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A level maths and further maths Edexel > AS Maths: to memorise > Flashcards

AS Maths: to memorise Flashcards

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1
Q

What is the logarithm law for multiplication?

A

logm + logN = log(mN)

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2
Q

What is the logarithm law for division?

A

logm - logN = log(m/N)

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3
Q

What is the logarithm law for exponentiation?

A

logm^p = p.logm

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4
Q

What does log a X = N imply?

A

a^N = X

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5
Q

What is the natural logarithm of X?

A

ln X = e^X

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6
Q

What is ln e?

A

ln e = 1

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7
Q

What is ln 1?

A

ln 1 = 0

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8
Q

What is the relationship between log e X and ln X?

A

log e X = ln X

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9
Q

What is ln e^X?

A

ln e^X = X

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10
Q

What is e^lnX?

A

e^lnX = X

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11
Q

What does the factor theorem state?

A

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

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12
Q

What is the cosine rule?

A

a² = b² + c² - 2bcCosA

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13
Q

How can CosA be expressed using the cosine rule?

A

CosA = (b² + c² - a²) / (2bc)

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14
Q

What is the sine rule?

A

a/SinA = b/SinB = c/SinC

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15
Q

How can SinA be expressed using the sine rule?

A

SinA/a = SinB/b = SinC/c

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16
Q

What is the area of a triangle using trigonometry?

A

1/2 absinC

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17
Q

What is the property of a tangent to a circle?

A

Tangent to a circle is perpendicular to the radius of the circle at the point of intersection.

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18
Q

What does the perpendicular bisector of a chord do?

A

Perpendicular bisector of a chord will go through the circle centre.

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19
Q

What is the property of a triangle formed across a circle?

A

If triangle forms across the circle, its diameter is the hypotenuse of the right-angled triangle.

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20
Q

What happens to the equations of the perpendicular bisectors of two different chords?

A

Equations of the perpendicular bisectors of two different chords will intersect at the circle centre.

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21
Q

How do you find the midpoint of two points?

A

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

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22
Q

What is the definition of gradient?

A

Rise over run

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23
Q

When are two lines perpendicular?

A

M1 x M2 = -1

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24
Q

What is the discriminant?

A

b² - 4ac

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25
What does D > 0 mean in the discriminant rules?
2 real solutions
26
What does D = 0 mean in the discriminant rules?
1 real solution
27
What does D < 0 mean in the discriminant rules?
2 imaginary solutions
28
What is the graph of y = k/x when k > 0?
Top right and bottom left
29
What is the graph of y = k/x when k < 0?
Top left and bottom right
30
What is the graph of y = k/x² when k > 0?
Both top
31
What is the graph of y = k/x² when k < 0?
Both bottom
32
What is the asymptote of y = e^x?
y = 0
33
What is the y-intercept of y = e^x?
1
34
What is the asymptote of y = 4e^x?
y = 0
35
What is the y-intercept of y = 4e^x?
4
36
What is the asymptote of y = e^x + 3?
3
37
What is the y-intercept of y = e^x + 3?
4
38
What is the difference in steepness of y = e^2x compared to y = e^x?
The line is steeper, else same as y = e^x
39
What is the equation of a circle?
(x-a)² + (y-b)² = r², centre (a,b)
40
What does the sine graph do?
Starts at 0, goes up to 1 (at π/2) then comes back down to 0 (at π)
41
What does the cosine graph do?
Starts at 1, goes down to 0 (at π/2), goes to -1 (at π)
42
What does the tan graph do?
At 0 degrees is at 0, and flicks up never quite touching 90 degrees.
43
What does f(x) + a do?
Moves up a on the y-axis
44
What does f(x + a) do?
Shifts left on the x-axis
45
What does a f(x) do?
Stretches in y
46
What does f(ax) do?
1/a stretches in x
47
What does -f(x) do?
Reflects in x-axis
48
What does f(-x) do?
Reflects in y-axis
49
What does |f(x)| do?
Makes all y values positive
50
What does f(|x|) do?
Makes all x values negative
51
What is the general rule for transformations?
Outside - do as expected, up and down directions; inside - do opposite, left and right directions.
52
What does AB-> mean?
OB-> - OA->
53
When are a and b parallel?
a = xb where x is constant
54
What is the magnitude of vector a?
|a| = sqrt(x² + y² + z²)
55
What is the unit vector of a?
â = a/|a|
56
What is the formula for combinations?
nCr = n!/r!(n-r)!
57
What is the relationship between 2π and degrees?
2π = 360°
58
What is the relationship between sin θ and cos θ?
sin θ/cos θ = tan θ
59
What is the Pythagorean identity for sine and cosine?
sin²(θ) + cos²(θ) = 1
60
What is the method for solving trigonometric equations graphically?
All science teacher crazy anti-clockwise starting and ++
61
What is the derivative of f(x)?
f'(x) = lim h->∞ (f(x+h) - f(x))/h
62
What does f'(x) < 0 indicate?
f(x) is decreasing
63
What does f'(x) = 0 indicate?
Stationary point
64
What does f'(x) > 0 indicate?
f(x) is increasing
65
What does f''(x) < 0 indicate?
Is a maximum
66
What does f''(x) = 0 indicate?
Is a point of inflection
67
What does f''(x) > 0 indicate?
Is a minimum
68
What is the derivative of ax^n?
dy/dx (ax^n) = anx^(n-1)
69
What is the derivative of a^x?
dy/dx (a^x) = ln(a)*a^x
70
What is the derivative of e^x?
dy/dx (e^x) = e^x
71
What is the derivative of lnx?
dy/dx (lnx) = 1/x
72
What is the derivative of sin x?
dy/dx (sin x) = cos x
73
What is the derivative of cos x?
dy/dx (cos x) = -sin x
74
What is the integral of ax^n?
Int (ax^n) = a/n+1 x^(n+1) + C
75
What is the integral of e^x?
Int (e^x) = e^x + C
76
What is the integral of 1/x?
Int (1/x) = ln |x| + C
77
What is the integral of cos x?
Int (cos x) = sin x + C
78
What is the integral of sin x?
Int (sin x) = -cos x + C
79
What is the area of a trapezium?
1/2(a+b)h

A level maths and further maths Edexel (2 decks)

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