Algebraic Functions and Graphs

New Topic: MiA Higher Ch2.2 Algebraic Functions and Graphs, pp30-44

By the end of this topic you will be able to:

• complete the square for quadratic functions

• recognise the probable form of a function from its graph

• draw graphs of related functions given f(x), f(x) being a simple polynomial or trigonometric function

• know the general features of the graphs of y=ax and y=logax

Homework: Algebraic Functions Set1

Due: Thursday 25th September

Composite & Inverse Functions

By the end of this topic you will:

• know domain, range, inverse, composite functions
• be able to find f(g(x)) given f(x) and g(x)

Homework: Composite and Inverse Functions Set1

Due: Thursday 11th September

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Higher Maths 2014 Solutions

Higher 2014 Paper 1 Solutions

Higher 2014 Paper 2 Solutions

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The Exponential & Logarithmic Function

New Topic: The Exponential and Logarithmic Functions

By the end of this topic you will be able to:
• recall and use the laws of logarithms
• solve simple exponential and logarithmic equations
• model mathematically situations involving the logarithmic or exponential function

Homework: Logs and Exponentials Set1

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Vectors

New Topic: Vectors, MiA Unit 3 Ch1

By the end of this topic you will be able to:

• know meaning of terms; vector (column, position, unit), scalar, magnitude, directed line segment, component

• add and subtract vectors and multiply a vector by a scalar

• determine the distance between two points in three dimensions

• determine and solve problems relating to parallel, perpendicular and collinear lines

• use and apply the scalar product

Homework: Vectors Set1

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The Circle

New Topic: The Circle, MiA Unit 2 Ch4

By the end of this topic you will:

• know that the equation of the circle centre (a,b) and radius r is (x – a)² + (y – b)² = r²

• know that x² + y² + 2gx + 2fy + c = 0 represents a circle centre (–g, –f) and
radius r = √(g² + f² – c), provided g² + f² – c > 0

• be able to determine the equation of a circle

• be able to solve problems with the intersection of a line and a circle,
and a tangent to a circle

• be able to determine whether two circles touch each other

Homework: Circles Set1

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Integration

New Topic: Integration, MiA Unit 2 Ch2

By the end of this topic you will be able to:

• know meaning of terms; integral, integrate, constant of integration,

definite integral, limits of integration, indefinite integral, area under curve

• calculate indefinite integrals

• evaluate definite integrals

• determine area between curve y = f(x), x-axis and lines x = a and x = b

• determine area bounded between two curves

• solve differential equations

Homework: