AS Flashcards
What are the indices rules?

When should you complete the square?
When a quadratic equation will not factorise easily
How do you complete the square? (using x2 +yx + c)
Write in the form (x + y/2)2 -(y/2)2 + c
Complete the square of x2 + 6x + 7?
(x+3)2 -32 + 7
= (x+3)2 -2
Complete the square of 2x2 + 8x + 7?
2[x2 + 4x + 7/2]
= 2[(x+2)2 -22 + 7/2)
= 2[(x+2)2 - 1/2]
= 2(x+2)2 - 1
How woulkd you complete the square of -x2 + 4x + 5
= -1[x2 -4x -5]
Then complete as normal to get
-1(x-2)2 + 9
What is the quadratic formula?

What is the discriminant of the quadratic formula?
b2 - 4ac
What happens when b2 - 4ac > 0 ?
There are two real distinct roots
What happens when b2 - 4ac = 0 ?
There is one real root (repeated)
What happens when b2 - 4ac < 0 ?
No real roots
What are the inequality symbols?
Same for not equal to but circle not shaded in

How can you tell the line of symetry from completing the square?
(x + y)2 + c
Curve is left by y and up by c
What is a transformation of y = f(x-a)?
Transformation of the graph by (x+a,y)
What is the transformation of y = f(a) + b?
Graph is transformed by (x,y+b)
What is the transformation of y = af(x)?
Graph is strechted by scale factor a (parallel to y-axis)
(x,ay)
What is the transformation of y = f(ax)?
Transformation of graph by 1/a parallel to x axis
((1/a) x, y)
What is the transformation of y = -f(x)
Reflection of graph in x-axis
(x, -y)
What is teh transformation of y = f(-x)?
Reflection of graph in y-axis
(-x, y)
What order should be done with 2f(x+1)?
Stretch then translate
What is the sine rule?
a/sinA = b/sinB = c/sinC
sinA/a = sinB/b = sinC/c
What is the cosine rule?
a2 = b2 + c2 -2bc x cosA
What is the area of a non-right angle triangle ?
Area = 1/2 x base x height
Area = 1/2 x a x b x sinC
What is the lowercase and uppercase letters in triangles?
Lowercase - side
Uppercase - Angle