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 x^{2} + 6x + 7?

(x+3)^{2} -3^{2} + 7

= (x+3)^{2} -2

Complete the square of 2x^{2} + 8x + 7?

2[x^{2} + 4x + 7/2]

= 2[(x+2)^{2} -2^{2} + 7/2)

= 2[(x+2)^{2} - 1/2]

= 2(x+2)^{2} - 1

How woulkd you complete the square of -x^{2} + 4x + 5

= -1[x^{2} -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?

b^{2} - 4ac

What happens when b^{2} - 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

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?

a^{2} = b^{2} + c^{2} -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

What are some values for the graph y=sinx ?

x = 0, y = 0

x = 90, y = 1

x = 180, y = 0

x = 270, y = -1

x = 360, y = 0

What are some values of y=cosx?

x = 0, y = 1

x = 90, y = 0

x = 180, y = -1

x = 270, y = 0

x = 360, y = 1

What is tanx equal to?

tanx = sinx/cosx

What are some values of y=tanx?

x = 0, y = 0

x = 90, y = ∞

x = 180, y = 0

x = 270, y = ∞

x = 360, y = 0

How do you find the values of sine after getting the principle value?

PV & 180 - PV

Repeat every 360

How do you find the values of cosine after getting the principle value?

PV, 360 - PV

Every 360

How do you find the values of tan after getting the principle value?

PV, PV +/- multiples of 180

What is the equation that links sin^{2}x and cos^{2}x?

sin^{2}x + cos^{2}x = 1