GCSE Flashcards
(104 cards)
1
Q
Area of a parallelogram
A
Base x perpendicular height
2
Q
Area of a trapezium
A
1/2 (a + b) x h, half the sum of the parallel sides times the distance between them
3
Q
Area of kite
A
Width x height / 2
4
Q
Area of circle
A
Pi r squared
5
Q
Circumference of circle
A
2 x pi x r
6
Q
Area of sector
A
Theta / 360 x pi x r squared
7
Q
Length of an arc
A
Theta / 360 x 2 x pi x r
8
Q
Volume of prism
A
Area of cross section x length
9
Q
Volume of pyramid
A
1/3 x base area x height
10
Q
Volume of a cone
A
1/3 x pi r squared x h
11
Q
Volume of sphere
A
4/3 x pi r cubed
12
Q
Volume of frustum
A
Vol of A - vol of B
13
Q
Curved surface area of a cone
A
Pi x r x l, to find l, l = h squared + r squared
14
Q
Surface area of sphere
A
4 x pi r squared
15
Q
What is the nth term for arithmetic sequences?
A
An + b
A being the common difference
n being the position
b being the zero term
16
Q
What is the nth term for quadratic sequences
A
an squared + bn + c
17
Q
What is the nth term for geometric sequences
A
a x r to the n - 1
a being the first term
r being the common ratio
n being position
18
Q
How do you calculate the median position?
A
n + 1 / 2
19
Q
How do you find the lower quartile?
A
n + 1 / 4
20
Q
How do you calculate the upper quartile?
A
3(n + 1) / 4
21
Q
What is the formula for suitable degree of accuracy?
A
M = square root of s / t
22
Q
How do you do suitable degree of accuracy?
A
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
23
Q
In corresponding angles…
A
They are equal ( F shape)
24
Q
In alternate angles….
A
They are equal ( Z shape)
25
In co-interior angles...
The angles add to 180° (c shape)
26
What must you remember for bearings?
3 DIGITS, eg. 005°
27
What is estimation
Rounding to 1 sf
28
Pressure =
Force / area FAP
29
Density =
mass / volume MVD
30
Speed =
Distance / time DST
31
What is conditional probability?
The probably of subsequent events depends on previous events occurring
32
What is the probability of b given a
P ( B | A )
33
P(not A)
1 - P (A)
34
P (A or B)
P(A) + P(B)
35
What is A n B
A intersection B = A and B = where’s you ge hashing
36
A u B
A union B = A or B = everything in the circles
37
A ‘
A complement = Not A
38
What is translation?
Slide
39
What is enlargement?
Change in size, centre of enlargement, scale factor
40
Acceleration =
Final velocity - initial velocity / time
41
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
```
42
What is the formula for direct proportion?
y = kx
k is the constant of proportionality
43
What is the formula for inverse proportion?
y Jesus fish 1/x
| y = k/x
44
y is directly proportional to the square of x
y = kx squared
| y fish x squared
45
Y is directly proportional to the cube of x
y fish x cubed
| y = kx cubed
46
Y is directly proportional to the square root of x
y fish root x
| y = k root x
47
y is inversely proportional to the square of x
y fish 1/x squared
| y = k/x squared
48
Formula for sampling
Sample size / population size x number he chooses to sample
49
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
50
How do you calculate frequency for histograms?
Frequency = F.D x width
51
What is an equation
It can be solved
52
What is an expression
Terms without an equals sign
53
What is a formula
An algebraic rule we substitute numbers into
54
How do you find the area of a triangle
1/2 x a x b x sinC
55
How do you find the height of a triangle
a x sinC
56
What is the sine rule for finding missing lengths
a / sin a = b / sin b = c / sin c
57
What is the sine rule for finding missing angles
Sin a / a = sin b / b = sin c / c
58
What is the cosine rule for finding missing sides
a squared = b squared + c squared - 2 x b x c x CosA
59
What is the cosine rule for finding missing angles
cosA = b squared + c squared - a squared / 2 x b x c
60
What does a positive and negative quadratic graph look like?
```
Positive = smile
Negative = sad face
```
61
What does a positive and negative reciprocal graph look like
Negative gradient in a quadrat
62
What does a positive and negative cubic graph look like
p- Up and down and up
| n- Down and up and down
63
What does an exponential graph look like?
Curve up but never touches 0
64
How do you do the upper bound and lower bound for dividing?
```
UB = UB / LB
LB = LB / UB
```
65
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
66
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
67
What is the probability of b given a? (Conditional probability)
P ( A n B ) / P (A)
68
Surface area of a cylinder
2 pi r squared + 2 x pi x r x l
69
How do you do frequency polygons?
- plot in middle of the group
| - straight lines joining points
70
How do you find the y intercept of a quadratic graph
y = ax squared + bx + c
It is the c part of the equation
71
What is a positive quadratic and negative quadratic in terms of minimum and maximum points?
Positive- minimum, no maximum
| Negative- no minimum, maximum
72
What is the quadratic formula?
- b +/- root b squared - 4 x a x c
Divided by 2a
73
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
74
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
75
How do you solve fractional equations?
Treat like a normal addition or subtraction and put everything with a common denominator, including the answer
76
How do you find the x and y intercept of a graph
Y intercept = make x equal 0
| X intercept = make y equal 0
77
How do you find the equation of the line of symmetry in a quadratic graph?
Go down the vertex
78
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
79
What happens when the graph y = x squared turns into y = (x + 1) squared?
It translates 1 to the left
80
What happens when the graph y = x squared turns into y = (x - 2) squared?
It goes right 2
81
What happens when the graph y = x squared turns into y = x squared + 3?
It goes up 3
82
What happens when the graph y = x squared turns into y = x squared - 2 ?
It goes down 2
83
How do you find the line of symmetry in completing the square?
a ( x + p ) squared + q
It is -p
84
How do you find the volume of a cone?
1/3 x pi x r squared x h
85
How do you find the volume of a sphere?
4/3 x pi x r cubed
86
How do you find the volume of a pyramid?
1/3 x base area x height
87
How do you find the curved surface area of a cone?
Pi x r x l
88
How do you find the surface area of a sphere?
4 x pi x r squared
89
What is the expression for an even number
2n
90
What is the expression for an odd number
2n + 1
91
What is the expression for a multiple of 3?
3n
92
What is the expression for a different odd number
Instead of 2n + 1 it is 2p + 1
93
What is the expression for a different even number
Instead of 2n it is 2p
94
What is the expression for a different multiple of 3
Instead of 3n it is 3p
95
What is the equation of a circle?
x squared + y squared = r squared
96
How would you solve gf(x)
Put the f into the g
97
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
98
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
99
What happens in -f (x)
Reflect in the x axis
Make the y coordinate negative
100
What happens in y = f(-x)
Reflected on the y axis
Make the x coordinate negative
101
What does the sin graph look like?
Goes through x axis at 0, 180 and 360. It goes up then down then up
102
What does the cos graph look like?
Goes through the x axis at 90, 270 and 360. Goes up down up down.
103
Volume of cylinder
Pi r squared x height
104
What is the point where an exponential graph always crosses the y axis?
(0,1)
