, including interest, hire
purchase, inflation, population growth and other real life problems.
2. Understand the implication of fluctuating foreign exchange rates (e.g. on petrol price,
imports, exports, oversees travel).
Test
NOTE:

COMPLETE THE DATES UNDER ‘DATES COMPLETED’ PER WEEK AS THE WORK HAS BEEN COMPLETED.
30 Nov 2021
6
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