Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

Maths A level > Year 2 Pure > Flashcards

Year 2 Pure Flashcards

1
Q

What form can a rational number be written in

A

a/b

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

What are the different types of functions

A

One to one
Many to one
Not a function

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

What is the relationship between f(x) and f-1(x)

A

they are the inverse of each other

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

What order should fg(x) be done in

A

Apply g(x) into f(x)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

What is y = l f(x) l

A

It is a reflection in the x-axis

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

What is y= f(lxl)

A

Reflection in the y-axis

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

What is f(x+a)

A

Horizontal translation of -a

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

What is f(x) + a

A

vertical translation of +a

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

what is f(ax)

A

horizontal stretch of 1/a

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

What is af(x)

A

Vertical stretch of scale factor a

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

What is f(-x)

A

refection in the y-axis

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

What is -f(x)

A

refection of f(x) in x-axis

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

What is an arithmetic sequence

A

The difference between consecutive terms is the same

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

What is the formula for the nth term in an arithmetic sequence

A

Un = a + (n-1)d
a=first term
d=common difference

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

What is an arithmetic series

A

It is the sum of the terms of an arithmetic sequence

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

What is the formula for the sum of the first n terms of an arithmetic sequence

A

Sn = n/2 (2a + (n-1)d)
a=first term
d=common difference
Sn = n/2 (a+l) where l is the last term

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

What is a geometric sequence

A

It is a sequence with a common ratio between consecutive terms

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

What is the formula for nth term of a geometric sequence

A

Un = ar(n-1)
a=first term
r=common ratio

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

What is the formula for the sum of the first n terms of a geometric sequence

A

Sn = a(1-rn)/1-r
a=first term
r=common ratio

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

What is the formula for the sum to infinity of a convergent geometric series

A

S = a/1-r

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

What is a recurrance relation

A

It defines each term of a sequence as a function of the previous term

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

What is the recurrence relation formula

A

Un+1 = f(Un)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
23
Q

What is the formula for binomial expansion of (1+x)n

A

1+nx+ n(n-1)x2/2! (x2) + n(n-1)(n-2)x3/3! (x3)

24
Q

What is 2 pi equal to in degrees

A

360 degrees

25
Q

what is the equation for arc length

A

l = r0
r=radius
0=is the angle in radians

26
Q

What is the equation for area of a sector

A

A=1/2 r20
r=radius
0=angle in radians

27
Q

What is sin0, cos0 and tan0 equal to when 0 is small

A

sin0 = 0
tan0 = 0
cos0 = 1-02/2

28
Q

What is secx equal to

A

1/cosx

29
Q

what is cosecx

A

1/sinx

30
Q

What is cotx equal to

A

1/tanx
cosx/sinx

31
Q

What does the graph y=secx look like

A

Symetrical in y axis
vertical asymptotes at -450,-270,-90,90,270 and 450
y is less than or equal to -1
y is greater than or equal to 1

32
Q

What does the graph y=cosecx look like

A

Vertical asymptotes at -360,-180,0,180,360
y is less than or equal to -1
y is greater than or equal to 1

33
Q

What does the graph of y=cotx look like

A

vertical asymptotes at -360,-180,0,180 and 360
Intersect x-axis at -270, -90, 90 and 270
equal to all value of y

34
Q

What are the 3 identities

A

sin2x + cos2x = 1
1+ tan2x = sec2x
1 + cot2x = cosec2x

35
Q

What is the inverse function of sinx, cosx and tanx

A

arcsinx
arccosx
arctanx

36
Q

What does arcsinx look like

A

domain is -1 < x < 1
Range is -pi/2 < y < pi/2
or -90 < y < 90
Goes through the origin

37
Q

What does arccosx look like

A

Domain is -1 < x < 1
Range is 0 < y < pi
or 0 < y < 180

38
Q

What does arctanx look like

A

Domain is all values of x
Range is -pi/2 < y < pi/2
with asymptotes at pi/2 and -pi/2
Goes through the origin

39
Q

What is sin (A + B) equal to

A

sinAcosB + cosAsinB

40
Q

What is cos (A + B) equal to

A

cosAcosB - sinAsinB

41
Q

What is tan(A+B) equal to

A

tanA + tanB / 1 - tanAtanB

42
Q

What is sin(A-B) equal to

A

sinAcosB - cosAsinB

43
Q

What is cos(A-B) equal to

A

cosAcosB + sinAsinB

44
Q

What is tan(A-B) equal to

A

tanA - tanB / 1 + tanAtanB

45
Q

What is sin2A equal to

A

2sinAcosA

46
Q

What is cos2A equal to

A

cos2A - sin2A
2cos2A -1
1 - 2sin2A

47
Q

What is tan2A equal to

A

2tanA / 1 - tan^2A

48
Q

What is asinx +- bcosx equal to

A

Rsin(x +- c)

49
Q

What is acosx +- bsinx equal to

A

Rcos(x -+ c)

50
Q

What is the rule if a series converges

A

l r l < 1

51
Q

How do you find the distance from the origin of the co-ordinate (x,y,z)`

A

square root(x^2 + y^2 + z^2)

52
Q

How do you find the distance between to points

A

Find the difference in points then
(xd^2 + yd^2 + zd^2) ^1/2

53
Q

Whats the equation for the angle that a vector a = xi + yj + zk makes with the x axis and x,y,z

A

Cos0x = x / l a l
Cos0y = y / l a l
Cos0z = z / l a l

54
Q

What happens to 0 when 0 is small

A

Disregard terms with 0 in them

55
Q

What is a period sequence

A

A sequence that repeats numbers

56
Q

what is a periodic sequence of order 3 mean

A

The sequences repeats numbers every 3 terms

57
Q

How do you calculate the shortest distance between 2 points when there is a variable “t”

A

Form an equation for the distance and then solve the quadratic to find minimum point
Minimum point x coordinate is the value of t and y coordinate is shortest distance

Maths A level (10 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions