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1
Q

A^0

A

1

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2
Q

A^-n

A

1/a^n

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3
Q

A^1/n

A

N root a

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4
Q

A^m/n

A

(N root a) ^m

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5
Q

A^-1

A

1/a

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6
Q

A^1/2

A

Root a

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7
Q

Power law fractions

A

Apply the power to the top and bottom

(15/7)^2 = 15^2/7^2

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8
Q

Power law negative power

A

Turn it upside down and take the positive power

E.g. (5/8)^-2=8^2/5^2

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9
Q

Trapezium area

A

1/2(a+b)h

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10
Q

Prism volume

A

Area of cross section x length

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11
Q

Cylinder volume

A

Pi r^2 h

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12
Q

Pyramid volume

A

1/3 x area of base x h

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13
Q

Speed

A

Distance/time

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14
Q

Density

A

Mass/volume

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15
Q

Pressure

A

Force/area

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16
Q

Pythagoras

A

A2+b2=c2

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17
Q

Sin area of a triangle

A

1/2ab sinC

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18
Q

Cosine rule

A

a2 = b2+c2-2bc(cosA)
CosA = b2+c2-a2
————
2bc

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19
Q

Co interior angle

A

180 degrees total

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20
Q

Corresponding angle

A

Same angle

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21
Q

Alternate angle

A
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22
Q

Congruent

A

Same shape and size but not facing the same way

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23
Q

Similar

A

Same shape but different size

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24
Q

Percentage change

A

(Difference/original) x 100

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25
Q

Difference of 2 squares

A

A2-b2=(a+b)(a-b)

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26
Q

State whether the following expressions represent length, area or volume
A) 2(x+y+z) b)xyz c)x2+z2

A

A) length
B) volume
C) area

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27
Q

Inequality

A

Same as normal equation

If you multiply/divide by negative number remember to flip inequality sign

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28
Q

Multiplying 2 powers

A

Add them

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29
Q

Dividing 2 powers

A

Subtract them

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30
Q

Raising 1 power to another (4^3)^4=4^12

A

Multiply them

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31
Q

Anything to the power of 1

A

Is itself

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32
Q

Anything to the power of 0

A

Is 1

33
Q

1 to the power of anything

A

Is 1

34
Q

Circle labelled

A
35
Q

frequency polygon

A

Find the midpoint of the category. 2to4 = 3
Multiply the midpoint and frequency. Frequency=6 3x6=18
Plot the points (midpoint,frequency) and join them up with a straight line (3,6)

36
Q

Midpoint of a line

A

(X1+x2. Y1+y2)
——— , ———
2. 2

37
Q

Completing the square

A

X2+bx+c = (x+b/2)^2 - (b/2)^2 + c

38
Q

Turning point

A

Once you’ve complete square turning point equals b/2 with a reverse sign so + if it was - and vice versa
Y=(b/2)^2 + c
E.g. (x-3)^2 - 16 = 0
Turning point: (3,-16)

39
Q

Inequalities square roots

A

2 solutions!

X2<36=-6

40
Q

Compound growth decay

A

No(1+-r/100)^n

No = initial amount
+ or - depends if increase or decrease
R= percentage
N= number of periods

41
Q

When products of factors = 0

A

At least one factor is 0

42
Q

Quadratic factorising

A

Ax^2 + bx + c =0
Add to make b and multiply to make c

When a = 1
(X ) (x ) = 0

When a>1
(Ax ) (x ) = 0

43
Q

Vector in opposite direction

A

Put a ‘-‘ infront

44
Q

X1. X2
+
Y1. Y2

A

X1+x2

Y1+y2

45
Q

X1. X2
-
Y1. Y2

A

X1-x2

Y1-y2

46
Q

C(x1

Y1)

A

Cx1

Cy1

47
Q

Simultaneous equations elimination

A
  • rearrange both equations so they’re in the format ax + by = c
  • multiply+eliminate+solve
48
Q

Substitution simultaneous equations

A

Make either x or y the subject of one of these two formulas and sub into the other equation

49
Q

Direct proportion

A

Y=kx

50
Q

Class width

A

Upperclass - lowerclass

51
Q

CLass boundaries

A

-value in between each interval

I.e 41-50 = 50.5
51-60 = 60.5
61-70= 70.5

52
Q

Simultaneous equations graphically

A
  • draw both graphs

- where they intersect = solution

53
Q

Frequency density

A

Frequency / class width

54
Q
A

Angle in a semi circle is 90 degrees

55
Q

Circle theorems - circumference centre

A

Angle at circumference is half the angle at the centre

56
Q

Radius tangent circle theorem

A

Angle between radius and tangent is 90 degrees

57
Q

Alternate segment circle theorem

A

Angle between chord and tangent is equal to opposite angle inside the triangle

58
Q

Same segment from chord circle theorem

A

angles in the same segment from a common chord are equal

59
Q

Cyclic quadrilateral circle theorem

A

Opposite angles in a cyclic quadrilateral add up to 180

60
Q

Tangent circle theorem

A
61
Q

Radius chord circle theorem

A
62
Q

Histogram

A

Looks like a bar chart

63
Q

Frequency of histogram

A

Area of bar

64
Q

What are the x and y axis in a histogram

A 
X= height 
Y= frequency density
65
Q

Median histogram

A

add up all the frequencies and add one then divide by 2. You then see what region that is in for which frequency column. You then see how many numbers in the frequency it is out of the total. Divide that by the total to give a percent. As a percentage of the width. Use class width and find the percentage of that is. Add that to the starting bit of the like total width

66
Q

Quartile ranges for histogram

A

Same as median

67
Q

Mean of histogram

A

multiply midpoint of each group by the frequency. Add them all together and divide by the total frequency.

68
Q

Assumptions in similar triangles

A

All of the angles are the same

If triangles are similar then the corresponding sides are in the same ratio

69
Q

Iterations between x=0 and x=1

A

show tht the first x is too low and the second x is too high.

70
Q

Average speed

A

Total distance/ total time

71
Q

Dividing 2 fractions

A

Flip 2nd fractions so it’s multiplying and you can cross cancel numerator of one with the denominator of the other

72
Q

Product rule for counting

A

find the total number of outcomes for two or more
events, multiply the number of outcomes for each event
together.

73
Q

If it’s like how many of them will have different digits

A

So number of options first time and then minus one and that’s the number of options next then minus one for number of options for the 3rd digit and then multiply them together

E.g. how many possible three digit numbers have 3 different digits from 5 options
= 5 x 4 x 3

74
Q

Ratio dependent probability 1

A
75
Q

2

A
76
Q

3

A
77
Q

Vectors a whengiven coordinates

A
78
Q

Working out vectors as column vectors from grids

A

Maths (1 decks)

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