## Maths

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### Equation solving

ES1 Linear equations are equations with one variable which may be solved using transposition skills to make the variable the subject of the equation.

### ES1 Linear equations

Equations with one variable may be solved using transposition skills to make the variable the subject of the equation.

### ES4 Quadratic formula

The solutions to any quadratic equation can be found by substituting the values a, b, c into the quadratic formula.

### ES5 Cubic equations, polynomial long division

One polynomial may be divided by another of lower degree by long division (similar to arithmetic long division).

### ES6 (ILS2.2) Exponential equations

Indicial (or exponential) equations have the form a to the power of x= b If we can write b as a number with a base a and an index, then we can equate the indices to find x. If two equal numbers are...

### FG1 Functions and relations

A relation is a set of ordered pairs.

### FG10 (T8) Graphs of sine and cosine functions

Both the functions y = sin x and y = cos x have a domain of R and a range of [-1,1].

### FG2 Interval notation

Often the domain of a function will be restricted to a subset of R. This subset is called an interval, and the end points are a and b.

### FG3 Inverse notation

If f to the power of -1 times (x) is the inverse function of a one-to-one function f(x) then f to the power of -1 times (x) is the set of ordered pairs obtained by interchanging the first and...

### FG4 Absolute value functions

The absolute value of a number x gives a measure of its size or magnitude regardless of whether it is positive or negative. If a number is plotted on a number line then its absolute value can be...

### FG5 Hybrid functions

Functions which have different rules for each subset of the domain are called hybrid functions. Sometimes they are referred to as piecewise defined functions.

### FG6 (T6) Circular functions

The trigonometric ratios that have been defined in right-angled triangles can be extended to angles greater than 90 degrees

### FG7 Linear graphs

Understanding a linear graph is the simplest way of representing data or a functional relationship. This module explains the equations and visuals of a linear graph.

### FG8 Quadratic graphs

The graph of a quadratic function is called a parabola.

### FG9 Graphs and transformations

The known graphs of some simple functions and relations can be used to sketch related, but more complicated functions.

### Fractions

How do we use fractions? A fraction is the easiest way to express a part of a whole. If you received 18/20 for your test, you got 18 marks correct out of the 20 marks available on the whole test...

### Functions and graphs

Information about functions and graphs to improve your maths skills in these areas

### ILS1.1 Indices

What is index notation? When a number such as 16 is written in the form 42 (which means 4 x 4) we say that it is written as an exponential, or in index notation. There are laws about multiplying and...

### ILS3.1 Simplifying surds

What happens if you want to take the root of larger surds? These may be factorised down to numbers that may or may not be surds.

### IN1 Antidifferentiation

Antidifferentiation (also called integration) is the opposite operation to differentiation. If you have the differentiation of a function, you can then obtain the original function via integration (...