pure

Question 1

discriminant is less than 0

Answer 1

no real solutions

Question 2

discriminant is more than 0

Answer 2

two distinct solutions

Question 3

discriminant is equal 0

Answer 3

one repeated solution

Question 4

indices laws

Answer 4

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

Question 5

Surd Laws

Answer 5

√a x √b = √ab

√a / √b = √(a/b)

Question 6

Rational number

Answer 6

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

Question 7

Ways to solve quadratic

Answer 7

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

Question 8

Tip for psuedo quadratics

Answer 8

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

Question 9

Domain

Answer 9

The domain of a function is a set of possible inputs

Question 10

Range

Answer 10

The range of a function is the set of possible inputs

Question 11

Range

Answer 11

The range of a function is the set of possible inputs

Question 12

Features to add when sketching quadratics

Answer 12

• roots
• minimum / maximum
• y-intercept

Question 13

And

Answer 13

∩

Question 14

Or

Answer 14

U

Question 15

N with a line through it

Answer 15

Set of natural numbers - all positive integers

Question 16

Z with a line through it

Answer 16

Set of all integers - including negative numbers and 0

Question 17

R with a line through it

Answer 17

Set of all real numbers including decimals

Question 18

E

Answer 18

‘is a member of’

Question 19

Below or above the line?

Answer 19

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

Question 20

Below or above the line?

Answer 20

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

Question 21

Point of inflection

Answer 21

When the curve goes from convex to concave

Question 22

f(x) + a

Answer 22

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

Question 23

f(x) - a

Answer 23

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

Question 24

y-axis is effected when…

Answer 24

The change is outside the brackets

Question 25

x-axis is effected when…

Answer 25

The change is inside the brackets

Question 26

f(x + a)

Answer 26

Goes ‘a’ units to the left, x-axis is effected - (x-a, y)

Question 27

f(x - a)

Answer 27

Goes ‘a’ units to the right, x-axis is effected - (x+a, y)

Question 28

-f(x)

Answer 28

Reflection in the x-axis, y-coordinate is effected (x,y) -> (x,-y)

Question 29

f(-x)

Answer 29

Reflection in the x-axis, y-coordinate is effected - (x,y) -> (-x,y)

Question 30

af(x)

Answer 30

Vertical stretch, y-coordinate is effected - (x,ay)

Question 31

f(ax)

Answer 31

Horizontal stretch, x-coordinate is effected - (x/a,y)

Question 32

Equation of a line

Answer 32

y - y1 = m(x - x1)

Question 33

Gradient

Answer 33

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’

Question 34

Perpendicular lines

Answer 34

• Have negative reciprocal gradients
• To show two lines are perpendicular:
  (m1)(m2) = -1

Question 35

Distance between two points

Answer 35

√(change in x) ² + (change in y) ²

Question 36

Linear relationship

Answer 36

There is a fixed increase/decrease in one variable each time the other variable goes up by one unit.