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
Small angle approximation of tan
TanΘ ~ Θ
26
Small angle approximation of Cos
CosΘ ~ 1- (1/2 x Θ^2)
27
Perpendicular gradients
M1 x M2 = -1
28
Equation of a line formula
y-y1 = m(x-x1)
29
What is the discriminant
b^2 - 4ac
30
2 real roots
Discriminant > 0
31
1 real root
Discriminant = 0
32
No real roots
Discriminant < 0
33
First principles of differentiation
Lim. (f(x+h) - f(x))/h h—>0
34
When is a function increasing
F’(x) ≥ 0
35
When is a function decreasing
F’(x) ≤ 0
36
When is a value a maximum
F’’(x) < 0
37
When is a value a minimum
F’’(x) > 0
38
Differentiate e^x
e^x
39
Differentiate e^kx
ke ^kx
40
Sin^2(x) + cos^2(x)
1
41
Sin(x)/cos(x)
Tan(x)
42
Midpoint of coordinates (a,b) and (c,d)
((a+c)/2, (b+d)/2)
43
Equation of a circle centre (a,b) radius r
(x-a)^2+(y-b)^2=r^2
44
Trapezium rule
1/2width(y0+2(y1+y2+y3+y….)+yn)
45
Inequalities on a number line: filled circle
≤ / ≥
46
Inequalities on a number line: non-filled circle
< / >
47
Inequalities on the Cartesian plane: solid line
≤ / ≥
48
Inequalities on the Cartesian plane: dotted line
< / >
49
Inequalities: set notation
{x: …inequality...} Using U and n when needed
50
U (union)
OR
51
n (intersect)
AND
52
Inequalities interval notation: ()
< / > Using U/n when needed
53
Inequalities interval notation: []
≤ / ≥ Using U/n when needed
54
Inequalities interval notation: when LB or UB not specified
Used +/- infinity
55
Inequalities interval notation: when LB or UB not specified
Used +/- infinity
56
Factor theorem
If f(p) = 0 Then (x-p) is a factor of f(x)
57
nCr formula
n!/r!(n-r)!
58
How many decimal places is a binomial approximation accurate to
Number of terms the expansion is completed to
59
Modelling with quadratics - max height
Use the term outside the brackets of completed square form
60
Modelling with quadratics - time at max height
Inside brackets of completed square = 0 Eg (t-1.5)^2 t-1.5=0 t=1.5
61
Turning point coordinates from completed square
a(x+p)^2+q (-p,q)