Maths Flashcards
sin 0°
0
sin 30°
1/2
sin 45°
√2/2
sin 60°
√3/2
sin 90°
1
sin =
opposite / hypotenuse
cos =
adjacent / hypotenuse
tan =
opposite / adjacent
tan-1(opp/adj) is an example of how to find..
an angle
tan30 = opp/adj is an example of how to find..
a side
Density =
Mass/volume
Cosine rule
a² = b² +c² - (2bcCosA)
Cosine rule for angles
CosA = b² + c² - a² / 2bc
Area of triangle using trigonometry
1/2abSinC
Sine rule
SinA/a = SinB/b = SinC/c
x² - 25 factorised
(x+5)(x-5)
Quadratic formula
−b ± √b² −4ac
_____________
2a
Tan30
1/√3
Tan 45
1
Tan60
√3
Cos30
√3/2
Angle at centre theorem
The angle at the centre is twice the size the angle at the circumference
The angle in a semi - circle is
A right angle
Angles in the same segments are
Equal
Opposite angles in a cyclic quadrilateral..
Sum up to 180°
Relationship between a tangent and a radius
They are perpendicular
Angles in alternate segments are
Equal
Tangents from a point are
Equal
Conditions for congruent triangles
SSS
ASA
SAS
RHS
When are triangles similar?
When all the angles are the same but the sides are different sizes
What are bearings?
3 digit angles measured in a clockwise direction from north
How to prove if 3 points are collinear
• The vectors are parallel
• The vectors share a common point
Mutually exclusive events
Events that cannot happen together
Independent events
Events whose outcomes do not affect each other
Sample
A collection taken from a larger group
Stratified sampling
Using the ratios between a given sample and population to create a new sample
Upper quartile is equal to
75%
Lower quartile is equal to
25%
Formula to calculate median
(n+1) / 2
Calculating the possible original number after 27000 is the rounded number to 2sf
• 2nd sf is 7
• 7 is in the thousands column
• 1000/2 = 500
• +/- 500
• 26500 - 27500
Interpreting box plots
• Compare the medians
• Compare the interquartile ranges
(Smaller IQR = consistent distribution)
Positive quadratic equations on a graph look like a
U
Truncation
Cutting off the numbers after a decimal place
eg 9.999 becomes 9
Curved surface area of cylinder formula
2πrh
Calculate HCF
Multiply the common prime factors between both numbers (each number only being counted once)
(A ∩ B)
Calculate LCM
Multiply all the prime factors between both numbers (with the common ones being counted once)
(A ∪ B)
Equation of a circle
x² + y² = r²
Equation of a circle with (a,b) as centre
(x - a)² + (y - b)² = r²
Completing the square:
How would you factorise 3x² + 18x - 1?
Factor out the 3:
3 (x² + 6x -1/3)
Completing the square for (x² + 6x -1/3):
Factorise (x² + 6x) by halving the 6
= (x+3)²
Take away 3² and 1/3 from the bracket:
(x+3)² - 3² - 1/3 = (x+3)² - 28/3
Multiply by the 3 we factored out:
3(x+3)² - 28
How do you work out acceleration in a velocity time graph?
The gradient of the line
How do you work out distance in a velocity time graph?
The area under the graph
What points need to be considered when describing an enlargement?
• Scale factor
• Centre of enlargement
What points need to be considered when describing an enlargement?
• Type of transformation
• Scale factor
• Centre of enlargement
What points need to be considered when describing a rotation?
• Angle of rotation
• Direction (clockwise or anti clockwise)
• The point it’s about
What points need to be considered when describing a rotation?
• Angle of rotation
• Direction (clockwise or anti clockwise)
• The point it’s about
Invariant vertex
Points that don’t change position after a transformation
What does 5! mean?
• 5 factorial
• 5 x 4 x 3 x 2 x 1
Calculate inverse function of f(x) = 2x² - 7
Switch y with x
• y = 2x² - 7
• x = 2y² - 7
Make y subject
= y = root x + 7
————— = Ans
2
Work out gf(x) when f(x) = 2x + 1 and g(x) = x² + 1
• f(x) = 2x + 1
• g(2x+1) = (2x + 1)² + 1
• gf(x) = 4x² + 4x + 2
Make f the subject in d = 3(1-f)
————
f - 4
• d(f-4) = 3(1-f)
• df- 4d = 3 - 3f
• df + 3f = 4d + 3
• f(d+3) = 4d + 3
f = 4d+ 3
———-
d + 3
How to work out mean with intervals and frequency
• Find the midpoint of the intervals and multiply them by the corresponding frequency
• Add up all the frequencies together
• Divide the answer from step 1 by answer from step 2
What are irrational numbers?
Numbers that can’t be expressed as a fraction eg e
What would you do to rationalise 5
—— ?
7 + √3
5 7 - √3
———- x ——— 7 + √3 7 - √3
Formula for geometric sequences|
with example: 2, 6, 18, 54
• a x r ^n-1
• Answer = 2 x 3 ^n-1
Work out nth term for 3,9,17,27 (quadratic sequence)
• Difference of differences = 2
2
• ——— = 1n² = n²
2
• Write out n² sequence and subtract it from original sequence
• New sequence = 2,5,8,11
• Work out formula for new sequence
• Answer = 3n - 1
• Combine answer with first formula
• Final Answer = n² + 3n - 1
Factorise 3x² + 8x + 4
(3x + 6) (3x + 2) ———————
3
=
(x + 2) (3x + 2)
