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A-level Maths > pure core > Flashcards

Flashcards in pure core Deck (50):
1

A^m/n

(n√a)^m

2

discriminant

b^2 - 4ac

3

b^2 - 4ac < 0

no real roots

4

b^2 - 4ac = 0

1 real root

5

b^2 - 4ac > 0

2 real roots

6

dotted line

<>

7

solid line

<= >=

8

[]

included in the range

9

()

not included in the range

10

midpoint

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

11

length of line

√(x1-x2)^2 + (y1-y2)^2

12

the angle in a semi circle is always

a right angle

13

the perpendicular line from the centre of a circle to a chord

perpendicularly bisects the chord

14

the tangent to a circle at a point

is perpendicular to the radius through that point

15

sin0

0

16

cos0

1

17

tan0

0

18

sin30

1/2

19

cos30

√3/2

20

tan30

√3/3

21

sin60

√3/2

22

co60

1/2

23

tan60

√3

24

sin45

√2/2

25

cos45

√2/2

26

tan45

1

27

sin90

1

28

cos90

0

29

tan90

undefined

30

tanx =

sinx/cosx

31

sin^2 x =

1 - cos^2 x

32

y = f(x) + 3

translation 3 in the y direction

33

y = f(x+3)

translation -3 in the x direction

34

y = 3f(x)

stretch of scale factor 3 in the y direction

35

y = f(3x)

stretch of scale factor 1/3 in the x direction

36

y = -f(x)

reflection in the x axis

37

y = f(-x)

reflection in the y axis

38

nCr

n! / r!(n-r)!

39

normal to curve

perpendicular to tangent at particular point

40

vector polar form

(r, θ)

41

vector/component form

(X, Y)
Xi + Yj

42

position vector

starts at the origin

43

unit vector

magnitude of 1
divide a direction by its magnitude to get its unit vector

44

vectors with common multiples

are parallel

45

vectors are perpendicular if

their dot/scalar product equals zero

46

Inverse of
"A to the power of X equals B"

log to the base a of b equals x

47

log(xy) =

log(x) + log(y)

48

log(x/y)

log(x)-log(y)

49

log1 =

0

50

log1/y =

-logy