# Core 1 Maths Revision

This is a general overview of the key points of the core 1 syllabus.

- Created by: Billy Radford
- Created on: 23-05-10 13:30

First 357 words of the document:

Core 1 Maths Revision.

Indices.

A to the power of x times a to the power of y is equal to a to the power of (x+y).

A to the power of half is equal to the square root of A.

A to the power of 0 is equal to 1.

A to the power of minus 1 is equal to (1 over a to the power of one).

Square root of 4 times square root of 3 equals square root of 12 or 2 root 3.

Discriminate.

The discriminate is b squared 4ac.

If the discriminate is less than 0 there are no real roots.

If the discriminante is more than 0 then there are two real roots.

If the discriminate equals 0 there are equal roots.

What is the quadratic formula?

The quadratic formula is minus b plus or minus the discriminate divided by 2 times a.

Equations and inequalities.

There are 2 methods of solving simultaneous equations: substitution and elimination.

When you multiply or divide an inequality by a negative number, you need to change the

inequality sign to its opposite.

Sketching curves.

Transformations of graphs:

If the change to the equation is inside the bracket it affects the x coordinates in the opposite

way to what you would expect. If it is outside the bracket then the transformation of the

graph is to the y coordinates and as you would expect.

F(x + a) is a translation of a in the x direction.

F(x) + a is a translation of +a in the y direction..

F (ax) is a stretch of 1 divided by a in the x direction (multiply x coordinates by 1 divided

by a).

af (x) is a stretch of a in the y direction ( multiply y coordinates by a).

Quadratic graphs

The general equation for a quadratic graph is a times x squared plus b times x plus c.

For the general equation c is the y intercept.

If the a times x squared is negative then the parabola is upside down.

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