FORM FOUR
YEARLY PLAN FOR MATHEMATICS
YEAR 2013
WEEK
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TOPIC & OBJECTIVES
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LEARNING OUTCOME
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REMARKS
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1.
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REGISTRATION
& ORIENTATION
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2.
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INTRODUCTION TO MATHEMATICS FORM 4
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TOPIC 1: STANDARD FORM
1.1
Significant
Figures
Understand and use the concept of significant
figure.
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(i).
Round on positive numbers to a given number of significant figures when the
numbers are
a) greater than 1
b) less than 1
(ii)
Perform operations of addition, subtraction, multiplication and division,
involving a few numbers and state the answer in specific significant figures.
(iii) Solve problems involving
significant figures.
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4.
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TOPIC 2: QUADRATIC EXPRESSIONS
AND EQUATIONS
2.1
Quadratic Expressions Understand the concept of quadratic expression
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(i) Identify quadratic
expressions.
(ii) Form quadratic expressions by
multiplying any two linear expressions.
(iii) Form quadratic expressions
based on specific situations.
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2.2 Factorization Of
Quadratic Expressions Factorise quadratic expression.
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(i) Factorise quadratic expressions of
the form
 
(ii) Factorise quadratic expression of
the form
square
(iii) Factorise quadratic expression of
the form
 
(iv) Factorise quadratic expression
containing coefficients with common factors.
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WEEK
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TOPIC & OBJECTIVES
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LEARNING OUTCOME
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REMARKS
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5.
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2.3 Quadratic Equations
Understand the concept of quadratic equation.
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(i) Identify quadratic equation
with one unknown.
(ii) Write quadratic equations
in general form
(iii) Form quadratic equations
based on specific situations.
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2.4 Roots of Quadratic Equations Understand and use the concept of roots of quadratic
equations to solve problems
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(i) Determine whether a given value is
a root of a specific quadratic equation.
(ii) Determine the solutions for
quadratic equations by :
a) trial and error method
b) factorization
(iii)
Solve problems involving quadratic equations.
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6.
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TOPIC 3: SETS
3.1
Sets
Understand the concept of set
To sort given objects into
groups.
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(i) Define sets by
a) description
b) using set notation
(ii)
Identify whether a given object is an element of a set and use the symbol
 or 
(iii)
Represent sets by using Venn diagrams.
(iv)
List the elements and state the numbers of element of a set
(v)
Determine whether a set is an empty set.
(vi)
Determine whether two sets are equal.
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3.2 Subsets, Universal Sets and Complement of a Set
Understand and use the
concept of subset, universal set and the compliment of a set.
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(i) Determine whether a given set is a
subset of a specific set and use the symbol
 or 
(i) Represent subset using the Venn
diagram.
(iii) List the subsets for a specific
sets.
(iv) Illustrate the relationship
between set and universal set using Venn diagram.
(v) Determine the complement of a given
set.
(vi) Determine the relationship between
set, subset, universal set and the complement of a set
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7.
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3.3 Operations on Sets
perform operations on sets.
¨
The
intersection of sets.
¨
The union of
sets.
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(i)
Determine the intersection of
a) two sets
b) Three sets.
and
use the symbol
(ii)
Represent the intersection of sets using Venn diagram.
(iii)
State the relationship between
a) A
B and A
b) A
B and B
(iv)
Determine the complement of the intersection of sets.
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WEEK
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TOPIC & OBJECTIVES
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LEARNING OUTCOME
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REMARKS
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(v)
Solve problems involving the intersections of sets.
(vi)
Determine the union of
a) two sets.
b) three sets.
and
use the symbol
(vii)
Represent the union of sets using Venn diagram
(viii)
State the relationship between
a) A
B and A
b) A
B and B
(ix)
Determine the complement of the union sets.
(x)
Solve problems involving the union of sets.
(xi)
Determine the outcome of combined operations on sets.
(xii) Solve problems involving combined
operation on sets.
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8.
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REVISION
TOPIC 1 - 3
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9
10
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PKBS 1 2012
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11
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(i) Determine whether a given sentence
is a statement.
(ii) Determine whether a given
statement is true or false.
(iii) Construct true or false statement
using given numbers and mathematical symbols.
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(i) Construct statements using the
quantifier:
a) all
b) Some.
(ii) Determine whether a statement that
contains the quantifier “all” is true or false.
(iii) Determine whether a statement can
be generalized to cover all cases by using the quantifier “all”.
(iv) Construct a true statement using
the quantifier “all” or “some”, given an object and a property.
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WEEK
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LEARNING OUTCOME
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REMARKS
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12
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(i) Change the truth value of a
given statement by placing the word “not” into the original statement.
(ii) Identify two statements from
a compound statement that contains the word “and”.
(iii) Form a compound statement by
combining two given statements using the word “and”
(iv) Identify two statement from a
compound statement that contains the word “or”
(v) Form a compound statement by
combining two given statements using the word “or”.
(vi) Determine the truth value of
a compound statement which is the combination of two statements in the word
“and”
(vii) Determine the truth value of
a compound statement which is the combination of two statements with the word
“or”?
