Equations Flashcards
When you multiply decimals…
You make them whole numbers and divide by their place value
When you divide decimals
You only make the division whole and reciprocate this to the dividend then divide
Is 0.25 bigger than 0.4
No it’s smaller
What are significant figures used in vs decimals place
Measurements, precision whereas decimals places are used in currency
How do you find the HCF? And the LCM
All common factors multiplied together once then multiply rest for LCM
Formula for rate?
Rate= Volume/
Time
Fraction to decimal
Simplify and divide
Decimals to percentage
X100
Decimals to fraction for example 0.6?
How many place values after decimals point? 10 so 6 over 10 then simplify :)
To estimate what sf is it normally?
2 or 1 depends so you get 0s
How do you write an error interval
Less than or equal to x less than
What is 2.4 truncated to 1 dp?
WHOLE UNIT bigger- 2.4 to 2.5
To calculate upper bound?
UB over LB
Geometric progression equation?
N= a x r to the power of n-1
Inequalities- When you multiply or divide by negative number?
You flip the sign
Proof- consecutive numbers?
N, n+1, n+2
Two even numbers
2n, 2m
Two odd numbers
2n+1 and 2m +1
Consecutive even numbers
2n, 2n+2, 2n+4
Consecutive odd numbers
2n +1, 2n+3, 2n+5
Show 2⁴⁰ -1 as a product of two consecutive numbers
Difference of squares- (2²⁰-1)(2²⁰+1) so 2²⁰ is even, both are odd
Graph transformations- Inside? Y(x-3) if its x inside then…
Changes x so right to left
Does the opposite x +3
Outside if y= f(x) -3
Changes y so up or down and -3
Same
Percentage change
Change/
Original x100
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
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
