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GCSEs > Maths > Flashcards

Maths Flashcards

1
Q

sin 0°

A

0

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2
Q

sin 30°

A

1/2

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3
Q

sin 45°

A

√2/2

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4
Q

sin 60°

A

√3/2

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5
Q

sin 90°

A

1

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6
Q

sin =

A

opposite / hypotenuse

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7
Q

cos =

A

adjacent / hypotenuse

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8
Q

tan =

A

opposite / adjacent

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9
Q

tan-1(opp/adj) is an example of how to find..

A

an angle

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10
Q

tan30 = opp/adj is an example of how to find..

A

a side

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11
Q

Density =

A

Mass/volume

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12
Q

Cosine rule

A

a² = b² +c² - (2bcCosA)

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13
Q

Cosine rule for angles

A

CosA = b² + c² - a² / 2bc

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14
Q

Area of triangle using trigonometry

A

1/2abSinC

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15
Q

Sine rule

A

SinA/a = SinB/b = SinC/c

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16
Q

x² - 25 factorised

A

(x+5)(x-5)

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17
Q

Quadratic formula

A

−b ± √b² −4ac
_____________
2a

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18
Q

Tan30

A

1/√3

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19
Q

Tan 45

A

1

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20
Q

Tan60

A

√3

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21
Q

Cos30

A

√3/2

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22
Q

Angle at centre theorem

A

The angle at the centre is twice the size the angle at the circumference

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23
Q

The angle in a semi - circle is

A

A right angle

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24
Q

Angles in the same segments are

A

Equal

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25
Q

Opposite angles in a cyclic quadrilateral..

A

Sum up to 180°

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26
Q

Relationship between a tangent and a radius

A

They are perpendicular

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27
Q

Angles in alternate segments are

A

Equal

28
Q

Tangents from a point are

A

Equal

29
Q

Conditions for congruent triangles

A

SSS
ASA
SAS
RHS

30
Q

When are triangles similar?

A

When all the angles are the same but the sides are different sizes

31
Q

What are bearings?

A

3 digit angles measured in a clockwise direction from north

32
Q

How to prove if 3 points are collinear

A

• The vectors are parallel
• The vectors share a common point

33
Q

Mutually exclusive events

A

Events that cannot happen together

34
Q

Independent events

A

Events whose outcomes do not affect each other

35
Q

Sample

A

A collection taken from a larger group

36
Q

Stratified sampling

A

Using the ratios between a given sample and population to create a new sample

37
Q

Upper quartile is equal to

A

75%

38
Q

Lower quartile is equal to

A

25%

39
Q

Formula to calculate median

A

(n+1) / 2

40
Q

Calculating the possible original number after 27000 is the rounded number to 2sf

A

• 2nd sf is 7
• 7 is in the thousands column
• 1000/2 = 500
• +/- 500
• 26500 - 27500

41
Q

Interpreting box plots

A

• Compare the medians
• Compare the interquartile ranges
(Smaller IQR = consistent distribution)

42
Q

Positive quadratic equations on a graph look like a

A

U

43
Q

Truncation

A

Cutting off the numbers after a decimal place
eg 9.999 becomes 9

44
Q

Curved surface area of cylinder formula

A

2πrh

45
Q

Calculate HCF

A

Multiply the common prime factors between both numbers (each number only being counted once)
(A ∩ B)

46
Q

Calculate LCM

A

Multiply all the prime factors between both numbers (with the common ones being counted once)
(A ∪ B)

47
Q

Equation of a circle

A

x² + y² = r²

48
Q

Equation of a circle with (a,b) as centre

A

(x - a)² + (y - b)² = r²

49
Q

Completing the square:
How would you factorise 3x² + 18x - 1?

A

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

50
Q

How do you work out acceleration in a velocity time graph?

A

The gradient of the line

51
Q

How do you work out distance in a velocity time graph?

A

The area under the graph

52
Q

What points need to be considered when describing an enlargement?

A

• Type of transformation
• Scale factor
• Centre of enlargement

53
Q

What points need to be considered when describing an enlargement?

A

• Type of transformation
• Scale factor
• Centre of enlargement

54
Q

What points need to be considered when describing a rotation?

A

• Angle of rotation
• Direction (clockwise or anti clockwise)
• The point it’s about

55
Q

What points need to be considered when describing a rotation?

A

• Angle of rotation
• Direction (clockwise or anti clockwise)
• The point it’s about

56
Q

Invariant vertex

A

Points that don’t change position after a transformation

57
Q

What does 5! mean?

A

• 5 factorial
• 5 x 4 x 3 x 2 x 1

58
Q

Calculate inverse function of f(x) = 2x² - 7

A

Switch y with x
• y = 2x² - 7
• x = 2y² - 7

Make y subject
= y = root x + 7
————— = Ans
2

59
Q

Work out gf(x) when f(x) = 2x + 1 and g(x) = x² + 1

A

• f(x) = 2x + 1
• g(2x+1) = (2x + 1)² + 1
• gf(x) = 4x² + 4x + 2

60
Q

Make f the subject in d = 3(1-f)
————
f - 4

A

• d(f-4) = 3(1-f)
• df- 4d = 3 - 3f
• df + 3f = 4d + 3
• f(d+3) = 4d + 3

f = 4d+ 3
———-
d + 3

61
Q

How to work out mean with intervals and frequency

A

• 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

62
Q

What are irrational numbers?

A

Numbers that can’t be expressed as a fraction eg e

63
Q

What would you do to rationalise 5
—— ?
7 + √3

A

5 7 - √3
———- x ——— 7 + √3 7 - √3

64
Q

Formula for geometric sequences|
with example: 2, 6, 18, 54

A

• a x r ^n-1
• Answer = 2 x 3 ^n-1

65
Q

Work out nth term for 3,9,17,27 (quadratic sequence)

A

• 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

66
Q

Factorise 3x² + 8x + 4

A

(3x + 6) (3x + 2) ———————
3
=
(x + 2) (3x + 2)

GCSEs (21 decks)

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