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
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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.
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