Unit 1

Question 1

Distance formula

Answer 1

d= √(x2-x1)²+(y2-y1)²

Question 2

Midpoint formula

Answer 2

(x1+x2/2),(y1+y2/2)

Question 3

Gradient formulas

Answer 3

m=y2-y1/x2-x1

m=tanø

Question 4

When are points collinear

Answer 4

When they lie on the same straight line

Question 5

Gradients of perpendicular lines

Answer 5

m x m_ = -1

Question 6

How to find a median

Answer 6

Midpoint
Gradient
Equation

Question 7

How to find an Altitude

Answer 7

Gradient
Perpendicular gradient
Equation

Question 8

How to find a perpendicular bisector

Answer 8

Midpoint
Gradient
Perpendicular gradient
Equation

Question 9

When are lines concurrent

Answer 9

If there is a point through which they all pass

Question 10

What is this

f^-1(x)

Answer 10

Inverse

Question 11

How to find the inverse of a function

Answer 11

Change notation from f(x) to y
Change subject to x
Change notation back to f^-1(x)
Change y in equation to x

Question 12

How to draw the graph of an inverse

Answer 12

Reflect it over the line y=x

Question 13

What is this

f(x)=a^x

Answer 13

Exponential function

Question 14

What points do the graphs of an exponential function always pass through

Answer 14

(0,1) (1,a)

Question 15

How to sketch the graph of an exponential function

Answer 15

Sub in x=0

Sub in x=1

Question 16

What is this

f(x)=log a x

Answer 16

Logarithm

Question 17

What points to the graph of a logarithmic function always pass through

Answer 17

(1,0) (a,1)

Question 18

How to change degrees to radians and radians to degrees

Answer 18

x 3.14 x 180

180 3.14

Question 19

Exact values table

Answer 19

30 45 60

sinx 1/2 1/√2 √3/√2

cosx √3/2 1/√2 1/2

tanx 1/√3 1 √3/1

Question 20

f(x)+a

Answer 20

Shifts graph up y axis

Question 21

f(x+a)

Answer 21

Shifts graph -a along x axis

Question 22

-f(x)

Answer 22

Reflects graph in x axis

Question 23

f(-x)

Answer 23

Reflects graph in y axis

Question 24

kf(x)

Answer 24

Scales graph vertically
Stretches if k>1
Compresses if k<1

Question 25

f(kx)

Answer 25

Scales graph horizontally compresses if k>1 stretches if k<1

Question 26

How to differentiate

Answer 26

Multiply first term by power | Minus 1 from power

Question 27

3 types of notation when differentiating

Answer 27

f’(x) dy/dx d/dx (term)

Question 28

How to find the rate of change/velocity of a function

Answer 28

Differentiate | Sub in x coordinate

Question 29

What is a tangent

Answer 29

A straight line that touches a curve

Question 30

How to find the equation of a tangent

Answer 30

Find coordinates of point Differentiate curve equation Sub in x coordinate to get gradient Write out equation

Question 31

When is a curve strictly increasing

Answer 31

derivative > 0

Question 32

When is a curve strictly decreasing

Answer 32

Derivative < 0

Question 33

How to find if a curve is strictly increasing/decreasing

Answer 33

Differentiate equation of curve Sub in x coordinate Look if dy/dx is < or >0

Question 34

How to find stationary points and determine their nature

Answer 34

Differentiate equation of curve Make derivative equal to zero Factories for x coordinates Sub each x coordinate into original equation of curve for y coordinates Draw nature table using x coordinates and derivative to determine nature

Question 35

How to sketch a curve

Answer 35

``` Find where cuts y axis when x=0 Find where cuts x axis when y=0 Find stationary points Do nature table Draw graph ```

Question 36

How to find the closed interval of a graph

Answer 36

Find stationary points Do nature table State interval ends by subbing values into original equation Find where cuts the x and y axis by subbing in zero Draw graph

Question 37

How to draw the graph of a derivative

Answer 37

Switch line directions when drawing

Question 38

What do A and B represent? | Un+1 = AUn + B

Answer 38

A is percent increase/decrease added/subtracted from 100, divided by 100 B is variable being introduced

Question 39

Limit of a sequence formula

Answer 39

l = b/1-a