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Corbettmaths Flashcards
Fichas del conjunto (93)
- 1Angles in parallel linesAlternate - interior 'Z' angles are equal
Corresponding -interior 'F' angles are equal
Cointerior - interior 'C' angles sum 180
Vertically opposite angles are equal - 2Angles in Polygons 1Triangle - Angles sum 180
Quadrilateral - Angles sum 360
Pentagon - Angles sum 540
Hexagon - Angles sum 720
Heptagon - Angles sum 900
Octagon - Angles sum 1080
Sum of interior - 180(n-2) - 3Angles in Polygons 2Sum of Exterior Angles = 360
Pentagon - 360/5 = 72
Interior + Exterior = 180
Pentagon = 180 - 72 = 108 - 4Arc lengthArc length = angle/360 x pi x d
- 5Area of a CircleArea = pi x r^2
If asked to give terms of pi then leave it without multiplying by pi. - 6Area of a SectorArea = angle/360 x pi x r^2
- 7Area of a TrapeziumArea = 0.5(a+b) x h
a and b are parallel lines
h is height between them - 8Area of a triangleArea = 0.5abSinC
a and b are two sides
C is the enclosed angle - 9BearingsBearings are a direction of travel
Find the bearing of Nottingham from Dublin
Join Dublin and Nottingham
Draw a north kine at dublin
Measure the angle clockwise from north
All bearing should have 3 figures - 10Changing the SubjectMake w the subject of
c = 4w + h
c - h = w
(c - h)/4 = w
Do the same on each side - 11Circle Theorems 1The angle in a semi-circle is 90
The angle at the circumference is half the angle at the centre
The angles in the same segment from a common chord are equal
The opposite angles in a cyclic quadrilateral always add up to 180 - 12Circle Theorems 2The angle between a radius and a tangent is 90
The tangents to a circle from the same point will be equal length
The radius through the midpoint of a chord will bisect the chord at 90 - 13Alternate segment theoremThe angle between the chord and the tangent is equal to opposite angle inside the triangle
- 14Parts of a circle 1Radius - half of the diameter
Diameter - a line going halfway through the middle
Circumference - the perimeter
Chord - a line connecting two points - 15Parts of a circle 2Arc - a small part of circumference
Tangent - a line 90 degrees from the radius
Sector - a 'pizza cut' of a circle
Segment - the area between chord and circumference - 16CircumferenceCircumference = pi x diameter
If only radius is given
Circumference = pi x 2 x radius - 17DensityDensity = Mass/Volume
Mass = Density x Volume
Volume = Mass/Density - 18PressurePressure = Force/Area
Force = Pressure x Area
Area = Force/Pressure - 19Speed, Distance and TimeSpeed = Distance/Time
Distance = Speed x Time
Time = Distance/Speed - 20Congruent TrianglesSSS - Side - Side - Side
ASA - Angle - Side - Angle
SAS - Side - Angle - Side
RHS - Right angle - Hypotenuse - Side - 21ConstructionsAngle Bisector
Perpendicular Bisector - 22LociA tree is planted closer to the fence than the wall. The tree is no more than 1 meter from the well.
Draw a circle around the well radius = 1
Angle bisector to find the wall:fence line - 23Cumulative FrequencyPosition of the median: 40/2 = 20
Draw across from 20 to the curve
Draw straight down from the curve
Read off the answer make sure you check the scale - 24Box PlotsInterquartile Range = Upper quartile - Lower quartile
Range = Highest value - lowest value - 25Recurring Decimals to FractionsWrite 0.45 (0.454545.....)
x = 0.45454545....
100x = 45.45454545...
99x = 45
x = 45/99
x = 5/11 - 26Equation of a Circlex^2 + y^2 = r^2
Centre = (0,0)
radius = r - 27Forming and solving equationsFind x on isosceles triangle with angle 1 being 2x and angle 2 and 3 being x + 20.
