Year 2 Pure

Question 1

What form can a rational number be written in

Answer 1

a/b

Question 2

What are the different types of functions

Answer 2

One to one
Many to one
Not a function

Question 3

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

Answer 3

they are the inverse of each other

Question 4

What order should fg(x) be done in

Answer 4

Apply g(x) into f(x)

Question 5

What is y = l f(x) l

Answer 5

It is a reflection in the x-axis

Question 6

What is y= f(lxl)

Answer 6

Reflection in the y-axis

Question 7

What is f(x+a)

Answer 7

Horizontal translation of -a

Question 8

What is f(x) + a

Answer 8

vertical translation of +a

Question 9

what is f(ax)

Answer 9

horizontal stretch of 1/a

Question 10

What is af(x)

Answer 10

Vertical stretch of scale factor a

Question 11

What is f(-x)

Answer 11

refection in the y-axis

Question 12

What is -f(x)

Answer 12

refection of f(x) in x-axis

Question 13

What is an arithmetic sequence

Answer 13

The difference between consecutive terms is the same

Question 14

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

Answer 14

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

Question 15

What is an arithmetic series

Answer 15

It is the sum of the terms of an arithmetic sequence

Question 16

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

Answer 16

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

Question 17

What is a geometric sequence

Answer 17

It is a sequence with a common ratio between consecutive terms

Question 18

What is the formula for nth term of a geometric sequence

Answer 18

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

Question 19

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

Answer 19

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

Question 20

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

Answer 20

S = a/1-r

Question 21

What is a recurrance relation

Answer 21

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

Question 22

What is the recurrence relation formula

Answer 22

Un+1 = f(Un)

Question 23

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

Answer 23

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

Question 24

What is 2 pi equal to in degrees

Answer 24

360 degrees

Question 25

what is the equation for arc length

Answer 25

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

Question 26

What is the equation for area of a sector

Answer 26

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

Question 27

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

Answer 27

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

Question 28

What is secx equal to

Answer 28

1/cosx

Question 29

what is cosecx

Answer 29

1/sinx

Question 30

What is cotx equal to

Answer 30

1/tanx cosx/sinx

Question 31

What does the graph y=secx look like

Answer 31

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

Question 32

What does the graph y=cosecx look like

Answer 32

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

Question 33

What does the graph of y=cotx look like

Answer 33

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

Question 34

What are the 3 identities

Answer 34

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

Question 35

What is the inverse function of sinx, cosx and tanx

Answer 35

arcsinx arccosx arctanx

Question 36

What does arcsinx look like

Answer 36

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

Question 37

What does arccosx look like

Answer 37

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

Question 38

What does arctanx look like

Answer 38

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

Question 39

What is sin (A + B) equal to

Answer 39

sinAcosB + cosAsinB

Question 40

What is cos (A + B) equal to

Answer 40

cosAcosB - sinAsinB

Question 41

What is tan(A+B) equal to

Answer 41

tanA + tanB / 1 - tanAtanB

Question 42

What is sin(A-B) equal to

Answer 42

sinAcosB - cosAsinB

Question 43

What is cos(A-B) equal to

Answer 43

cosAcosB + sinAsinB

Question 44

What is tan(A-B) equal to

Answer 44

tanA - tanB / 1 + tanAtanB

Question 45

What is sin2A equal to

Answer 45

2sinAcosA

Question 46

What is cos2A equal to

Answer 46

cos2A - sin2A 2cos2A -1 1 - 2sin2A

Question 47

What is tan2A equal to

Answer 47

2tanA / 1 - tan^2A

Question 48

What is asinx +- bcosx equal to

Answer 48

Rsin(x +- c)

Question 49

What is acosx +- bsinx equal to

Answer 49

Rcos(x -+ c)

Question 50

What is the rule if a series converges

Answer 50

l r l < 1

Question 51

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

Answer 51

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

Question 52

How do you find the distance between to points

Answer 52

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

Question 53

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

Answer 53

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

Question 54

What happens to 0 when 0 is small

Answer 54

Disregard terms with 0 in them

Question 55

What is a period sequence

Answer 55

A sequence that repeats numbers

Question 56

what is a periodic sequence of order 3 mean

Answer 56

The sequences repeats numbers every 3 terms

Question 57

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

Answer 57

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