 ## 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.

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.

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 (...