2x+x+20+x+20 = 180
4x + 40 = 180
x = 35 - 28Expanding Two BracketsExpand: (x+3)(x-7)
= X^2 - 7x + 3x - 21
= x^2 -4x -21 - 29Factorising Quadraticsplace y at the front of both brackets
The numbers will multiply to give (eg) -15 add to give (eg) 2
-3 + 5 = 2
(y - 3)(y + 5) - 30Solving Quadratics by FactorisingSolve x^2 - 3x -10 = 0
(x - 5)(x + 2) = 0
x = 5 or x = -2
(to make the brackets equal 0) - 31Adding FractionsWork out 1/4 + 7/10
5/20 + 14/20 = 19/20 - 32Dividing FractionsWork out 2/5 / 7/9
KFC = Keep Flip Change
2/5 x 9/7 = 18/35 - 33Multiplying FractionsWork out 3/4 x 2/5
Multiply numerators together and denominators together
= 6/20
=3/10 - 34Composite Functions: fg(x)GIven f(x) = 2x +1 and g(x) = x^2 + 5
Substitute g(x) into f(x)
fg(x) = 2(x^2 + 5) + 1
= 2x^2 + 10 + 1
= 2x^2 + 11 - 35Composite Functions: gf(x)Given f(x) = 2x + 1 and g(x) = x^2 + 5
gf(x) = (2x + 1)^2 + 5
=(2x + 1)(2x + 1) + 5
= 4x^2 + 4x + 1 + 5
= 4x^2 + 4x + 6 - 36Inverse FunctionsGIven f(x) = 3x + 2 find f-1(x)
y = 3x + 2
make x subject
(y - 2)/3 = x
f-1(x) = (x -2)/3 - 37Graphs of Exponential Functionsy = 2^x
x -2 -1 0 1 2 3
y 1/4 1/2 1 2 4 8 - 38Graphs of Reciprocal Functionsy = 1/x
- 39Cubic Graphsy = ax^3 - bx - c
- 40Transformations of Graphs 1y = -f(x) is a reflection of y = f(x) in the x axis
y = f(-x) is a reflection of y = f(x) in the y axis - 41Transformations of Graphs 2y = f(x) + a moves y = f(x) a square upwards
y = f(x+a) moves y + f(x) a square to the left - 42Graphs of trigonometric Functionsy = sin x
y = cos x
y = tan x - 43Drawing HistogramsFrequency Density = Frequency/Class Width
- 44Reading HIstogramsFrequency = Frequency Density x class width
- 45Fractional Indicesx^1/n = n root x
x ^m/n = (n root x)^m
27 ^2/3 = 9 - 46Laws of Indicesm^3 x m^4 = m^7 (Add)
m^8 / m^2 = m^6 (Subtract)
(m^3)^2 = m^6 (Multiply - 47Negative Indicesx ^-n = 1/x^n
x^0 = 1 - 48Limits of accuracyThe height of a lighthouse is 48m to the nearest metre. Find the lower and upper bound.
Lower = 47.5
Upper = 48.5 - 49Drawing linear graphsDraw y = 2x - 1
x -2 -1 0 1 2
y -5 -3 -1 1 3 - 50Equation of a liney = mx + c
m = Gradient
c = y - intercept
Gradient = rise/run - 51GradientGradient = rise/run
- 52Parallel LinesParallel lines have the same gradient
Equation has the same m value - 53Perpendicular linesPerpendicular lines cross at 90
If the gradient of one line is m
The gradient of the other is -1/m
(Negative reciprocal) - 54Equation of a tangent to a CirlceFind gradient of OP (origin,point)
Find the gradient of the perpendicular tangent
Substitute into y = 1/2x + c - 55Estimated Mean(Frequency x Midpoint) / Frequency
- 56Nth term fir Linear SequencesFind the difference between each number in sequence
Multiply the original number by the difference
Subtract this from the original number sequence - 57Nth term for Quadratic Sequencesnth term = an^2 + bn + c
Sequence = a + b + c
First difference = 3a + b
Second sequence = 2a - 58Percentage ChangePercentage Change = Change/Original x 100
- 59Compound intrestInitial x Multiplier^Time
- 60Reverse PercentagesDivide by Numerator
Multiply by Denominator - 61Drawing Pie ChartsFind the total frequency
Divide 360 by total frequency
To find the angle, multiply the frequency by the angle per person
Draw and label the pie chart - 62Tree DiagramsDraw a line from a point for each possibility
multiply each possibility by the probability - 63Product of PrimesWrite 60 as a product of primes
Draw two lines out of 60 and a pair of factors
Draw a circle around any primes and continue to write pairs until there are only primes. - 64LCM & HCF using product of primesThe LCM is found by multiplying all the numbers in the Venn Diagram
The HCF is found by multiplying the numbers in the middle of the venn diagram. - 65Direct ProportionC is directly proportional to the square of D
