pure year 1

Question 1

a^x x a^y

Answer 1

A^x+y

Question 2

a^x / a^y

Answer 2

a^x-y

Question 3

(a^b)^y

Answer 3

a^bxy

Question 4

(ab)^y

Answer 4

a^y x b^y

Question 5

root (ab)

Answer 5

root (a) x root (b)

Question 6

root (a/b)

Answer 6

root(a) / root(b)

Question 7

quadratic formula

Answer 7

x = (-b +- root(b^2 - 4ac)) / 2a

Question 8

What is the domain

Answer 8

The set of possible inputs for a function

Question 9

What is the range

Answer 9

The set of possible outputs for a function

Question 10

What are the roots of a function?

Answer 10

the values of x for which f(x) = 0

Question 11

if the completed square was:
f(x) = (x+p)^2 + q
what would the turning point be?

Answer 11

(-p, q)

Question 12

What is the discriminant?

Answer 12

b^2 - 4ac

Question 13

How many roots does b^2 - 4ac > 0 have?

Answer 13

two distinct real roots

Question 14

How many roots does b^2 - 4ac = 0 have?

Answer 14

One repeated root

Question 15

How many roots does b^2 - 4ac < 0 have?

Answer 15

no real roots

Question 16

What is x is greater than a or x is smaller than or equal to b in set notation?

Answer 16

{x:x is greater than a} u {x:x is smaller than or equal to b}

Question 17

{x:x is greater than a} u {x:x is smaller than or equal to b}

Answer 17

{x: a is smaller than x which is smaller than or equal to b}

Question 18

Is the circled filled in or empty for x is greater than or equal to y?

Answer 18

filled in

Question 19

Is the circled filled in or empty for x is greater y?

Answer 19

empty

Question 20

is y is greater than f(x) dotted or solid?

Answer 20

dotted

Question 21

is y greater than or equal to f(x) dotted or solid?

Answer 21

solid

Question 22

and

Answer 22

n

Question 23

or

Answer 23

u

Question 24

if x^3 is positive where does the graph start?

Answer 24

bottom left

Question 25

if x^3 is negative where does the graph start?

Answer 25

top left

Question 26

f(x) + a

Answer 26

vertical by a

Question 27

f(x+a)

Answer 27

horizontal by -a

Question 28

a X f(x)

Answer 28

stretch by factor of a vertically

Question 29

f(a X x)

Answer 29

stretch by a scale factor of 1/a horizontally

Question 30

-f(x)

Answer 30

reflection of f(x) in x axis

Question 31

f(-x)

Answer 31

reflection of f(x) in the y axis

Question 32

What do parallel lines have that are the same?

Answer 32

gradient

Question 33

How are the gradients of two perpendicular lines found?

Answer 33

There gradients will multiply to make -1

Question 34

Where does a perpendicular bisector pass through?

Answer 34

The mid point

Question 35

The equation of a circle with centre (a,b) and radius = r is?

Answer 35

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

Question 36

What is a tangents relationship with the radius?

Answer 36

perpendicular

Question 37

What will the perpendicular bisector of a chord do?

Answer 37

Go through the centre of a circle

Question 38

The angle in a semicircle is always a…

Answer 38

right angle

Question 39

What does it mean to prove a mathematical statement true by exhaustion?

Answer 39

Breaking the statement into smaller cases and proving each case seperately

Question 40

What does it mean to prove a mathematical statement not true by counter-example?

Answer 40

A counter-example is one example that does not work for the statement, you do not need to give more than one example, as one is sufficient to disprove a statement

Question 41

What does it mean to prove a mathematical statement true by deduction?

Answer 41

Starting from known factors or definitions, then using logical steps to reach the desired conclusion

Question 42

What is the general formula for binomial expansion? Using (a+b)^n as an example

Answer 42

a^n + nC1a^(n-1)b + nC2a^(n-2)b^2 + nC3a^(n-3)b^3 + … + b^n

Question 43

Cosine rule for a missing side

Answer 43

a^2 = b^2 + c^2 - 2bc cos(A)

Question 44

Sine rule for finding missing side

Answer 44

a / sin(A) = b / sin(B) = c / sin(C)

Question 45

Sine rule for finding missing angle

Answer 45

sin(A) / a = sin(B) / b = sin(C) / c

Question 46

Trigonometric formula for area of a triangle

Answer 46

area = 1/2 ab sin(C)

Question 47

sin^2(x) + cos^2(x) =

Answer 47

1

Question 48

sin(x) / cos(x)

Answer 48

tan(x)

Question 49

Equation for differentiating from first principles

Answer 49

f’(x) = lim of h–> 0 of (f(x+h)-f(x)) / (h)

Question 50

How do you find the derivitive usually?

Answer 50

Times by the power and then minus one from the power

Question 51

if f’‘(a) > 0 then

Answer 51

the point is a local minimum

Question 52

if f’‘(a) < 0 then

Answer 52

the point is a local maximum

Question 53

What is a unit vector? How are they usually denoted?

Answer 53

A vector of length 1, usually denoted by i and j, for x and y respectively

Question 54

What are position vectors?

Answer 54

vectors giving the position of a point, relative to a fixed origin

Question 55

Generally how do you integrate?

Answer 55

Add one to the power and then divide the coefficient by the value of the new power

Question 56

Why is e special?

Answer 56

The derivative of e^x = e^x

Question 57

What is a^x = n as a log?

Answer 57

log(a)n = x

Question 58

log x + log y =

Answer 58

log xy

Question 59

log x - log y =

Answer 59

log x/y

Question 60

log x^k =

Answer 60

k * log x

Question 61

ln x =

Answer 61

log(e) x

Question 62

e^(ln x) =

Answer 62

ln e^x = x

Question 63

How can you use logs to understand non-linear data?

Answer 63

Mess around with the equation till you have a linear equation with logs, e.g. (log y = n * log x + log a) is the same as y = mx + c