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Topic Sub Topics Learning Objectives Week
Term I 16
Sets and Venn Diagrams
• Introduction to set notation
• Venn diagrams, universal set and
compliment of a set.
• Intersection of two sets
• Combining universal set,
compliment of a set, subset,
intersection and union of a sets
• Application of Venn Diagrams in
problem sums
• Formulas in set theory
• use language, notation and Venn diagrams to describe sets
• define and identify an empty set, a universal set,
equal sets, disjoint sets and complement of a set and to give
Examples of the sets
• define and distinguish subsets and proper subsets of
a given set
• define the intersection and union of sets and the
relationships between sets by using Venn diagrams
• use Venn diagrams to solve problems
• represent relationships between sets
• definition of sets:
e.g.
A = {x : x is a natural number}
B = {(x, y): y = mx + c}
C = {x : a ≤ x ≤ b}
D = {a, b, c…}
4
Subject Name: Mathematics 4024
Syllabus Break up Class O2
(First Term)
The Quaid-e-Azam Group of Schools & Colleges
O Level Campus Mardan
Topic Sub Topics Learning Objectives Week
Further Trigonometry and bearing
Sine and cosine of obtuse angles
• Area of triangle
• Sine Rule
• Cosine Rule
• Bearing
• Three dimensional problems
• extend sine and cosine functions to angles between 90°
and 180°
• solve problems using the sine and cosine rules for any
triangle and the formula
area of a triangle = ½ ab sin C
[angles will be quoted in, and answers required in, degrees
and decimals of a degree to one decimal place]
• interpret and use three figure bearings
•measure clockwise from the north, i.e 000ᵒ - 360ᵒ
e.g. Find the bearing of A from B if the bearing of B from A is
125ᵒ
• solve simple trigonometric problems in three dimensions
(calculations of the angle between two planes or of the
angle between a straight line and plane will not be required)
4
Function and Notation
• Relations and Functions
• Functions involving higher order
expressions
• Inverse functions
• use function notation to describe simple functions.
•find inverse functions
1
Topic Sub Topics Learning Objectives Week
Graphs of functions
• Graphs of quadratic functions.
• Graph of cubic functions,
reciprocal and exponential
functions,
• Gradient of a curve.
• construct tables of values and draw graphs for functions
of the form y = axn, where a is a rational constant
and n= −2,−1, 0, 1, 2, 3 and simple sums of not
more than three of these and for functions of the form kax.
•draw graphs for
given functions and use them to solverelated equations
graphically
• interpret the graphs of the given functions
• use graphs to estimate the unknown value(s) of x for a
given value of y and vice versa
• solve associated equations approximately by graphical
methods
• estimate gradients of curves by drawing tangents
• sketch graphs of quadratic functions
4
Personal and Household Finance(all
concepts) (revision)
2
Algebraic Manipulation(revision)
1
Topic Sub Topics Learning Objectives Week
Term II 11
Properties of circles
• Symmetric properties of circles.
• Angle properties
• use the following symmetry properties of circles:
a) equal chords are equidistant from the centre b)
the perpendicular bisector of a chord passes through the
centre
c) tangents from an external point are equal in length
•angle properties of circles
a) angle in a semicircle
b) angle between tangent and radius of a circle
c) angle at the centre of a circle is twice the angle at the
circumference
d) angles in the same segment are equal
e) angles in opposite segments are supplementary
3
Matrices
• Introduction to Matrices
• Addition and subtraction of
Matrices
• Matrix multiplication
• Determinant of a Matrix
• Inverse of a Matrrix
• Application of Matrices
• display information in the form of a matrix of any order
• solve problems involving the calculation of the sum and
product (where appropriate) of two matrices and interpret
the results
• calculate the product of a matrix and a scalar quantity
• use the algebra of 2 × 2 matrices including the zero
and identity 2 × 2 matrices
• calculate the determinant l A l and inverse of a non-
singular matrix A
2
Topic Sub Topics Learning Objectives Week
Kinematics Application of Graphs in real world.
• interpret and use graphs in practical situations including
travel graphs and conversion graphs
• draw graphs from the given data
• apply the idea of rate of change to easy kinematics
involving distance-time and speed-time graphs, acceleration
and deceleration
• Calculate distance travelled as area under a linear speed-
time graph.