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(i) Identify the antecedent and
consequent of an implication “if p, then q”.
(ii) Write two implications from a
compound statement containing “if and only if”
(iii) Construct mathematical statement
in the form of implication
a) if p, then q
b) p if and only if q.
(iv)
Determine the converse of a given implication.
(v)
Determine whether the converse of an implication is true or false.
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13
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(i) Identify the premise and
conclusion of a given simple argument.
(ii) Make a conclusion based on
two given premises for:
a) Argument Form I.
b) Argument Form II
c) Argument Form III
(iii)
Complete an argument given a premise and the conclusion.
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WEEK
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LEARNING OUTCOME
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REMARKS
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14
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(i) Determine whether a conclusion is
made trough
a)
Reasoning by
deduction.
b)
Reasoning by
induction.
(ii)
Make a conclusion for a specific case based on a given general statement by
deduction
(iii)
Make a generalization based on the pattern of a numerical sequence by
induction.
(iv)
Use deduction and induction in problem solving.
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15
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(i) Determine the vertical and
horizontal distances between two given points on a straight line.
(ii) Determine the ratio of vertical
distance to horizontal distance.
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(i) Derive the formula for the gradient
of a straight line.
(ii) Calculate the gradient of a
straight line passing trough two points.
(iii) Determine the relationship
between the value of the gradient and the
a) steepness
b) direction of inclinication of a straight line.
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16
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(i) Ddetermine the x-intercept and the
y-intercept of a straight line.
(ii) Derive the formula for the
gradient of a straight lines in terms o the x-intercept and the y-intercept.
(iii) Perform calculations involving
gradient, x-intercept and y-intercept.
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(i) Draw the graph given an equation of
the form
(ii) Determine whether a given point
lies on a specific straight line.
(iii) Write the equations of the
straight line the gradient and y-intercept.
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(i) Verify that two
parallel lines have the same gradient and vice versa.
(ii) Determine from the
given equations whether two straight lines are parallel.
(iii) Find the equation
of the straight line that passes trough a given point and is parallel to another
straight line.
(iv) Solve problems
involving equations of straight lines.
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WEEK
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LEARNING OUTCOME
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REMARKS
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17
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(i) Complete the class interval for a
set of data given one of the class interval.
(ii) Determine
a)
The upper limit
and lower limit.
b)
The upper
boundary and lower boundary of a class in a grouped data.
(iii)
Calculate the size of a class interval.
(iv)
Determine the class interval, given a set of data and the number of classes.
(v)
Determine a suitable class interval for a given set of data.
(vi)
Construct a frequency table for a given set of data.
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(i) Determine the modal class from
the frequency table of grouped data.
(ii) Calculate the midpoint of a
class.
(iii) Verify the formula for the
mean of grouped data.
(iv) Calculate the mean from the
frequency table f grouped data.
(v) Discuss the effect of the size
of class interval on the accuracy of the mean for a specific set of grouped
data.
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18
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(i) Draw a histogram based on the
frequency table of a grouped data.
(ii) Interpret information from a given
histogram.
(iii) Solve problems involving
histograms.
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(i) Draw the polygon based in :
a) a histogram
b) a frequency table.
(ii)
Interpret information from a given frequency polygon.
(iii)
Solve problems involving frequency polygon.
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19
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(i) Cconstruct the cumulative frequency
table for
a)
ungrouped data
b)
grouped data.
(ii)
Draw the ogive for
a)
ungrouped data.
b)
Grouped data.
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(i) Determine the range of a set of
data.
(ii) Determine
a)
the median
b)
the first
quartile
c)
the third
quartile
d)
the
interquartile range; from the ogive.
(iii)
Interpret information from an ogive.
(iv) Solve problems involving
representations and measures of dispersion.
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WEEK
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LEARNING OUTCOME
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REMARKS
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20
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21
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2012 MID YEAR EXAM. POST MORTEM
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22
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TOPIC 7: PROBABILITY I
7.1 Sample Space Understand the concept of sample space.
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(i) Determine whether an outcome of an
experiment.
(ii) List all outcomes of an experiment
a) from activities.
b) By reasoning.
(iii)
Determine the sample space of an experiment.
(iv)
Write the sample space by using set notations.
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7.2 Events
Understand the concept of events.
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(i) Identify the elements of a sample
space which satisfy given conditions.
(ii) List all the elements of a sample
space which satisfy certain conditions using set notations.
(iii) Determine whether an event is
possible for a sample space.
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23
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7.3 Probability of an Event
Understand and use the
concept of probability of an event to solve problems.
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(i) Find the ratio of the number of
times an event occurs to the number of ‘trials’.
(ii) Find the probability of an event
from a big enough number of ‘trials’.
(iii) Calculate the expected number of
times an event will occur given the probability of the event and number of
trials.
(iv) Solve problems involving
probability
(v) Predict the occurrence f an outcome
and make a decision based on unknown information.
