Download Year 9 Extended

Mathematics DPT
Year 7
Unit
Content
Number 1
Decimal system, place value, ordering and rounding
Number2
Decimal numbers, rounding
Shape, Space and
Measures 1
Units, Perimeter and Area
Number 3
Six operations, BIDMAS, directed numbers, co-ordinates
Algebra 1
Algebraic expressions and formulae
Handling Data
Collecting, Organising, Displaying and Analysing Data
Shape, Space and
Measures 2
Angles, Shapes and Construction
Year 8
Unit
Content
Number 1
Integers, fractions, decimals, powers and roots
Number 2
Decimals, Indices and Standard Form
Algebra 1
Expressions and formulae
Handling Data 1
Probability
Shape, Space and
Measures 1
Angles, shapes and constructions
Number 3
Percentages, Ratio and Proportion
Shape, Space and
Measures 2
Symmetry and Transformations
Algebra 2
Equations and inequalities
Shape, Space and
Measures 3
Perimeter, area and volume
Year 9 Extended
Unit
Content
Number 1
Basic number work, rounding and accuracy
Algebra 1
Algebraic manipulation 1
Shape, Space and
Measures 1
Algebra 2
Angles, shapes and constructions
Circle Theorems
Linear equations, inequalities and formulae
Shape, Space and
Measures 2
Number 2
Pythagoras and Trigonometry (right angled triangles)
Handling Data 1
Probability
Algebra 3
Algebraic manipulation 2
Handling Data 2
One variable statistics
Shape, Space and
Measures 3
Perimeter, Area and Volume
Sets of numbers and set theory
Year 9 Core (James´s group)
Unit
Content
Number 1
Basic number work, rounding and accuracy
Algebra 1
Algebraic manipulation 1
Shape, Space and
Measures 1
Angles and shapes
Handling Data 1
Probability
Number 2
Sets of numbers and set theory
Algebra 2
Linear equations, inequalities and formulae
Shape, Space and
Measures 2
Pythagoras and Trigonometry (right angled triangles)
Algebra 3
Straight line graphs
Year 11 Studies
Unit
Content
Number 1
Sets
Approximation
Standard form
Currency conversions
Algebra 1
Arithmetic series
Geometric series
Sets and Logic
Set theory
Logic theory
Probability
Probability
Coordinates in two dimensions
Equation of a straight line
Coordinate geometry
Simultaneous equations
Linear functions
Functions
Domain and range
Plot functions
Quadratic functions
Quadratic equations
Quadratic functions
One variable
statistics
Types of data
Organising data
Displaying data
Cumulative frequency
Measures of central tendency
Year 11 Standard
Unit
Content
Revision
Revision: algebra.
Sets of numbers.
Real numbers.
Surds.
Equation of a straight line.
Functions 1
Functions, function notation, images.
Domain, range, roots, max and min values.
Equations and graphs of a variety of functions
Use of GDC.
Composite functions. Inverse function.
Transformations of functions: translations, stretches, reflections in the
axes.
Functions 2:
Transformations
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The graph of y  f ( x) as the reflection in the line y =x of the graph of y
= f (x) .
Composite transformations.
Use of GDC and Geogebra.
Different forms of the quadratic function:
f ( x)  ax 2  bx  c , f ( x)  a( x  h)2  k ,
f ( x)  a( x   )( x   )
Functions 3:
Quadratic functions
Graphs of quadratic functions. Vertex, axes intercepts, axis of symmetry.
Quadratic equations. The quadratic formula.
The discriminant   b  4ac and the nature of the roots.
Application of quadratic functions.
Other polynomial functions.
2
Functions 4:
Exponential and
logarithmic functions
Laws of exponents; exponential equations. Exponential functions and their
graphs. Horizontal asymptote.
Definition of logarithms. Laws of logarithms. Logarithmic functions and
their graphs. Logarithmic equations. Vertical asymptote.
Relationships between these functions.
a x  e x ln a ; log a a x  x, a loga x  x, x  0
The number e. Natural logarithms.
Change of base.
Applications: Growth and decay problems.
Unit
Content
1
x ,x0
x
The reciprocal function
: its
graph and self-inverse nature.
Functions 5:
Rational functions
x
ax  b
cx  d and its
The rational function
graph.
Vertical and horizontal asymptotes.
Informal idea of limits. Limit notation.
Polynomial and rational functions
f ( x)  lim(
Calculus 1
f ( x  h)  f ( x )
)
h
h 0
Definition of derivative as
Derivative interpreted as a gradient function and as a rate of change.
