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Flashcards in C1 Deck (12)
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Rules of Indices


Surd Rules


Rationalising Surds 1


Rationalising Surds 2


Difference of two squares


General form of a quadratic equation

y = ax2 + bx + c


a, b and c are constants

a cannot equal zero


Completing the Square Example




Remember to factor out any coefficient on the a

Remember to half the coefficient of b

Remember to minus any other bits



Quadratic Formula

 ax2 + bx + c = 0 can be solved with the quadratic formula




Sketching Quadratic Graphs

If a>0 = smiley shaped curve

if a<0 = unhappy shaped curve

put y=0 to find the x-axis crossing points

put x=0 to find the y-axis crossing points

The discriminant:

equal roots: b=4ac (equals x axis points)

real roots: b2>4ac (crosses x axis points)

no real roots: b2<4ac (doesn't cross x axis)



Simultaneous Equations

Both elimination and substitution for linear equations

Use substitution for one linear and one quadratic


How to solve a quadratic inequality

Solve the corresponding quadratic equation

Sketch the graph of the quadratic function

Use the sketch to find the required set of values

ie, if equation > 0 look above x axis (separate inequalities)

if equation < 0 look below x axis (joined inequalities)


If question has another equation, sketch both on a graph and then calculate the set of values for x which satisfy the inequalities


What should be done when multiplying or dividing an inequality by a negative number?

The inequality sign should be flipped