GCSE Flashcards
Area of a parallelogram
Base x perpendicular height
Area of a trapezium
1/2 (a + b) x h, half the sum of the parallel sides times the distance between them
Area of kite
Width x height / 2
Area of circle
Pi r squared
Circumference of circle
2 x pi x r
Area of sector
Theta / 360 x pi x r squared
Length of an arc
Theta / 360 x 2 x pi x r
Volume of prism
Area of cross section x length
Volume of pyramid
1/3 x base area x height
Volume of a cone
1/3 x pi r squared x h
Volume of sphere
4/3 x pi r cubed
Volume of frustum
Vol of A - vol of B
Curved surface area of a cone
Pi x r x l, to find l, l = h squared + r squared
Surface area of sphere
4 x pi r squared
What is the nth term for arithmetic sequences?
An + b
A being the common difference
n being the position
b being the zero term
What is the nth term for quadratic sequences
an squared + bn + c
What is the nth term for geometric sequences
a x r to the n - 1
a being the first term
r being the common ratio
n being position
How do you calculate the median position?
n + 1 / 2
How do you find the lower quartile?
n + 1 / 4
How do you calculate the upper quartile?
3(n + 1) / 4
What is the formula for suitable degree of accuracy?
M = square root of s / t
How do you do suitable degree of accuracy?
1) calculate the lower bound for the answer
2) calculate the upper bound for the answer
3) choose the accurate value that both bounds round to
In corresponding angles…
They are equal ( F shape)
In alternate angles….
They are equal ( Z shape)
In co-interior angles…
The angles add to 180° (c shape)
What must you remember for bearings?
3 DIGITS, eg. 005°
What is estimation
Rounding to 1 sf
Pressure =
Force / area FAP
Density =
mass / volume MVD
Speed =
Distance / time DST
What is conditional probability?
The probably of subsequent events depends on previous events occurring
What is the probability of b given a
P ( B | A )
P(not A)
1 - P (A)
P (A or B)
P(A) + P(B)
What is A n B
A intersection B = A and B = where’s you ge hashing
A u B
A union B = A or B = everything in the circles
A ‘
A complement = Not A
What is translation?
Slide
What is enlargement?
Change in size, centre of enlargement, scale factor
Acceleration =
Final velocity - initial velocity / time
What is capture- recapture
N = Mn/m
M = number of fish caught then released n = size of recapture sample m= number of fish in second capture
What is the formula for direct proportion?
y = kx
k is the constant of proportionality
What is the formula for inverse proportion?
y Jesus fish 1/x
y = k/x
y is directly proportional to the square of x
y = kx squared
y fish x squared
Y is directly proportional to the cube of x
y fish x cubed
y = kx cubed
Y is directly proportional to the square root of x
y fish root x
y = k root x
y is inversely proportional to the square of x
y fish 1/x squared
y = k/x squared
Formula for sampling
Sample size / population size x number he chooses to sample
How do you do cumulative frequency curves?
1) find cumulative frequency
2) Plot points at the upper end of each group
3) Find the UQ , LQ and median
How do you calculate frequency for histograms?
Frequency = F.D x width
What is an equation
It can be solved
What is an expression
Terms without an equals sign
What is a formula
An algebraic rule we substitute numbers into
How do you find the area of a triangle
1/2 x a x b x sinC
How do you find the height of a triangle
a x sinC
What is the sine rule for finding missing lengths
a / sin a = b / sin b = c / sin c
What is the sine rule for finding missing angles
Sin a / a = sin b / b = sin c / c
What is the cosine rule for finding missing sides
a squared = b squared + c squared - 2 x b x c x CosA
What is the cosine rule for finding missing angles
cosA = b squared + c squared - a squared / 2 x b x c
What does a positive and negative quadratic graph look like?
Positive = smile Negative = sad face
What does a positive and negative reciprocal graph look like
Negative gradient in a quadrat
What does a positive and negative cubic graph look like
p- Up and down and up
n- Down and up and down
What does an exponential graph look like?
Curve up but never touches 0
How do you do the upper bound and lower bound for dividing?
UB = UB / LB LB = LB / UB
How do you find either sin, cos or tan 30, 60
Draw out equilateral triangle and cut it in half, shortest side is 1, hyp is 2
How do you find sin cos tan 45?
Draw out isosceles, angles are 90, 45 and 45, two sides of 1 as equal and shortest
What is the probability of b given a? (Conditional probability)
P ( A n B ) / P (A)
Surface area of a cylinder
2 pi r squared + 2 x pi x r x l
How do you do frequency polygons?
- plot in middle of the group
- straight lines joining points
How do you find the y intercept of a quadratic graph
y = ax squared + bx + c
It is the c part of the equation
What is a positive quadratic and negative quadratic in terms of minimum and maximum points?
Positive- minimum, no maximum
Negative- no minimum, maximum
What is the quadratic formula?
- b +/- root b squared - 4 x a x c
Divided by 2a
How do you complete the square?
Half the ax value and then put that in the bracket. Then find the negative square of that number and then add or minus the c part of the equation
How would you complete the square if there was a number in front of the x squared?
Take the number out to make it x squared
At the end times everything by the numbers except from the. (x +2) part but still keep the number outside of the brackets
How do you solve fractional equations?
Treat like a normal addition or subtraction and put everything with a common denominator, including the answer
How do you find the x and y intercept of a graph
Y intercept = make x equal 0
X intercept = make y equal 0
How do you find the equation of the line of symmetry in a quadratic graph?
Go down the vertex
How do you find the x and y coordinate of the vertex from completing the square?
Y coordinate = make it an x squared + bx + c equation and it’ll be the c value
X coordinate = factorise it into two brackets and it is the x value
What happens when the graph y = x squared turns into y = (x + 1) squared?
It translates 1 to the left
What happens when the graph y = x squared turns into y = (x - 2) squared?
It goes right 2
What happens when the graph y = x squared turns into y = x squared + 3?
It goes up 3
What happens when the graph y = x squared turns into y = x squared - 2 ?
It goes down 2
How do you find the line of symmetry in completing the square?
a ( x + p ) squared + q
It is -p
How do you find the volume of a cone?
1/3 x pi x r squared x h
How do you find the volume of a sphere?
4/3 x pi x r cubed
How do you find the volume of a pyramid?
1/3 x base area x height
How do you find the curved surface area of a cone?
Pi x r x l
How do you find the surface area of a sphere?
4 x pi x r squared
What is the expression for an even number
2n
What is the expression for an odd number
2n + 1
What is the expression for a multiple of 3?
3n
What is the expression for a different odd number
Instead of 2n + 1 it is 2p + 1
What is the expression for a different even number
Instead of 2n it is 2p
What is the expression for a different multiple of 3
Instead of 3n it is 3p
What is the equation of a circle?
x squared + y squared = r squared
How would you solve gf(x)
Put the f into the g
What are the steps to finding the inverse function
1) replace f(x) with y
2) trade x and y places
3) make y the subject of the formula
4) y = inverse function of x
How do you do the transformations of graphs using functions?
When the number is in the brackets it goes left or right
When the number is out of the brackets it goes up or down
What happens in -f (x)
Reflect in the x axis
Make the y coordinate negative
What happens in y = f(-x)
Reflected on the y axis
Make the x coordinate negative
What does the sin graph look like?
Goes through x axis at 0, 180 and 360. It goes up then down then up
What does the cos graph look like?
Goes through the x axis at 90, 270 and 360. Goes up down up down.
Volume of cylinder
Pi r squared x height
What is the point where an exponential graph always crosses the y axis?
(0,1)
