Pure Maths Year 2

Question 1

What’s a term to term rule example?

Answer 1

U1 = 2
U(n+1) = Un + 6

Question 2

What’s a position to term rule example?

Answer 2

Un = 3n - 7

Question 3

How do you find a limit for a convergent sequence?

Answer 3

Let U(n+1) = Un = L
Then solve for L

e.g L= 0.5L +5

Question 4

What’s the nth term for an arithmetic sequence?

Answer 4

Un = a + (n-1)d

Question 5

What’s the formula for arithmetic series?

Answer 5

In the formula book

Question 6

What’s the formula for geometric sequences?

Answer 6

Un = ar ^(n-1)

Question 7

What’s the formula for geometric series?

Answer 7

In formula book

Question 8

What’s the formula for infinite geometric series?

Answer 8

In formula book

Question 9

How would you prove a sequence is increasing?

Answer 9

Show Un+1 - Un > 0

Question 10

What does Sn - Sn-1 equal?

Answer 10

Un

Question 11

How do you test if a mapping is a function?

Answer 11

Vertical line test

many-one or one-one

Question 12

What’s the domain?

Answer 12

Input values

e.g x > 2 or x E R

Question 13

What’s the range?

Answer 13

Possible outputs of a function

e.g f(x) < 6

Question 14

What functions have an inverse

Answer 14

One-one functions only

Question 15

How do you sketch a modulus function?

Answer 15

Sketch the graph and then reflect any parts below the x axis in the x axis

Question 16

Write the intervals out for these modulus inequalities

|x-a|<b>b |x-2|>6<6</b>

Answer 16

• b < x-a < b
• 4 < x -3 < 4

x-a > b or x-a < -b

x-2 > 6 or x-2 < -6

Question 17

What’s the factor theorem?

Answer 17

If f(3) = 0 then (x-3) is a factor

Question 18

What’s an extension on the factor theorem?

Answer 18

If f(3/4) = 0 then (4x-3) is a factor

Question 19

How do you find a quotient and remainder?

Answer 19

Divide by the denominator for quotient and remainder over denominator is what’s left

Question 20

What must you do for a repeated factor in partial fractions?

Answer 20

A B C
——— + ——— + ———
ax + b cx + d (cx + d)²

Question 21

What’s the formula for general binomial expansion?

Answer 21

In formula book

Question 22

When is general binomial expansion valid?

Answer 22

|x|<1

Question 23

Describe the graph

y=a sin(bx) and y=a cos(bx)

Answer 23

Amplitude is a

Period is 2π/b

Question 24

Length of an arc

Answer 24

l=rθ

Question 25

Area of a sector

Answer 25

A =1/2 r²θ

Question 26

Where do you find small angle approximations

Answer 26

Formula book

Question 27

Sin (A+B)

Answer 27

sinA cosB + cosA sinB

Question 28

Cos(A+B)

Answer 28

cosA cosB - sinA sinB

Question 29

tan (A+B)

Answer 29

In formula book

Question 30

sin(2A)

Answer 30

2sinAcosA

Question 31

cos(2A)

Answer 31

cos²(A) -sin²(A)
2cos²(A) -1
1-2sin²(A)

Question 32

tan(2A)

Answer 32

2tan(A)
—————
1- tan²(A)

Question 33

asinx + b cosx

Answer 33

Rewrite as R sin(x+a) and expand the brackets
Equate coefficients to get Rsina and Rcosa
Use Pythagoras for R
For a do tana = sinA/cosA

Question 34

Sec

Answer 34

Cos^-1

Question 35

Cosec

Answer 35

Sin^-1

Question 36

Sec²(x)

Answer 36

Sec²(x)=1+tan²(x)

Question 37

Cosec²(x)

Answer 37

Cosec²(x)=1+cot²(x)

Question 38

What do you get if you differentiate e^x?

Answer 38

e^x

Question 39

What do you get if you differentiate ln x

Answer 39

1/x

Question 40

What’s the sin cos ladder?

Answer 40

S
C
-S
-C

Question 41

What do you get if you differentiate tan x?

Answer 41

sec²x

Question 42

What’s the chain rule?

Answer 42

dy dy du
— = — + —
dx du dx

Question 43

What do you get if you differentiate inverse trig functions?

Answer 43

The formula book

Question 44

What’s the product rule?

Answer 44

dy dv du
— = — U + — V
dx dx dx

Question 45

What’s the quotient rule?

Answer 45

In formula book

Question 46

How do you differentiate implicitly?

Answer 46

Differentiate with respect to y then multiply by dy/dx

Question 47

What do you get if you differentiate a^x?

Answer 47

a^x ln a

You can prove this by writing ln y = xln a and differentiating implicitly

Question 48

What methods can you use for integration?

Answer 48

Integration by substitution

Integration by parts - in formula book

Question 49

What substitution would you use for ∫√a²-x² dx

Answer 49

x = a sinθ

Question 50

What is ∫f’(x)/f(x) dx

Answer 50

ln |f(x)| + c

Question 51

What is a concave and convex curve?

Answer 51

Concave: d²y/dx² < 0 /’’’’\
Convex: d²y/dx² < 0 .…/

Question 52

What is a point of inflection?

Answer 52

d²y/dx² = 0

Question 53

When does Newton Raphson Method fail?

Answer 53

If starting point is stationary point or too close to a stationary point