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A Level Maths > Pure Year 1 > Flashcards

Pure Year 1 Flashcards

1
Q

How do you get from e to ln(x)

A

e^ln(x)=x

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2
Q

a^x x a^y

A

a^(x+y)

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3
Q

(a^x)^y

A

a^xy

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4
Q

(a^x)/(a^y)

A

a^(x-y)

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5
Q

(ab)^x

A

a^x x b^x

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6
Q

a^-x

A

1/a^x

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7
Q

(a/b)^-x

A

(b/a)^x = b^x/a^x

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8
Q

a^(p/q)

A

(qroota)^p

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9
Q

a^0

A

1

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10
Q

root ab =

A

roota x rootb

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11
Q

root a/b =

A

roota/rootb

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12
Q

Coordinate geometry length

A

root [(y2-y1)²+(x2-x1)²]

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13
Q

Coordinate geometry gradient

A

(y2-y1)/(x2-x1)

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14
Q

Coordinate geometry midpoint

A

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

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15
Q

Perpendicular

A

m1xm2=-1

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16
Q

Perpendicular bisector

A

A line that passes through the midpoint of two points and is 90° to the original line

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17
Q

Linear modelling

A

Y=ax+b

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18
Q

Why may a linear model not be suitable

A

May not account for other factors (named)

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19
Q

Why may a linear model be suitable if drawn on a graph

A

The data/points lie close to a straight line

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20
Q

Interpret the meaning of a and b in y=ax+b

A

a= the increase in y as x increases by

The value of (named y) increases/decreases per (x)

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21
Q

Completed square form

A

y = a(x-b)^2 + c

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22
Q

How to solve a quadratic

A

Calculator
Completing the square
Quadratic formula

23
Q

Graph of 0<a></a>

A

Exponential decay
Passes through y=1
Asymptote y=0
Vertical flip of exponential growth

24
Q

Graph of a>1, a^x

A

Exponential growth
Passes through y=1
Asymptote y=0
Never negative y

25
Q

9^x in terms of 3^x

A

3^2x

26
Q

Caution with logs

A

Can’t be negative inside

27
Q

List for day

A 
Read Q properly
Signs
Mental maths vs calculator
Reread question
Signs in logs
Will a graph help
Something common for something simple (x/y)
Dividing by negative logs with inequalities
28
Q

Natural logarithm of x

A

ln(x)

29
Q

Interpret the meaning of a and b in P=ab^x

A

The population at the start when x is 0

The proportional increase in … per year after …

30
Q

Dealing with multiple translations

A

Y:
R
S
T

X:
T
S
R

31
Q

N/Z+

A

Natural numbers

Positive integers

32
Q

Z

A

Integers

33
Q

Q

A

Rational numbers

Numbers that can be written as p/q where p and q are integers

34
Q

R

A

Real numbers

All numbers on a number line

35
Q

Proof by deduction

Direct proof

A

Complete the square, odd vs even etc for everything

36
Q

Proof by exhaustion

A

Try it for all values necessary

37
Q

Important for proof with trig

A

Trig graphs repeat, can prove in small range

38
Q

Proof by counter example

A

Give 1 example only

Sub numbers in to disprove

39
Q

Always, sometimes and never truth

A

If you think it’s always true or never true, prove it

If you think it’s sometimes, sub numbers in and get one for true and one for not true

40
Q

i vs j

A

i is x
j is y

Should underline i and j

41
Q

|v| for vectors

A

Square root of x^2 + y^2

42
Q

Unit vector

A

(1/|v|) x v

43
Q

How do you write a position vector or vector

A

Either with i, j and/or k or as a column vector

44
Q

Vector AB

A

OB-OA

45
Q

Trapezium in vectors

A

When AB and DC are parallel/scalar multiples

46
Q

How to find the angle vector xi+yj+zk makes with the positive x axis for angle x, y and z

A

Cos(x)=x/(|v|)

Cos(y)=y/(|v|)

Cos(z)=z/(|z|)

47
Q

Approximation for a number from binomial

A

Equate the two, cancel powers and get x

X should be small

48
Q

Find h in trapezium rule

A

h=(b-a)/n

b=max x
a=min x

n=number of strips

Basically h is the width of the rectangles

49
Q

Binomial expansion for positive integer powers

A

Use long NCR method

50
Q

Binomial expansion for negative or fraction

A

Complicated formula

Start with ~ or end with …

51
Q

Range of values for valid binomial notation

A

lxl<1

or

-1

52
Q

How do you find the range of valid substitutions in binomial expansions

A

Take what is inside the bracket and solve for x

Modulus of value

53
Q

How do you remove a negative in integrating in terms of the limits

A

Removing negative means the limits flip

54
Q

How do you show a polynomial has no further linear factors

A

Factorise and solve equal to zero

Use b²-4ac and if its less than 0 for a quadratic then it has no roots and no other linear factors

A Level Maths (6 decks)

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