UCAS Exam Key Points - Pure Maths

Question 1

Transformation: f(x)+d

Answer 1

Vertical shift up

Question 2

Transformation: f(x)-d

Answer 2

Vertical shift down

Question 3

Transformation: f(x+d)

Answer 3

Horizontal shift left

Question 4

Transformation: f(x-d)

Answer 4

Horizontal shift right

Question 5

Transformation: -f(x)

Answer 5

Reflection in x axis

Question 6

Transformation: f(-x)

Answer 6

Reflection in y axis

Question 7

Transformation: af(x), a>1

Answer 7

Vertical stretch

Question 8

Transformation: af(x) a<1

Answer 8

Vertical compression

Question 9

Transformation: f(ax) a>1

Answer 9

Horizontal compression

Question 10

Transformation: f(ax) a<1

Answer 10

Horizontal stretch

Question 11

Cosine rule missing side

Answer 11

a^2= b^2+c^2-2bcCosA

Question 12

Cosine rule missing angle

Answer 12

CosA= (b^2+c^2-a^2)/2bc

Question 13

Sine rule missing side

Answer 13

a/SinA = b/SinB = c/SinC

Question 14

Sine rule missing angle

Answer 14

SinA/a = SinB/b = SinC/c

Question 15

Trig area of a triangle

Answer 15

1/2 abSinC

Question 16

How many degrees in 1 radian

Answer 16

180/pi

Question 17

How many radian in 1 degree

Answer 17

Pi/180

Question 18

180° in radian

Answer 18

Pi

Question 19

360° in radian

Answer 19

2pi

Question 20

Arc length in radian

Answer 20

l = rΘ

Question 21

Arc length in degrees

Answer 21

l = (Θ/360) x pi x d

Question 22

Area of a sector in radian

Answer 22

A = 1/2 x r^2 x Θ

Question 23

Área of a sector in degrees

Answer 23

A = (Θ/360) x pi x r^2

Question 24

Small angle approximation of sine

Answer 24

SinΘ ~ Θ

Question 25

Small angle approximation of tan

Answer 25

TanΘ ~ Θ

Question 26

Small angle approximation of Cos

Answer 26

CosΘ ~ 1- (1/2 x Θ^2)

Question 27

Perpendicular gradients

Answer 27

M1 x M2 = -1

Question 28

Equation of a line formula

Answer 28

y-y1 = m(x-x1)

Question 29

What is the discriminant

Answer 29

b^2 - 4ac

Question 30

2 real roots

Answer 30

Discriminant > 0

Question 31

1 real root

Answer 31

Discriminant = 0

Question 32

No real roots

Answer 32

Discriminant < 0

Question 33

First principles of differentiation

Answer 33

Lim. (f(x+h) - f(x))/h h—>0

Question 34

When is a function increasing

Answer 34

F’(x) ≥ 0

Question 35

When is a function decreasing

Answer 35

F’(x) ≤ 0

Question 36

When is a value a maximum

Answer 36

F’’(x) < 0

Question 37

When is a value a minimum

Answer 37

F’’(x) > 0

Question 38

Differentiate e^x

Answer 38

e^x

Question 39

Differentiate e^kx

Answer 39

ke ^kx

Question 40

Sin^2(x) + cos^2(x)

Answer 40

1

Question 41

Sin(x)/cos(x)

Answer 41

Tan(x)

Question 42

Midpoint of coordinates (a,b) and (c,d)

Answer 42

((a+c)/2, (b+d)/2)

Question 43

Equation of a circle centre (a,b) radius r

Answer 43

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

Question 44

Trapezium rule

Answer 44

1/2width(y0+2(y1+y2+y3+y….)+yn)

Question 45

Inequalities on a number line: filled circle

Answer 45

≤ / ≥

Question 46

Inequalities on a number line: non-filled circle

Answer 46

< / >

Question 47

Inequalities on the Cartesian plane: solid line

Answer 47

≤ / ≥

Question 48

Inequalities on the Cartesian plane: dotted line

Answer 48

< / >

Question 49

Inequalities: set notation

Answer 49

{x: …inequality...} Using U and n when needed

Question 50

U (union)

Answer 50

OR

Question 51

n (intersect)

Answer 51

AND

Question 52

Inequalities interval notation: ()

Answer 52

< / > Using U/n when needed

Question 53

Inequalities interval notation: []

Answer 53

≤ / ≥ Using U/n when needed

Question 54

Inequalities interval notation: when LB or UB not specified

Answer 54

Used +/- infinity

Question 55

Inequalities interval notation: when LB or UB not specified

Answer 55

Used +/- infinity

Question 56

Factor theorem

Answer 56

If f(p) = 0 Then (x-p) is a factor of f(x)

Question 57

nCr formula

Answer 57

n!/r!(n-r)!

Question 58

How many decimal places is a binomial approximation accurate to

Answer 58

Number of terms the expansion is completed to

Question 59

Modelling with quadratics - max height

Answer 59

Use the term outside the brackets of completed square form

Question 60

Modelling with quadratics - time at max height

Answer 60

Inside brackets of completed square = 0 Eg (t-1.5)^2 t-1.5=0 t=1.5

Question 61

Turning point coordinates from completed square

Answer 61

a(x+p)^2+q (-p,q)