pure Flashcards
discriminant is less than 0
no real solutions
discriminant is more than 0
two distinct solutions
discriminant is equal 0
one repeated solution
indices laws
am × an = am + n
am / an = am – n
a0 = 1 (where a ≠ 0)
(am)n = am × n
(a × b)m = am × bm
(a / b)m = am / bm
a-n = 1 / an
√a = a1/2
Surd Laws
√a x √b = √ab
√a / √b = √(a/b)
Rational number
Any number that can be expressed as a/b where a and b are integers
Ways to solve quadratic
- factorising
- quadratic formula
- completing the square
- calculator
Tip for psuedo quadratics
Check for valid solutions after solving the equation - sometimes you can generate false solutions
Domain
The domain of a function is a set of possible inputs
Range
The range of a function is the set of possible inputs
Range
The range of a function is the set of possible inputs
Features to add when sketching quadratics
- roots
- minimum / maximum
- y-intercept
And
∩
Or
U
N with a line through it
Set of natural numbers - all positive integers
Z with a line through it
Set of all integers - including negative numbers and 0
R with a line through it
Set of all real numbers including decimals
E
‘is a member of’
Below or above the line?
If y is on the smaller side then region is below the line
If y is on the greater side, region is above the line
Below or above the line?
If y is on the smaller side then region is below the line
If y is on the greater side, region is above the line
Point of inflection
When the curve goes from convex to concave
f(x) + a
Goes up ‘a’ units, y-axis is affected - (x, y+a)
f(x) - a
Goes down ‘a’ units, y-axis is effected (x, y-a)
y-axis is effected when…
The change is outside the brackets
x-axis is effected when…
The change is inside the brackets
f(x + a)
Goes ‘a’ units to the left, x-axis is effected - (x-a, y)
f(x - a)
Goes ‘a’ units to the right, x-axis is effected - (x+a, y)
-f(x)
Reflection in the x-axis, y-coordinate is effected (x,y) -> (x,-y)
f(-x)
Reflection in the x-axis, y-coordinate is effected - (x,y) -> (-x,y)
af(x)
Vertical stretch, y-coordinate is effected - (x,ay)
f(ax)
Horizontal stretch, x-coordinate is effected - (x/a,y)
Equation of a line
y - y1 = m(x - x1)
Gradient
What y changes by as x increases by 1
e.g. the gradient in a graph which shows selling price and profit would mean ‘the change in the profit as the selling price increases by 1’
Perpendicular lines
- Have negative reciprocal gradients
- To show two lines are perpendicular:
(m1)(m2) = -1
Distance between two points
√(change in x) ² + (change in y) ²
Linear relationship
There is a fixed increase/decrease in one variable each time the other variable goes up by one unit.
