C1 Basic Algebra Summary

advertisement
C1 – Basic Algebra Summary
 Properties of surds:
a  b = ab
a
b

 Properties of surds:
a b



a  b = ab
a c  b c  ( a  b) c
a
b
a
b
 To rationalise the denominator, in general
1
C1 – Basic Algebra Summary
1
, multiply its numerator and its denominator by a  b
a b

Expressing a quadratic in the form y  ( x  p)  q is called completing
the square.
In summary,
Halve the coefficient of x to obtain p.
Subtract the square of the constant to obtain q.

2
2

2

Nb/ take care when the coefficient of x is not 1.
Quadratic Formula

 b  b  4ac
2a
D  b 2  4ac is called the discriminant of the quadratic equation.


a
b
 To rationalise the denominator, in general
General form of a quadratic y  ax  bx  c , with a  0 .
When a > 0 the graph of y is  shaped and y has a minimum value.
When a < 0 the graph of y is  shaped and y has a maximum value.
Quadratic factors used to give information about the graph and to solve the
equation.
x

a c  b c  ( a  b) c
General form of a quadratic y  ax  bx  c , with a  0 .
When a > 0 the graph of y is  shaped and y has a minimum value.
When a < 0 the graph of y is  shaped and y has a maximum value.
Quadratic factors used to give information about the graph and to solve the
equation.
2
Expressing a quadratic in the form y  ( x  p)  q is called completing
the square.
In summary,
Halve the coefficient of x to obtain p.
Subtract the square of the constant to obtain q.
2
2

Nb/ take care when the coefficient of x is not 1.
Quadratic Formula

 b  b 2  4ac
2a
D  b 2  4ac is called the discriminant of the quadratic equation.
2
When D > 0, the equation has two distinct real roots.
When D < 0, the equation has no real roots.
When D = 0, the equation has one repeated root.
To solve a quadratic inequality you should sketch a graph of the quadratic
function involved.
Simultaneous Equations, one linear and one quadratic. Substitute the
linear equation into the quadratic equation.
, multiply its numerator and its denominator by a  b
x


When D > 0, the equation has two distinct real roots.
When D < 0, the equation has no real roots.
When D = 0, the equation has one repeated root.
To solve a quadratic inequality you should sketch a graph of the quadratic
function involved.
Simultaneous Equations, one linear and one quadratic. Substitute the
linear equation into the quadratic equation.
Download
Related flashcards

Abstract algebra

19 cards

Category theory

14 cards

Abstract algebra

18 cards

Algebra

23 cards

Create Flashcards