Pure Maths Key Mistakes +C

Question 1

Coefficient of x is…

Answer 1

Any term that is in-front of x, can be a letter aswell

Question 2

(x + h) ^3

Answer 2

x^3 + 3x^2h + 3xh^2 + h^3

Question 3

Gradient on differentiation

Answer 3

as h➡️0, 6xh➡️0, 2h^2➡️0
so f’(x)= 6x^2 , whatever has no H

Question 4

Differentiate from first principles

Answer 4

DY/DX = f’(x)= lim = equation
h➡️0
Gradient at end after h➡️0
f’(x)= 6x2

Question 5

ax^n

Answer 5

DY/DX =anx^n-1

Question 6

Stationary point…

Answer 6

Gradient of 0

Question 7

Decreasing function

Answer 7

Dy/dx < 0

Question 8

Increasing

Answer 8

Dy/dx > 0

Question 9

Differentiate once

Answer 9

DY/DX to find gradient

Question 10

Differentiate twice

Answer 10

D^2y / dx^2
Min or max

Question 11

n!

Answer 11

n x (n-1) x (n-2) x (n-3) x … x 3 x 2 x 1

Question 12

^nCr⬇️

Answer 12

=(n). n!/ r!(n-r)!
(r).

Question 13

0!

Answer 13

1

Question 14

(N-2)!

Answer 14

(n-2) x (n-3) x ….

Question 15

2!

Answer 15

2

Question 16

3!

Answer 16

3 x 2 x 1 = 6

Question 17

Differentiating e^x

Answer 17

e^x

Question 18

e^kx

Answer 18

ke^kx

Question 19

Drawing 4e^0.5x + 3

Answer 19

It would be increasing
Asymptote at 3
It’s only decreasing if it was y=0.5^x

Question 20

Y= -e^x

Answer 20

Same as e^x but reflection in x axis

Question 21

F(-x)

Answer 21

e^-x
Reflect in y axis
) to (

Question 22

What does the 1000 in e^x + 1000 mean

Answer 22

It will always be more than 1000

Question 23

Show that it is increasing by…

Answer 23

Rate of change
Differentiate

Question 24

What is the significance of a sign at the start of the derivative

Answer 24

Decreases exponentially

Question 25

Loga(1/x)=

Answer 25

Loga(x^-1] = -logax

Question 26

LogaA

Answer 26

1

Question 27

Loga1

Answer 27

0

Question 28

Multiplication law

Answer 28

LogaX + logaY=logaXY

Question 29

Division law

Answer 29

Logax-Logay = Loga(x/y)

Question 30

Loga(x^k)

Answer 30

KlogaX

Question 31

In logs Whenever f(x) = g(x)

Answer 31

LogaF(x) = LogaG(x)

Question 32

Lnx = 2

Answer 32

x= e^2

Question 33

e^lnx

Answer 33

Ln (e^x) = x

Question 34

e^x is always …

Answer 34

Positive. Cannot be ln-7

Question 35

If there’s a question with e^x and e^-x

Answer 35

Multiply each term by ex

Question 36

Ln1

Answer 36

0

Question 37

e^10x in terms of U= e^5x

Answer 37

U^2

Question 38

(Lnx-1)^2

Answer 38

Multiply it out, don’t square root other side

Question 39

Y= ln x is…

Answer 39

Defined for x>0 Reflection of y= e^x in y=x I

Question 40

Give the exact coordinates

Answer 40

Give X AND Y

Question 41

Evaluate your model regarding this information

Answer 41

On the model. V= …. And A…. So it is reliable

Question 42

Exponential model equation

Answer 42

P= Ae(^kt)

Question 43

Normal to a curve

Answer 43

-1/ x

Question 44

Local maximum

Answer 44

Positive,e 0, negative

Question 45

Local minimum

Answer 45

Negative, 0, positive

Question 46

Inflection

Answer 46

+ , 0, +

Question 47

12.10 positive gradient

Answer 47

Above x- axis

Question 48

Negative gradient

Answer 48

Below x-axis

Question 49

Horizontal asymptote

Answer 49

At the x-axis

Question 50

Vertical asymptote

Answer 50

Vertical asymptote

Question 51

Inflection point

Answer 51

Touches-axis

Question 52

Touches x axis

Answer 52

Nothing

Question 53

Max or minimum

Answer 53

Cuts x axis

Question 54

Whenever square root something…

Answer 54

-get 2 values - positive and negative - if it’s a length it’s positive

Question 55

Circumference of a full circle with radius x

Answer 55

2TTX

Question 56

Find min/max value

Answer 56

Just differentiate once

Question 57

x^-2 = 1/4

Answer 57

Reciprocal of 1/4 4 Root 4 = +- 2

Question 58

When given a curve, the derivate

Answer 58

Or gradient function is F’(x)= lim h>0

Question 59

F’(x)

Answer 59

Is the differentiated

Question 60

Sin2feta

Answer 60

+ cos2feta = 0

Question 61

Tan feta

Answer 61

Sinfeta/cosfeta

Question 62

PQ + QP

Answer 62

0

Question 63

Vector parallel to a

Answer 63

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