When C = 200, D = 2. Find C when D = 5
C = k x D^2
200 = k x 4
K = 50
C = 1250 - 66Inverse proportionP is inversely proportional to the cube of Q
When P = 10, Q = 2. Find P when Q = 4
10 = k/8
k = 80
P = 80/64
P = 1.25 - 67Pythagoras 1a^2 + b^2 = c^2
a and b = length of shorter side
c = length of hypotenuse - 68Pythagoras 2a^2 + b^2 = c^2
If only short side and hypotenuse is given rearrange the equation - 69Quadratic FormulaA quadratic equation in the form
ax^2 + bx + c = 0
x = (-b +/- root(b^2 - 4ac)) / 2a - 70Quadratic InequalitiesIf the sign is 'less than' sketch it as '=' then only use values below the x-axis
If the sign is 'greater than' sketch it as '=' then only use values above the x-axis - 71RatioFind the total number of parts by adding the values in the ratio
Divide the total amount of money by the total number of parts to find one part
Multiply the amount of money in one part by the number of parts each person receives - 72Scatter GraphsFor estimation, draw a line of best fit through the results.
go along the x-axis to information required and draw a vertical line connection to the line of best fit. Draw another horizontal line from this point to the y-axis and read. - 73CorrelationPositive - ascending from left to right
Negative - ascending from right to left
No Correlation - no pattern - 74Significant figuresThe first number that is not a zero is the first significant figure. The second is the second sf
- 75Similar ShapesIf the scale factor for the sides is n
- the scale factor for the area is n^2
- the scale factor for the volume is n^3 - 76Simultaneous EquationsMultiply the equations to give a common multiple. If the operations are the same then subtract these two and solve the equation. If they are different then add.
Then substitute this into A - 77Standard formStandard form is a really useful way of writing very large or very small numbers quickly and easily.
a x 10^n
A is between 0-10
n is a whole number - 78Surdsroot(a) x root(b) = root(ab)
root(a) x root(a) = a
root(a) / root(b) = root(a/b) - 79Rationalising the denominatorTo rationalise the denominator we multiply both the numerator and denominator of the fraction by the denominator
- 80EnlargementsIf the scale factor is 2.
Each point of the triangle will move twice as far away from the center of enlargement. - 81Enlargements with Negative Scale FactorsIf the scale factor is -3
Each point of the triangle will moves three times as far away from the center of enlargement in the opposite direction. - 82ReflectionsIf the question was:
Reflect shape A in the line x = 6
Draw a line at x = 6 and use this as a mirror to draw the reflection - 83RotationsMark the center of rotation and trace triangle A onto the tracing paper
Rotate 90 clockwise keeping the cross on the origin. Draw the triangle onto the grid. - 84TranslationsThe top number is the horizontal movement
The bottom number is the vertical movement - 85TrigonometrySin(x) = Opposite /Hypotenuse
Cos(x) = Adjacent / hypotenuse
Tan(x) = opposite /adjacent - 86Cosine Rulea^2 = b^2 + c^2 - 2bc CosA
- 87Exact Trig ValuesAngle sin cos tan
0 0 1 0
30 1/2 root(3)/2 root(3)/3
45 root(2)/2 root(2)/2 1
60 root(3)/2 1/2 root(3)
90 1 0 undefined - 88Sine Rulea/SinA = b/SinB = c/SinC
- 89VectorsOAB is a triangle OA = a OB = b
AB = AO + OB
AB = -a + b
AB = b - a - 90Venn DiagramsA = All in A section
B = All in B section
A' = everything but A
B' = everything but B
A U B = All of A and B sections
A n B = anything A and B (the middle bit) - 91Volume of a ConeVolume = 1/3 pi r^2 h
- 92Volume of a PrismVolume = Cross-Sectional Area x Length
- 93Volume of a SphereVolume = 4/3 pi r^3
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- A level (All Topics (brief)) Maths Fichas sobre Corbettmaths Flashcards, creado por Holly Martin el 24/04/2018.
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