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Mathematics > Equations > Flashcards

Equations Flashcards

1
Q

When you multiply decimals…

A

You make them whole numbers and divide by their place value

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2
Q

When you divide decimals

A

You only make the division whole and reciprocate this to the dividend then divide

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3
Q

Is 0.25 bigger than 0.4

A

No it’s smaller

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4
Q

What are significant figures used in vs decimals place

A

Measurements, precision whereas decimals places are used in currency

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5
Q

How do you find the HCF? And the LCM

A

All common factors multiplied together once then multiply rest for LCM

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6
Q

Formula for rate?

A

Rate= Volume/
Time

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7
Q

Fraction to decimal

A

Simplify and divide

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8
Q

Decimals to percentage

A

X100

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9
Q

Decimals to fraction for example 0.6?

A

How many place values after decimals point? 10 so 6 over 10 then simplify :)

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10
Q

To estimate what sf is it normally?

A

2 or 1 depends so you get 0s

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11
Q

How do you write an error interval

A

Less than or equal to x less than

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12
Q

What is 2.4 truncated to 1 dp?

A

WHOLE UNIT bigger- 2.4 to 2.5

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13
Q

To calculate upper bound?

A

UB over LB

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14
Q

Geometric progression equation?

A

N= a x r to the power of n-1

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15
Q

Inequalities- When you multiply or divide by negative number?

A

You flip the sign

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16
Q

Proof- consecutive numbers?

A

N, n+1, n+2

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17
Q

Two even numbers

A

2n, 2m

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18
Q

Two odd numbers

A

2n+1 and 2m +1

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19
Q

Consecutive even numbers

A

2n, 2n+2, 2n+4

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20
Q

Consecutive odd numbers

A

2n +1, 2n+3, 2n+5

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21
Q

Show 2⁴⁰ -1 as a product of two consecutive numbers

A

Difference of squares- (2²⁰-1)(2²⁰+1) so 2²⁰ is even, both are odd

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22
Q

Graph transformations- Inside? Y(x-3) if its x inside then…

A

Changes x so right to left
Does the opposite x +3

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23
Q

Outside if y= f(x) -3

A

Changes y so up or down and -3
Same

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24
Q

Percentage change

A

Change/
Original x100

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25
Q

Compound interest

A

Amount x multiplier ^time

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26
Q

Speed

A

Distance/ time km/h, m/s

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27
Q

Density

A

Mass over volume kg/m³, g/cm³

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28
Q

Pressure

A

Force/Area n/m²

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29
Q

When do you use cosine rule?Length,
Square root if needed

A

Non right angle triangle, 2 lengths and angle in between

a²-b²+c²-2bc cos(A)

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30
Q

Cosine(angle) all sides given

A

B²+c²-a²/2bc then cos-1(ans)

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31
Q

Sine rule- length

A

A/sinA =b/sinB

32
Q

Area with sine rule

A

½absinC

33
Q

Surface area of cylinder

A

2πrh + 2πr²

34
Q

Surface area of a sphere

A

4πr²

35
Q

Surface area of a cone

A

πrh + πr²

36
Q

Surface area of a cuboid

A

2lw+ 2wh+2lh

37
Q

Volume of a cylinder

A

πr²h

38
Q

Prism

A

Cross section x length

39
Q

Volume of a sphere

A

4/3 πr³

40
Q

Volume of a cone

A

⅓xπr² x h

41
Q

Frequency density?

A

Frequency/class width

42
Q

Akin spends 3/7 of his money to get a book and left with 220. Cost he spent?

A

1-3/7=4/7
4/7x=220
=385

43
Q

A man gave 1/3 to A, 1/5 to B and C is 35,000, find the total

A

1-1/3-1/5=7/15
7/15x=35000

44
Q

AND RULE-Independent events(tree diagrams)

A

Not affected each other.
P(A)xP(B)
E.g.if a ball is replaced
You roll a die and flip a coin

45
Q

Dependent events

A

P(A)xP(B after A)
Affected
E.g.non replacement

46
Q

Mutually exclusive OR RULE(tree diagrams)

A

P(A)+P(B)
Outcomes cannot happen at the same time
E.g.Rolling a six and 3

47
Q

Conditional probability(diagrams)

A

Probability of an event given another event has occurred so dependent on first outcome.
P(A|B) = P(AnB)/P(B)

48
Q

Non mutually exclusive=

A

P(A U B)= P(A)+P(B)- P(A n B)
Events which can occur together

49
Q

Venn diagrams- P(A and B’)=

A

P(A)=P(A n B)
So intersection

50
Q

√5 ÷√5

A

5

51
Q

2.4 as a fraction

A

Make denominator 10, multiply numerator by 10
12/5

52
Q

What is 3:2

A

for every 5 students , there are 3 girls and 2 boys

53
Q

20% of 3/5

A

Convert to fraction then simplify and multiply

54
Q

4 tanks, diameter 80cm, height 160cm
The 4 tanks will be filled completely with fertile and water in ratio 1 : 100 by volume. She has 32 litres of fertiliser.
1 litre =1000cm³. Does she have enough fertiliser?