Tangent and normal lines.
The second derivative. Higher derivatives.
Maximum and minimum points. Points of inflexion.
f , f , f  . Optimization.
Graphical behaviour of
Applications to kinematics.
Function analysis
Differentiation rules
The circle: radian measure of angles.
Length of an arc; area of a sector.
The unit circle. Definition of sine and cosine in the unit circle. Definition of
sin x
2
2
tangent as cos x . The Pythagorean identity sin   cos   1 .
0,
Trigonometry 1
Exact values of the trigonometric ratios
multiples.
   
, , ,
6 4 3 2 and their
Simple trigonometric equations with an without calculator i.e sin x  0.6 ;
cos x  
2
2 in the interval 0, 2  .
Trigonometric functions: their domains and ranges; amplitude, their
periodic nature. Their graphs.
Transformations of trigonometric functions.
Unit
Content
Statistics 1:
Bivariate data
Linear correlation of bivariate data.
Pearson’s product–moment correlation
coefficient, r.
Scatter diagrams; lines of best fit.
Equation of the regression line of y on x.
Use of the equation for prediction purposes. Interpolation, extrapolation.
Mathematical and contextual interpretation.
Year 11 Higher
Unit
Content
Algebra Revision
 Expansion of brackets.
 Simultaneous equations.
 Radical equations and extraneus solutions.
Algebra of linear and
quadratic expressions
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The real number line and corresponding interval notation.
Linear inequalities, including their graphical representation.
Number systems, rational and irrational numbers.
Surds as one subset of irrational numbers.
The definition of the absolute value of a number.
Equations with absolute value.
Absolute value inequalities.
Quadratic equation.
Quadratic formula and the discriminant.
Completing the square.
Quadratic function.
Sketching the graph of a quadratic function.
Quadratic inequalities.
Simultaneous equations involving linear and quadratic equations.
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Definition of polynomial functions.
Synthetic division.
The remainder and the factor theorems.
Polynomial inequations.
Sketching polynomials and graphical significance of roots: unique single
factors, repeated squared factors, repeated cubed factors.
Algebra of polynomials
Binomial theorem
 The binomial theorem.
 Pascal´s triangle to find the coefficients.
 The general term.
 Combinatorial numbers.
Sequences and Series
 Arithmetic and geometric sequences.
 Sum of finite and infinite geometric series.
 Compound interest and superannuation.
Exponential and
logarithmic functions
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Revision of indices.
Exponents and logarithms.
Logarithmic function and its inverse.
Laws of exponents.
Laws of logarithms.
Change of base.
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Concept of domain, range, image value.
Identification of horizontal, vertical and oblique asymptotes.
Composite functions and inverse functions.
Domain restriction.
The graph of a function.
The quadratic function in its three forms, in standard form, vertex form
and x-intercepts form.
Solution of f(x)=g(x) graphically and analytically.
Solution of f(x)=0 to a given accuracy.
The circle as an example of a many to many relation.
Equation of the circle and mid-point.
Functions and Relations
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Transformations of
graphs
 Transformations of standard functions, absolute value function,
reciprocal, polynomial, etc.
 Horizontal and vertical translation.
 Dilation parallel to the x- and y- axis.
 Reflections in coordinate axes and the graph of the inverse function as
the reflection in the line y=x.
 The reciprocal of a function.
Mathematical Induction
 Proof by mathematical induction.
 Forming conjectures to be proved by mathematical induction.
Circular trigonometric
functions
 The circle: radian measure of angles, length of an arc, and area of a
sector.
 Definition of (cos x, sin x) in terms of the unit circle.
 The six circular functions: sin x, cos x, tan x, csc x, sec x, cot x; their
domains, ranges, periodic nature graphs.
The Algebra of Complex
Numbers
 Introduction to complex numbers and notation.
 The real imaginary part of a complex number in the form z=a + bi.
 Operations of complex numbers.
 Geometrical representation of complex numbers: the modulus of z and
the Polar form of complex numbers z = (cosα + isinα).
 De Moivre's theorem, proof by mathematical induction.
 Polynomials over the complex field.
 nth roots of unity.
 Vectors as displacements in the plane and in three dimensions.
 components of a vector.
 Column representation.
Vectors
 The sum of vectors, the zero vectors, the inverse vector.
 Multiplication by a scalar.
 Magnitude of a vector.
 Position vector
 Unit vectors i, j, k.