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maths > PURE YEAR 1 > Flashcards

PURE YEAR 1 Flashcards

1
Q

what is a^m x a^n

A

a^(m+n)

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2
Q

what is (a^m)^n

A

a^mn

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3
Q

what is a^m / a^n

A

a^(m-n)

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4
Q

what is (ab)^n

A

a^n b^n

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5
Q

what is a^(1/m)

A

m root a

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6
Q

what is a^-m

A

1/a^m

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7
Q

what is a^(n/m)

A

m root a^n

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8
Q

what is a^0

A

1

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9
Q

simplify sqrt(ab)

A

sqrt(a) x sqrt(b)

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10
Q

simplify sqrt(a/b)

A

sqrt(a)/sqrt(b)

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11
Q

what is the domain

A

the set of possible inputs for a function

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12
Q

what is the range

A

the set of possible outputs of a function

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13
Q

what are the roots for a function

A

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

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14
Q

how to find turning point of a quadratic graph

A

complete the square
f(x)= a(x+p)^2 +q
turning point (-p, q)

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15
Q

different cases of discriminants

A

b^2-4ac
if >0, 2 roots
if =0, 1 root
if <0, 0 roots

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16
Q

when is an inequality represented with a dotted line

A

if y>f(x) or y<f(x), the curve y=f(x) is not included in the region and is represented by a dotted line

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17
Q

when is an inequality represented with a solid line

A

if y≥f(x) or y≤f(x), the curve y=f(x) is included in the region and is represented by a solid line

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18
Q

where do the graphs y=k/x and y=k/x^2 have asymptotes

A

x=0
y=0

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19
Q

y=-f(x) transformation description

A

reflection of y=f(x) in x-axis

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20
Q

y=f(-x) transformation description

A

reflection of y=f(x) in y-axis

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20
Q

gradient formula

A

m= (y2-y1)/(x2-x1)

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21
Q

product of gradients of perpendicular lines

A

-1

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22
Q

equation of distance between 2 points

A

d= sqrt((x2-x1)^2 + (y2-y1)^2)

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23
Q

when are 2 quantities said to be in direct proportion
what is the graph of these quantities

A

when they increase at the same rate
a straight line through the origin

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24
Q

midpoint of a line segment equation

A

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

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25
Q

what is the perpendicular bisector of line segment AB

A

straight line perpendicular to AB that passes through midpoint of AB

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26
Q

equation of circle w centre 0,0

A

x^2 + y^2 = r^2

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27
Q

equation of circle w centre (a,b)

A

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

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28
Q

tangent to circle property

A

perpendicular to radius at point of intersection

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29
Q

perpendicular bisector of a chord property

A

goes through centre of circle

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30
Q

property of right angle in circle

A

if angle PRQ=90 then R lies on circle w diameter PQ
angle in semicircle is always a right angle

31
Q

how to find centre of a circle given any 3 points

A

find the equations of the perpendicular bisectors of 2 different chords
find coordinates of intersection of the perpendicular bisectors

32
Q

factor theorem of polynomials

A

if f(p)=0, then (x-p) is a factor of f(x)

33
Q

3 methods of proof

A

deduction
exhaustion
counter-example

34
Q

cosine rule w a^2 as subject

A

a^2= b^2 + c^2 - 2bc cosA

35
Q

cosine rule w A as subject

A

A= cos^-1 ( (b^2 + c^2 - a^2)/2bc )

36
Q

sine rule

A

sinA/ a = sinB/ b
(or reciprocal)

37
Q

sin(x) is same as what

A

sin (180-x)

38
Q

area of triangle

A

1/2 ab sinC

39
Q

how often does y=sin(x) repeat

A

every 360 degrees

40
Q

where does y=sin(x) cross x-axis

A

-180
0
180
360

41
Q

how often does y=cos(x) repeat

A

every 360 degrees

42
Q

where does y=cos(x) cross x-axis

A

-90
90
270
450

43
Q

how often does y=tan(x) repeat

A

every 180 degrees

44
Q

where does y=tan(x) cross x-axis

A

-180
0
180
360

45
Q

where are asymptotes of y=tan(x)

A

-90
90
270

46
Q

if vectors PQ=RS what is to say

A

equal in length
parallel

47
Q

if vectors AB=-BA:

A

AB is equal in length, parallel and in opposite direction to BA

48
Q

triangle law for vector addition

A

AB + BC = AC
is AB=a, BC=b, AC=c, a + b = c

49
Q

what does adding vectors PQ and QP give

A

the zero vector 0

50
Q

what can any vector parallel to vector a be written as

A

λa
λ is a non-zero scalar

51
Q

how to multiply a column vector by a scalar

A

multiply each component by the scalar
λ(p q)= (λp λq)

52
Q

how to add 2 column vectors

A

add the x- components tgt
add the y- components tgt

53
Q

how is the magnitude of vector xi + yj given

A

sqrt(x^2 + y^2)

54
Q

what is a unit vector in the direction of a

A

a / |a|
(a over magnitude of a)

55
Q

equation for differentiating from first principles

A

f’(x)= lim h->0 (f(x+h)-f(x)) / h

56
Q

derivative of x^n

A

n x^(n-1)

57
Q

derivative of ax^n

A

an x^(n-1)

58
Q

when is a function said to be increasing

A

if, on an interval, f’(x)>0

59
Q

when is a function said to be decreasing

A

if, on an interval, f’(x)<0

60
Q

local maximum?

A

f’(x)=0
f’‘(x)<0

61
Q

local minimum?

A

f’(x)=0
f’‘(x)>0

62
Q

derivative of e^x

A

e^x

63
Q

derivative of e^kx

A

ke^kx

64
Q

what is loga n = x equivalent to

A

a^x=n

65
Q

loga x + loga y =

A

loga xy

66
Q

loga x - loga y =

A

loga (x/y)

67
Q

loga (x^k) =

A

k loga x

68
Q

loga (1/x) =

A

-loga x

69
Q

loga a =

A

1

70
Q

log a 1=

A

0

71
Q

what is the graph of y= lnx a reflection of

A

the graph y=e^x in the line y=x

72
Q

e^lnx =

A

ln (e^x) = x

73
Q

if y= a x^n , what is graph of log y against log x

A

straight line
gradient n
vertical intercept log a

74
Q

if y= a b^x , what is the graph of log y against log x

A

straight line
gradient log b
vertical intercept log a

75
Q
A

maths (4 decks)

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