Equations Flashcards by Melanie Mazalrey

When you multiply decimals…

You make them whole numbers and divide by their place value

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When you divide decimals

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

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Is 0.25 bigger than 0.4

No it’s smaller

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What are significant figures used in vs decimals place

Measurements, precision whereas decimals places are used in currency

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How do you find the HCF? And the LCM

All common factors multiplied together once then multiply rest for LCM

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Formula for rate?

Rate= Volume/
Time

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Fraction to decimal

Simplify and divide

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Decimals to percentage

X100

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Decimals to fraction for example 0.6?

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

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To estimate what sf is it normally?

2 or 1 depends so you get 0s

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How do you write an error interval

Less than or equal to x less than

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What is 2.4 truncated to 1 dp?

WHOLE UNIT bigger- 2.4 to 2.5

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To calculate upper bound?

UB over LB

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Geometric progression equation?

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

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Inequalities- When you multiply or divide by negative number?

You flip the sign

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Proof- consecutive numbers?

N, n+1, n+2

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Two even numbers

2n, 2m

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Two odd numbers

2n+1 and 2m +1

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Consecutive even numbers

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

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Consecutive odd numbers

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

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Show 2⁴⁰ -1 as a product of two consecutive numbers

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

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

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

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Outside if y= f(x) -3

Changes y so up or down and -3
Same

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Percentage change

Change/
Original x100

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Compound interest

Amount x multiplier ^time

Speed

Distance/ time km/h, m/s

Density

Mass over volume kg/m³, g/cm³

Pressure

Force/Area n/m²

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

Non right angle triangle, 2 lengths and angle in between a²-b²+c²-2bc cos(A)

Cosine(angle) all sides given

B²+c²-a²/2bc then cos-1(ans)

Sine rule- length

A/sinA =b/sinB

Area with sine rule

½absinC

Surface area of cylinder

2πrh + 2πr²

Surface area of a sphere

4πr²

Surface area of a cone

πrh + πr²

Surface area of a cuboid

2lw+ 2wh+2lh

Volume of a cylinder

πr²h

Prism

Cross section x length

Volume of a sphere

4/3 πr³

Volume of a cone

⅓xπr² x h

Frequency density?

Frequency/class width

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

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

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

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

AND RULE-Independent events(tree diagrams)

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

Dependent events

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

Mutually exclusive OR RULE(tree diagrams)

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

Conditional probability(diagrams)

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

Non mutually exclusive=

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

Venn diagrams- P(A and B')=

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

√5 ÷√5

2.4 as a fraction

Make denominator 10, multiply numerator by 10 12/5

What is 3:2

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

20% of 3/5

Convert to fraction then simplify and multiply

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?

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

Interior angle of a regular polygon

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

Exterior angle of a regular polygon

360/n

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

T:A 5:3 +2 parts difference=£70 So 1 part is... £35 !

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

2:4:3 £90= 3 parts £30=1part

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

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

(X ^½)² = (y³ z)²

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

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

12+48 =60

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

270/6 = 45

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

86/6=14.3 recurring km

The mean

Is the average of all values

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

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

Independent tree diagrams- both tree diagrams are the same...

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

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?

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

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

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

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?

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

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?

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

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

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

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?

£100x0.91⁸= 47.03

Vectors- number on top represents...

Left or right

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

3÷1=3 6÷2=3 3:1=6:2

How to calculate smaller cone radius of cone?

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