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24
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TOPIC 8: CIRCLES III
8.1 Tangents to a Circle
Understand and use the
concept of tangents to a circle
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(i) Identify tangents to a circle
(ii) Make inference that the tangent to
a circle is a straight line perpendicular to the radius that passes trough
the contact point.
(iii) Construct the tangent to circle
passing through a point
a) on the circumference of the circle.
b) Outside the circle
(iv)
Determine the properties related to two tangents to a circle from a given
point outside the circle.
(v)
Solve problems involving tangents to a circle
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WEEK
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TOPIC & OBJECTIVES
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LEARNING OUTCOME
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REMARKS
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8.2 Angles in Alternate Segments Understand and use the properties of angle between
tangent and chord to solve problems.
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(i) Identify the angle in alternate
segment which is subtended by the chord trough the contact point of the
tangent.
(ii) Verify the relationship between
the angle formed by the chord through the contact point of the tangent.
(iii) Perform calculations involving
the angle in alternate segment.
(iv) Solve problems involving tangent
to a circle and angle in alternate segment.
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25
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8.3 Common Tangents
Understand and use the
concept of common tangents to solve problems.
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(i) Determine the number of common
tangent which can be drawn to two circles which
a) intersect at two points
b) intersect only at one point
c) do not intersect.
(ii)
Determine the properties related to the common tangent to two circles.
a) Intersect at two points.
b) Intersect only at one point.
c) Do not intersect.
(iii) Solve problems involving tangents and common
tangents.
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26
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PKBS 2 2012
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27
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28
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PKBS 2,
2012 – POST MORTEM
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29
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TOPIC 9: TRIGONOMETRY II
9.1 Values of
 To understand and use the concept of the values
of  and to solve problems. |
(i) Identify the quadrants and angles
in the unit circle.
(ii) Determine
a) the value of y-coordinate
b) the value of x-coordinate
c) the ratio of y-coordinate to x-coordinate
of several points on the circumference of the unit
circle.
(iii)
Verify that, for an angle in quadrant I of the unit circle
a) sin
 coordinate
b) cos
 coordinate
c) tan
(ix)
State the relationships between the value of
a)
sine
b)
cosine
c)
tangent
of an angles in quadrant II, III, and IV with their
respective values of the corresponding angle in quadrant I.
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WEEK
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TOPIC & OBJECTIVES
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LEARNING OUTCOME
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REMARKS
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30
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(x)
Find the values of sine, cosine and tangent of the angles between 90o and
360o.
(xi)
Find the angles between 0o and 3600,given the values of
sine, cosine and tangent.
(xii) Solve problems involving sine,
cosine and tangent.
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31
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9.2 Graphs of Sine, Cosine and Tangent Draw and use the graphs of sine, cosine and
tangent.
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(i) Draw the graphs of sine, cosine and
tangent for angles between 0o and 360o
(ii) Compare the graph of sine,cosine
and tangent for angles between 0o and 360o
(iii) Solve problems involving graphs
of sine, cosine and tangent.
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32
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TOPIC 10: ANGLES OF ELEVATION AND DEPRESSION
10.1 Angle of Elevation and Angle of Depression Understand and use the concept of elevation and
angle of depression to solve problems.
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(i) Identify
a) the horizontal line
b) the angle of elevation
c) the angle of depression.
for a particular situation
(ii)
Represent a particular situation involving
a) the angle of elevation
b) the angle of depression; using diagrams.
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33
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(iii)
Solve problems involving the angle of elevation and the angle of depression.
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34
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TOPIC 11: LINES AND PLANES IN
3-DIMENSIONS
11.1 Angles between Lines and Planes Understand and use the concept of angle between
lines and planes to solve problems.
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(i) Identify planes.
(ii) Identify horizontal planes,
vertical planes and inclined planes.
(iii) Sketch a three dimensional shape
and identify the specific planes.
(iv) Identify
a) lines that lies on plane
b) lines that intersect with a plane
(v)
Identify normal to a given plane
(vi)
Determine the orthogonal projection of a line on a plane.
(vii)
Draw and name the orthogonal projection of a line on a plane.
(viii)
Determine the angle between a line on a plane.
(ix)
Solve problems involving the angle between a line and a plane.
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WEEK
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TOPIC & OBJECTIVES
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LEARNING OUTCOME
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REMARKS
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35
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11.2 Angles between Two Planes Understand and use the concept of angle between two
planes to solve problems.
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(i) Identify the line of intersection
between two planes.
(ii) Draw a line on each plane which is
perpendicular to the line of intersection of the two planes ot a point on the
line of intersection.
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36
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(iii) Determine the angle between two
planes on a model and a given diagram
(iv) Solve problems involving lines and
planes in 3-dimensional shapes.
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37
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Revision of Form 4 topics through solving
& discussion of Past Years Questions (2004 – 2011)
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38
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Revision of Form 4 topics through solving
& discussion of Past Years Questions (2004 – 2011)
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39
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Revision of Form 4 topics through solving
& discussion of Past Years Questions (2004 – 2011)
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40
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Year End Examination, 2013
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41
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