Mistakes I've made Flashcards
Gradient of a line going down
IS NEGATIVE!!!
What is h in the trapezium rule?
The width of each bar, not the number of strips.
If ff(x) = x
Then f^-1 (x) = f(x)
If they ask to give a formula in a certain way
Then give it in that way- how hard is that?
Places I tend to make the most mistakes- so be VERY careful here
Inputting limits into an integration equation.
How to go from 1/x to 1/3x-6?
Stretch by a scale factor of 1/3 parallel to the x-axis.
And translate by 6 units to the positive x-direction.
Total moment?
Make sure to include the direction - anti-clockwise etc?
Any possible sequences questions
You have to give a statement explaining what the numbers mean.
If a graph is concave upwards, and you have used the trapezium rule to figure out the area of it, is it an overestimate, or an underestimate?
It is an overestimate.
A curve which is concave upwards forms a U.
So, the tops of the trapezia are above the curve and so the trapezia include extra area.
Explaining why (x+5) etc. is a factor of f(x)
By the factor theorem, it is a factor
Projectiles: if an object is falling down from a certain height, then y = original height - etc!!!
!!!
How to identify a negative skew?
It is more right-sided.
Reasons for why the Newton- Raphson method fails?
- Gradient is zero, so tangent never touched the x-axis.
- Being right next to the turning point, so it converges to a larger root.
Weaknesses in selecting a sample
Sample isn’t random
Have they removed any outliers?
Is the removal of the outliers justifiable?
Explain why something generates a simple random sample?
Each group has the same chance of being picked.
State a modelling assumption that is necessary to be able to use binomial distribution
That the events are independent of each other.
How to calculate unit vector
Find the vector.
Then, find the magnitude of the vector.
Divide the vector by the magnitude vector.
And then put into I,j,k vector.
Features of data which means you can model it as Normal Distribution
The median is nearly equal to the mean.
And the quartiles are symmetrical about the mean.
Define population
All the individuals that can be chosen.
Define a sample
A set of items chosen from a population.
What is discrete data
It can take a specific value.
What is continuous data?
It can be any value, so in between 2 discrete values.
How to identify an outlier?
It must be 2 s.d away from the mean.
OR
1.5 IQR from the nearest quartile.
For mutual exclusive events, P(A n B) =
0.
When to use binomial distribution
An experiment happens a certain number of times.
There are only 2 outcomes, success or fail.
The probability of success is the same every time.
The probability of success is independent of what has happened in previous trials.
The random variable of interest is the “the number of success”
What does “mutually exclusive” mean?
It means that they cannot occur at the same time.
On a venn diagram, this is the same as saying that the 2 circles don’t overlap.
What to make sure about when doing Newton Raphson method
Make sure your calculator is always in radians.
If you see a complicated ln(…) or e^ … expression
SPLIT IT UP!!!
Whenever in doubt- especially for proof questions-
See if you can form a quadratic expression.
For proof questions - talking about prime numbers
Quite likely to just throw in numbers till you can prove or disprove the statement.
Hypothesis testing questions
Be careful! And define the probability or the mean clearly.
Is it population mean or sample mean?
To calculate the domain of a composite function
Of fg (x) Calculate the domain of g(x) and any values for which the composite function may not work for.
For iterative equations- you have to use the
Equation of the gradient.
Probability questions - when you have to find out how many times to repeat something to get a certain percentage
(1-p)^n = 1-%.
How to calculate midrange
It is the max+ min/2
Usefulness of mean, median and mode
Mean:
- Uses all values.
- Can be affected by any outliers
Median:
- No affected by outliers
Mode:
- Not affected by outliers
- Can be bimodal though.
