pure Flashcards

1
Q

discriminant is less than 0

A

no real solutions

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2
Q

discriminant is more than 0

A

two distinct solutions

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3
Q

discriminant is equal 0

A

one repeated solution

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4
Q

indices laws

A

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

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5
Q

Surd Laws

A

√a x √b = √ab

√a / √b = √(a/b)

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6
Q

Rational number

A

Any number that can be expressed as a/b where a and b are integers

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7
Q

Ways to solve quadratic

A
  1. factorising
  2. quadratic formula
  3. completing the square
  4. calculator
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8
Q

Tip for psuedo quadratics

A

Check for valid solutions after solving the equation - sometimes you can generate false solutions

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9
Q

Domain

A

The domain of a function is a set of possible inputs

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10
Q

Range

A

The range of a function is the set of possible inputs

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11
Q

Range

A

The range of a function is the set of possible inputs

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12
Q

Features to add when sketching quadratics

A
  • roots
  • minimum / maximum
  • y-intercept
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13
Q

And

A

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14
Q

Or

A

U

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15
Q

N with a line through it

A

Set of natural numbers - all positive integers

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16
Q

Z with a line through it

A

Set of all integers - including negative numbers and 0

17
Q

R with a line through it

A

Set of all real numbers including decimals

18
Q

E

A

‘is a member of’

19
Q

Below or above the line?

A

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

20
Q

Below or above the line?

A

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

21
Q

Point of inflection

A

When the curve goes from convex to concave

22
Q

f(x) + a

A

Goes up ‘a’ units, y-axis is affected - (x, y+a)

23
Q

f(x) - a

A

Goes down ‘a’ units, y-axis is effected (x, y-a)

24
Q

y-axis is effected when…

A

The change is outside the brackets

25
x-axis is effected when…
The change is inside the brackets
26
f(x + a)
Goes ‘a’ units to the left, x-axis is effected - (x-a, y)
27
f(x - a)
Goes ‘a’ units to the right, x-axis is effected - (x+a, y)
28
-f(x)
Reflection in the x-axis, y-coordinate is effected (x,y) -> (x,-y)
29
f(-x)
Reflection in the x-axis, y-coordinate is effected - (x,y) -> (-x,y)
30
af(x)
Vertical stretch, y-coordinate is effected - (x,ay)
31
f(ax)
Horizontal stretch, x-coordinate is effected - (x/a,y)
32
Equation of a line
y - y1 = m(x - x1)
33
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’
34
Perpendicular lines
- Have negative reciprocal gradients - To show two lines are perpendicular: (m1)(m2) = -1
35
Distance between two points
√(change in x) ² + (change in y) ²
36
Linear relationship
There is a fixed increase/decrease in one variable each time the other variable goes up by one unit.