√a x √b

=√ab

√a/b

=√a/√b

√ab/√b

=√a

ax^2+bx+c=f(x)
what happens when you:
increase b? decrease b?
increase a? decrease a?

increase b = translates up the y axis
decrease b = translates down the y axis
increase a = translates left
decrease a = translates right

ax^2+bx+c=f(x)
what shape is the graph is the quadratic is:
positive?
negative?

positive: the graph will make a 'u' shape
negative: the graph will make an 'n' shape

If you use (x1+x2)/2 to find the x value of the root, how do you find the y value?

Substitute the x value into the 'y=' equation of the quadratic

To complete the square, what does ax^2+bx+c turn into?

(xd)^2e

Where does (x+2)^2+2 translate to on a graph?

(x+2) = translates left (along x axis) by 2
+2 = translates up the y axis by 2

What is the quadratic formula?

86aa4bfc477e4e90b30ee09123bf9077.jpg (image/jpg)

What part of the quadratic equation is the discriminant and what does the discriminant mean in terms of roots?

b^24ac
b^24ac<0 = no relevant roots
b^24ac=0 = two repeated roots
b^24ac>0 = two distinct roots

What are the three ways of solving a quadratic?

1. factorising (always try first)
2. quadratic equation (if doesn't factorise or 'b' isn't even)
3. complete the square (only use if 'b' is even)

What is the factor theorem?

f(7)=0 ∴ (x7) is a factor of f(x)
f(a)=0 ∴ (xa) is a factor of f(x)

What is the equation of a circle?

(xa)^2+(xb)^2=r^2

How do you work out the distance between two points?

Pythagoras' theorem

What equation do you use to find the midpoint of a line?

e57a2191ae1648f0adc981ad21e625ae.png (image/png)

What do you use to find the equation of a line?

y  y1 = m (x  x1)

What is the difference between a perpendicular and parallel line?

Perpendicular: have gradients that are opposite signed (+/) and reciprocals
Parallel: have the same gradients but different y intercepts

What circle theorem is this?
bf0940b15604471488fe390ef2d98d35.gif (image/gif)

Angles in a semi circle: angle on the arch is always a right angle (perpendicular lines)

What circle theorem is this?
d2105c2d91a24d7db1f0afce631872c8.gif (image/gif)

Any chord, perpendicular line is drawn through center of circle, will bisect the chord

What circle theorem is this?
930a69095bb04744bba436e7cb5b31b1.png (image/png)

From any point outside the circle, there is exactly two tangents. The radius to the tangent is perpendicular.

What is this line?
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Tangent (Has one repeated root)

What is this line?
4cccf716d6f44607b4a014872fdefabb.png (image/png)

Secant (two distinct roots)

What is a scew line?

A line that has no real roots/intersections with a circle

What does dy/dx equal?

The gradient

What is:
f(x)
f'(x)
f''(x)

f(x) = before differentiation
f'(x) = first derivative
f''(x) = second derivative

What is
d^2y/dx^2 > 0

Minimum

What is
d^2y/dx^2 < 0

maximum

If f(x) represents displacement, what does f'(x) and f''(x) represent?

f'(x) represents velocity
f''(x) represents acceleration

What is an 'increasing function'?

An increasing function is a function f(x) such that f'(x) > 0 for all values of x>
(a function that is always increasing)

What is a 'decreasing function'?

A decreasing function is a function f(x) such that f'(x) < 0 for all values of x
(A function that is always decreasing)

Describe the graph transformations taking place from:
f(x) = x^2
=2x^2
=2(x)^2

x^2 = original formulae
2x^2 = stretched in y direction by scale factor of 2
2(x)^2 = stretched in x axis by scale factor of 0.5

What is the difference in transformations if the number is inside or outside the bracket?

inside the bracket : x direction
outside the bracket : y direction

What does xn = a + d(n1) calculate?

Any number in a sequence (arithmetic)

What is a
Sigma?

The big E symbol. It means 'sum up'

What does this mean?
S = (n/2) × (2a + (n1)d)

It calculates the sum of the first 'n' terms of an arithmetic series

What does xn = ar(n1) calculate?

Any term in a geometric progression

What is the sine rule?

8fd535ebd64b4b9c9ca82af4b992845d.png (image/png)

What is the cosine rule?

4984d5d711b04a50b802c1a309d48b52.jpg (image/jpg)

How do you find the area of a triangle?

0.5(base x height)
OR
0.5absinC

How do you work out the area of a sector?

DEGREES: (θ/360) x πr^2
RADIANS: θr^2/2

How do you work arc length?

DEGREES: (θ/360) x 2πr
RADIANS: rθ

What does a tan graph look like?

f55228a7edb24468a277594881549de8.gif (image/gif)

What does a cos graph look like?

8b18fe38df2f45c09d8519c83b6bbf9b.png (image/png)

What does a sin graph look like?

626b0d26ad20453d9ed5216582c177dc.png (image/png)

What does a CAST diagram look like?
(DEGREES)

a1b4002c431144408ba8a468fcd8da86.jpg (image/jpg)

What are the trig identities?

63ebc9966a654d4e8b5504ef513caaf4.jpg (image/jpg)

What are the log rules?

0084e4c67a0f40db9a8b6eface639e02.png (image/png)

How do you find the area of a trapezium?

A = 0.5(a+b)h

What is the trapezium rule?

5c32e51a9b0d48558dc3e44cc56fef1a.jpg (image/jpg)
