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A-level Maths (pure) > UCAS Exam Key Points - Pure Maths > Flashcards

UCAS Exam Key Points - Pure Maths Flashcards

1
Q

Transformation: f(x)+d

A

Vertical shift up

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2
Q

Transformation: f(x)-d

A

Vertical shift down

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3
Q

Transformation: f(x+d)

A

Horizontal shift left

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4
Q

Transformation: f(x-d)

A

Horizontal shift right

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5
Q

Transformation: -f(x)

A

Reflection in x axis

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6
Q

Transformation: f(-x)

A

Reflection in y axis

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7
Q

Transformation: af(x), a>1

A

Vertical stretch

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8
Q

Transformation: af(x) a<1

A

Vertical compression

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9
Q

Transformation: f(ax) a>1

A

Horizontal compression

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10
Q

Transformation: f(ax) a<1

A

Horizontal stretch

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11
Q

Cosine rule missing side

A

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

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12
Q

Cosine rule missing angle

A

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

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13
Q

Sine rule missing side

A

a/SinA = b/SinB = c/SinC

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14
Q

Sine rule missing angle

A

SinA/a = SinB/b = SinC/c

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15
Q

Trig area of a triangle

A

1/2 abSinC

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16
Q

How many degrees in 1 radian

A

180/pi

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17
Q

How many radian in 1 degree

A

Pi/180

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18
Q

180° in radian

A

Pi

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19
Q

360° in radian

A

2pi

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20
Q

Arc length in radian

A

l = rΘ

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21
Q

Arc length in degrees

A

l = (Θ/360) x pi x d

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22
Q

Area of a sector in radian

A

A = 1/2 x r^2 x Θ

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23
Q

Área of a sector in degrees

A

A = (Θ/360) x pi x r^2

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24
Q

Small angle approximation of sine

A

SinΘ ~ Θ

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25
Q

Small angle approximation of tan

A

TanΘ ~ Θ

26
Q

Small angle approximation of Cos

A

CosΘ ~ 1- (1/2 x Θ^2)

27
Q

Perpendicular gradients

A

M1 x M2 = -1

28
Q

Equation of a line formula

A

y-y1 = m(x-x1)

29
Q

What is the discriminant

A

b^2 - 4ac

30
Q

2 real roots

A

Discriminant > 0

31
Q

1 real root

A

Discriminant = 0

32
Q

No real roots

A

Discriminant < 0

33
Q

First principles of differentiation

A

Lim. (f(x+h) - f(x))/h
h—>0

34
Q

When is a function increasing

A

F’(x) ≥ 0

35
Q

When is a function decreasing

A

F’(x) ≤ 0

36
Q

When is a value a maximum

A

F’’(x) < 0

37
Q

When is a value a minimum

A

F’’(x) > 0

38
Q

Differentiate e^x

A

e^x

39
Q

Differentiate e^kx

A

ke ^kx

40
Q

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

A

1

41
Q

Sin(x)/cos(x)

A

Tan(x)

42
Q

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

A

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

43
Q

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

A

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

44
Q

Trapezium rule

A

1/2width(y0+2(y1+y2+y3+y….)+yn)

45
Q

Inequalities on a number line: filled circle

A

≤ / ≥

46
Q

Inequalities on a number line: non-filled circle

A

< / >

47
Q

Inequalities on the Cartesian plane: solid line

A

≤ / ≥

48
Q

Inequalities on the Cartesian plane: dotted line

A

< / >

49
Q

Inequalities: set notation

A

{x: …inequality…}

Using U and n when needed

50
Q

U (union)

A

OR

51
Q

n (intersect)

A

AND

52
Q

Inequalities interval notation: ()

A

< / >

Using U/n when needed

53
Q

Inequalities interval notation: []

A

≤ / ≥

Using U/n when needed

54
Q

Inequalities interval notation: when LB or UB not specified

A

Used +/- infinity

55
Q

Inequalities interval notation: when LB or UB not specified

A

Used +/- infinity

56
Q

Factor theorem

A

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

57
Q

nCr formula

A

n!/r!(n-r)!

58
Q

How many decimal places is a binomial approximation accurate to

A

Number of terms the expansion is completed to

59
Q

Modelling with quadratics - max height

A

Use the term outside the brackets of completed square form

60
Q

Modelling with quadratics - time at max height

A

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

A-level Maths (pure) (7 decks)

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