Pure Year 1

Question 1

How do you get from e to ln(x)

Answer 1

e^ln(x)=x

Question 2

a^x x a^y

Answer 2

a^(x+y)

Question 3

(a^x)^y

Answer 3

a^xy

Question 4

(a^x)/(a^y)

Answer 4

a^(x-y)

Question 5

(ab)^x

Answer 5

a^x x b^x

Question 6

a^-x

Answer 6

1/a^x

Question 7

(a/b)^-x

Answer 7

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

Question 8

a^(p/q)

Answer 8

(qroota)^p

Question 9

a^0

Answer 9

1

Question 10

root ab =

Answer 10

roota x rootb

Question 11

root a/b =

Answer 11

roota/rootb

Question 12

Coordinate geometry length

Answer 12

root [(y2-y1)²+(x2-x1)²]

Question 13

Coordinate geometry gradient

Answer 13

(y2-y1)/(x2-x1)

Question 14

Coordinate geometry midpoint

Answer 14

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

Question 15

Perpendicular

Answer 15

m1xm2=-1

Question 16

Perpendicular bisector

Answer 16

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

Question 17

Linear modelling

Answer 17

Y=ax+b

Question 18

Why may a linear model not be suitable

Answer 18

May not account for other factors (named)

Question 19

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

Answer 19

The data/points lie close to a straight line

Question 20

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

Answer 20

a= the increase in y as x increases by

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

Question 21

Completed square form

Answer 21

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

Question 22

How to solve a quadratic

Answer 22

Calculator
Completing the square
Quadratic formula

Question 23

Graph of 0<a></a>

Answer 23

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

Question 24

Graph of a>1, a^x

Answer 24

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

Question 25

9^x in terms of 3^x

Answer 25

3^2x

Question 26

Caution with logs

Answer 26

Can't be negative inside

Question 27

List for day

Answer 27

``` 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 ```

Question 28

Natural logarithm of x

Answer 28

ln(x)

Question 29

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

Answer 29

The population at the start when x is 0 The proportional increase in … per year after …

Question 30

Dealing with multiple translations

Answer 30

Y: R S T X: T S R

Question 31

N/Z+

Answer 31

Natural numbers | Positive integers

Question 32

Z

Answer 32

Integers

Question 33

Q

Answer 33

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

Question 34

R

Answer 34

Real numbers | All numbers on a number line

Question 35

Proof by deduction | Direct proof

Answer 35

Complete the square, odd vs even etc for everything

Question 36

Proof by exhaustion

Answer 36

Try it for all values necessary

Question 37

Important for proof with trig

Answer 37

Trig graphs repeat, can prove in small range

Question 38

Proof by counter example

Answer 38

Give 1 example only | Sub numbers in to disprove

Question 39

Always, sometimes and never truth

Answer 39

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

Question 40

i vs j

Answer 40

i is x j is y Should underline i and j

Question 41

|v| for vectors

Answer 41

Square root of x^2 + y^2

Question 42

Unit vector

Answer 42

(1/|v|) x v

Question 43

How do you write a position vector or vector

Answer 43

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

Question 44

Vector AB

Answer 44

OB-OA

Question 45

Trapezium in vectors

Answer 45

When AB and DC are parallel/scalar multiples

Question 46

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

Answer 46

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

Question 47

Approximation for a number from binomial

Answer 47

Equate the two, cancel powers and get x X should be small

Question 48

Find h in trapezium rule

Answer 48

h=(b-a)/n b=max x a=min x n=number of strips Basically h is the width of the rectangles

Question 49

Binomial expansion for positive integer powers

Answer 49

Use long NCR method

Question 50

Binomial expansion for negative or fraction

Answer 50

Complicated formula | Start with ~ or end with ...

Question 51

Range of values for valid binomial notation

Answer 51

lxl<1 or -1

Question 52

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

Answer 52

Take what is inside the bracket and solve for x | Modulus of value

Question 53

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

Answer 53

Removing negative means the limits flip

Question 54

How do you show a polynomial has no further linear factors

Answer 54

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