Mathematics Grade 7

About Course

Course Content

Equations, expressions, identities and inequalities
gain further understanding for manipulating quadratic expressions and solving quadratic equations

complete the square for a quadratic function

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discriminant of a quadratic polynomial

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identities and equations

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solve equations

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equation of a graph (quadratic and cubic)

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solve quadratic inequalities

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Graphs and Functions
understand the concept of function and use function notation

Coordinate Geometry
Gain further understanding for solving problems involving coordinate geometry

Algebra
Gain further understanding for manipulating algebraic expressions and solving absolute value equations and inequalities

Sequences and Series
Gain further understanding of sequences and series

Logarithmic and Exponential functions
understand the connection between logarithm and indices and solve problems involving logarithm and exponential function

Circular Measures
understand the relationship between radians and degrees and solve problems involving arc length and sector area.

Vectors in 3-Dimensions
understand and use vectors in three dimensions.

Trigonometry 1
Understand and use trigonometric ratios and their identities

Trigonometry 2
Gain further understanding for the use of trigonometric ratios and their identities.

Differentiation 1
Know how to find a derivative of a function and use derivatives to solve problems

Differentiation 2
Acquire further understanding for finding the derivative of a function

Integration 1
Know how to integrate derivatives to find their functions and use integration to solve geometric problems Know how to use integration to determine areas and volumes and solve problems involving easy kinematics

Integration 2
Extend their knowledge for integrating derivatives

Numerical solutions of equations
Understand alternative methods for locating roots of equations and use iterative formula

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About Course

Course Content

Equations, expressions, identities and inequalities gain further understanding for manipulating quadratic expressions and solving quadratic equations

complete the square for a quadratic function

discriminant of a quadratic polynomial

identities and equations

solve equations

equation of a graph (quadratic and cubic)

solve quadratic inequalities

Graphs and Functions understand the concept of function and use function notation

Types of function

Domain and the Range

The one-one, and its inverse function

composite functions

sketch graphs of functions and their inverses

Coordinate Geometry Gain further understanding for solving problems involving coordinate geometry

Graph and algebraic equation

Intersection of graphs

Tangent to a curve and Repeated root of an equation

Algebra Gain further understanding for manipulating algebraic expressions and solving absolute value equations and inequalities

Algebraic notation , solving equations and inequalities

Interpret and sketch the graphs of the functions

A polynomial

The remainder and factor theorems to polynomials

Sequences and Series Gain further understanding of sequences and series

Expansion

Arithmetic and Geometric progressions

The sum of arithmetic or geometric progressions

The Sigma notation

The sum to infinity

Logarithmic and Exponential functions understand the connection between logarithm and indices and solve problems involving logarithm and exponential function

Logarithms and Indices

Definition and properties of ex and lnx

Use logarithms to solve equations of the form ax = b

Use logarithms to solve equations of the form ax = b

The gradient and/or intercept

Circular Measures understand the relationship between radians and degrees and solve problems involving arc length and sector area.

Dgrees and Radians

Arc length and Sector area

Vectors in 3-Dimensions understand and use vectors in three dimensions.

Three dimensions and standard notations for vectors.

Addition and Subtraction of vectors

Multiplication of a vector by a scalar

Unit vectors, Displacement vectors and Position vectors

Magnitude of a vector and the scalar product of two vectors

The angle between two directions

Trigonometry 1 Understand and use trigonometric ratios and their identities

Sketch and use graphs of the sine, cosine and tangent functions

The amplitude and period

Sketch graphs of the form y = asin(bx) + c, y = a cos(bx) + c, and y = a tan(bx) + c

use the exact values of the sine, cosine and tangent of 30°, 45°, 60°, and related angles

The inverse trigonometric

The trigonometric identities

Degrees or Radians and within a specified interval.

Trigonometry 2 Gain further understanding for the use of trigonometric ratios and their identities.

The secant, cosecant and cotangent functions

Further trigonometrical identities

Differentiation 1 Know how to find a derivative of a function and use derivatives to solve problems

Interpret the idea of the gradient of a curve, and use the notations

Derivative of xn

Composite functions using the chain rule

stationary points, and maximum and minimum points and points of inflexion

Differentiation 2 Acquire further understanding for finding the derivative of a function

Use the derivatives of ex, lnx, sinx, cosx, tanx

Differentiate products and quotients

First derivative of Parametrically or Implicitly functions

Integration 1 Know how to integrate derivatives to find their functions and use integration to solve geometric problems Know how to use integration to determine areas and volumes and solve problems involving easy kinematics

Interpret integration

Solve problems involving the evaluation of a constant of integration

Evaluate definite integrals

the area of a region bounded by a curve and a line, or between two curves – a volume of revolution about one of the axes – displacement, velocity and acceleration

Integration 2 Extend their knowledge for integrating derivatives

further the idea of „reverse differentiation

Trigonometrical relationships – Double-angle formulae

The trapezium rule to estimate the value of a definite integral

Use trapezium rule to give an over-estimate or under-estimate

Numerical solutions of equations Understand alternative methods for locating roots of equations and use iterative formula

A root of an equation,

Interpret the idea of a sequence of approximations

simple iterative formula of the form xn + 1 = F(xn)

Equations, expressions, identities and inequalities
gain further understanding for manipulating quadratic expressions and solving quadratic equations

Graphs and Functions
understand the concept of function and use function notation

Coordinate Geometry
Gain further understanding for solving problems involving coordinate geometry

Algebra
Gain further understanding for manipulating algebraic expressions and solving absolute value equations and inequalities

Sequences and Series
Gain further understanding of sequences and series

Logarithmic and Exponential functions
understand the connection between logarithm and indices and solve problems involving logarithm and exponential function

Circular Measures
understand the relationship between radians and degrees and solve problems involving arc length and sector area.

Vectors in 3-Dimensions
understand and use vectors in three dimensions.

Trigonometry 1
Understand and use trigonometric ratios and their identities

Trigonometry 2
Gain further understanding for the use of trigonometric ratios and their identities.

Differentiation 1
Know how to find a derivative of a function and use derivatives to solve problems

Differentiation 2
Acquire further understanding for finding the derivative of a function

Integration 1
Know how to integrate derivatives to find their functions and use integration to solve geometric problems Know how to use integration to determine areas and volumes and solve problems involving easy kinematics

Integration 2
Extend their knowledge for integrating derivatives

Numerical solutions of equations
Understand alternative methods for locating roots of equations and use iterative formula