• use tangents to calculate the speed and acceleration from
the non-linear distance-time and speed-time graphs
• interpret the distance-time graphs and speed-time graphs
3
Revision 3

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O2 Math.pdf

  • 1. Topic Sub Topics Learning Objectives Week Term I 16 Sets and Venn Diagrams • Introduction to set notation • Venn diagrams, universal set and compliment of a set. • Intersection of two sets • Combining universal set, compliment of a set, subset, intersection and union of a sets • Application of Venn Diagrams in problem sums • Formulas in set theory • use language, notation and Venn diagrams to describe sets • define and identify an empty set, a universal set, equal sets, disjoint sets and complement of a set and to give Examples of the sets • define and distinguish subsets and proper subsets of a given set • define the intersection and union of sets and the relationships between sets by using Venn diagrams • use Venn diagrams to solve problems • represent relationships between sets • definition of sets: e.g. A = {x : x is a natural number} B = {(x, y): y = mx + c} C = {x : a ≤ x ≤ b} D = {a, b, c…} 4 Subject Name: Mathematics 4024 Syllabus Break up Class O2 (First Term) The Quaid-e-Azam Group of Schools & Colleges O Level Campus Mardan
  • 2. Topic Sub Topics Learning Objectives Week Further Trigonometry and bearing Sine and cosine of obtuse angles • Area of triangle • Sine Rule • Cosine Rule • Bearing • Three dimensional problems • extend sine and cosine functions to angles between 90° and 180° • solve problems using the sine and cosine rules for any triangle and the formula area of a triangle = ½ ab sin C [angles will be quoted in, and answers required in, degrees and decimals of a degree to one decimal place] • interpret and use three figure bearings •measure clockwise from the north, i.e 000ᵒ - 360ᵒ e.g. Find the bearing of A from B if the bearing of B from A is 125ᵒ • solve simple trigonometric problems in three dimensions (calculations of the angle between two planes or of the angle between a straight line and plane will not be required) 4 Function and Notation • Relations and Functions • Functions involving higher order expressions • Inverse functions • use function notation to describe simple functions. •find inverse functions 1
  • 3. Topic Sub Topics Learning Objectives Week Graphs of functions • Graphs of quadratic functions. • Graph of cubic functions, reciprocal and exponential functions, • Gradient of a curve. • construct tables of values and draw graphs for functions of the form y = axn, where a is a rational constant and n= −2,−1, 0, 1, 2, 3 and simple sums of not more than three of these and for functions of the form kax. •draw graphs for given functions and use them to solverelated equations graphically • interpret the graphs of the given functions • use graphs to estimate the unknown value(s) of x for a given value of y and vice versa • solve associated equations approximately by graphical methods • estimate gradients of curves by drawing tangents • sketch graphs of quadratic functions 4 Personal and Household Finance(all concepts) (revision) 2 Algebraic Manipulation(revision) 1
  • 4. Topic Sub Topics Learning Objectives Week Term II 11 Properties of circles • Symmetric properties of circles. • Angle properties • use the following symmetry properties of circles: a) equal chords are equidistant from the centre b) the perpendicular bisector of a chord passes through the centre c) tangents from an external point are equal in length •angle properties of circles a) angle in a semicircle b) angle between tangent and radius of a circle c) angle at the centre of a circle is twice the angle at the circumference d) angles in the same segment are equal e) angles in opposite segments are supplementary 3 Matrices • Introduction to Matrices • Addition and subtraction of Matrices • Matrix multiplication • Determinant of a Matrix • Inverse of a Matrrix • Application of Matrices • display information in the form of a matrix of any order • solve problems involving the calculation of the sum and product (where appropriate) of two matrices and interpret the results • calculate the product of a matrix and a scalar quantity • use the algebra of 2 × 2 matrices including the zero and identity 2 × 2 matrices • calculate the determinant l A l and inverse of a non- singular matrix A 2
  • 5. Topic Sub Topics Learning Objectives Week Kinematics Application of Graphs in real world. • interpret and use graphs in practical situations including travel graphs and conversion graphs • draw graphs from the given data • apply the idea of rate of change to easy kinematics involving distance-time and speed-time graphs, acceleration and deceleration • Calculate distance travelled as area under a linear speed- time graph. • use tangents to calculate the speed and acceleration from the non-linear distance-time and speed-time graphs • interpret the distance-time graphs and speed-time graphs 3 Revision 3