Core 1 Maths Revision

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

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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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The factorised form of a quadratic gives the x intercepts.
The completed square form gives the minimum point.
The quadratic equation form gives the y intercept.
Coordinate geometry in the x, y plane.
The general form of a straight line is y = mx +c. For this equation "c" is the intercept of the y
axis and "m" is the gradient.
The gradient of a straight line is: the change in y divided by the change in x.…read more

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