A

31.85litres
π(40)²x 160
1 tank= 256000πcm³
4 tanks= 3216990.877cm³
You’re correct that the ratio is in volumes, which means we don’t technically need to convert to litres if we’re working in cm³ throughout. Since the ratio represents a comparison of volumes, it applies the same whether we’re working in cm³ or litres.

Let’s break it down without converting to litres, staying in cm³.

Step 1: Calculate the total volume of the tanks

We already know that the total volume of 4 tanks is 3,216,988 cm³.

Step 2: Use the ratio 1:100

The ratio 1:100 means that for every 101 parts of the mixture, 1 part is fertiliser and 100 parts are water.

So 1 over 101 times 3216.99 = fertiliser

55
Q

Interior angle of a regular polygon

A

N-2 x 180 /n
Where n is number of sides

56
Q

Exterior angle of a regular polygon

A

360/n

57
Q

Tom and ningi get money in ratio 5:3.Tom gets £70 more than ningi.
Work out how much each they recieve

A

T:A
5:3
+2 parts difference=£70

So 1 part is… £35 !

58
Q

F, L and J share money 2:4:3.Jam gets £90
Work out F and J amount

A

2:4:3
£90= 3 parts
£30=1part

59
Q

How do we know if fraction will recurring ot terminating? Prime factorised

A

Recurring- other than 2 or 5
Terminating- only 2 or 5

60
Q

(X ^½)² = (y³ z)²

A

Multiply each term by 2
So 1/2 x 2 is 1

61
Q

30% are in a football team. If the ratio of football team members to non is 1:4 how many students are in school ?

A

12+48 =60

62
Q

The mean of 8 numbers is 41.
The mean of 2 of the numbers is 29
Work out the mean of the other 6.

A

270/6 = 45

63
Q

Mowi ran a mean distance of 13m2km in 5 days. Next day he ran 20km. Find the mean distance, he ran in 6 days.

A

86/6=14.3 recurring km

64
Q

The mean

A

Is the average of all values

65
Q

A ninth of people are left handed.write ratio of left handed to right handed

A

1_ 1/9 =8/9
So 1/9÷8/9 to simplify is 1:8

66
Q

Independent tree diagrams- both tree diagrams are the same…

A

A counter is replaced
so both probabilities are the same for both picks.

67
Q

Conditional probability- dependent from the first event. Two counters from bag, if doesn’t say it is put back, assume he doesn’t. What is the denominator out of for 2nd pick?

A

2nd pick:
Red is 2/6
Blue 4/6
Red 3/6
Blue 3/6
Probability he take a red or blue counter

68
Q

Simple interest- same rate each year
£3000 at 5%, 5 years

A

Amount x % as decimal × years
= £750 this is the interest you earn
Final amount= £3750

69
Q

Compound interest- interest added on each year do we always add to 1.
£4000 for 3 years at a 2.4% compound interest per annum. After 3 years amount?

A

4000x1.024³ = 4294.97 This is the total amount he earns. If it asks for interest subtract both.

70
Q

Compound interest- £8000 in 3 years saving account. 2.4% compound interest in first year then 0.5% the following years. Amount after 3 years?

A

Calculate the years separately
Y1 8000 x 1.025= £8192
Y2 8192x1.005²= £8274.12

71
Q

£8000 for 3 years .x% and £8589.93 at the end of 3 years. Find x.

A

8000 x X³= 8589.93
÷8000
Cube root both sides
X= 1.023999818
So 2.4%( percentage)

72
Q

Each year the value of a car depreciates by 9%. After how many years will the value be worth 47% of its original value when new?

A

£100x0.91⁸= 47.03

73
Q

Vectors- number on top represents…

A

Left or right

74
Q

Vectors 3 over 6 and 1 over 2. Check if they are parallel and as a ratio.

A

3÷1=3
6÷2=3
3:1=6:2

75
Q

How to calculate smaller cone radius of cone?

A

Similar shapes- SF
E.g. Divide by 2
Radius of bigger÷ 2 so 7.5cm
Bigger- smaller cone

Mathematics (3 decks)

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