Mistakes I've made

Question 1

Gradient of a line going down

Answer 1

IS NEGATIVE!!!

Question 2

What is h in the trapezium rule?

Answer 2

The width of each bar, not the number of strips.

Question 3

If ff(x) = x

Answer 3

Then f^-1 (x) = f(x)

Question 4

If they ask to give a formula in a certain way

Answer 4

Then give it in that way- how hard is that?

Question 5

Places I tend to make the most mistakes- so be VERY careful here

Answer 5

Inputting limits into an integration equation.

Question 6

How to go from 1/x to 1/3x-6?

Answer 6

Stretch by a scale factor of 1/3 parallel to the x-axis.

And translate by 6 units to the positive x-direction.

Question 7

Total moment?

Answer 7

Make sure to include the direction - anti-clockwise etc?

Question 8

Any possible sequences questions

Answer 8

You have to give a statement explaining what the numbers mean.

Question 9

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?

Answer 9

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.

Question 10

Explaining why (x+5) etc. is a factor of f(x)

Answer 10

By the factor theorem, it is a factor

Question 11

Projectiles: if an object is falling down from a certain height, then y = original height - etc!!!

Answer 11

!!!

Question 12

How to identify a negative skew?

Answer 12

It is more right-sided.

Question 13

Reasons for why the Newton- Raphson method fails?

Answer 13

• Gradient is zero, so tangent never touched the x-axis.

- Being right next to the turning point, so it converges to a larger root.

Question 14

Weaknesses in selecting a sample

Answer 14

Sample isn’t random
Have they removed any outliers?
Is the removal of the outliers justifiable?

Question 15

Explain why something generates a simple random sample?

Answer 15

Each group has the same chance of being picked.

Question 16

State a modelling assumption that is necessary to be able to use binomial distribution

Answer 16

That the events are independent of each other.

Question 17

How to calculate unit vector

Answer 17

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.

Question 18

Features of data which means you can model it as Normal Distribution

Answer 18

The median is nearly equal to the mean.

And the quartiles are symmetrical about the mean.

Question 19

Define population

Answer 19

All the individuals that can be chosen.

Question 20

Define a sample

Answer 20

A set of items chosen from a population.

Question 21

What is discrete data

Answer 21

It can take a specific value.

Question 22

What is continuous data?

Answer 22

It can be any value, so in between 2 discrete values.

Question 23

How to identify an outlier?

Answer 23

It must be 2 s.d away from the mean.
OR
1.5 IQR from the nearest quartile.

Question 24

For mutual exclusive events, P(A n B) =

Answer 24

0.

Question 25

When to use binomial distribution

Answer 25

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”

Question 26

What does “mutually exclusive” mean?

Answer 26

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.

Question 27

What to make sure about when doing Newton Raphson method

Answer 27

Make sure your calculator is always in radians.

Question 28

If you see a complicated ln(…) or e^ … expression

Answer 28

SPLIT IT UP!!!

Question 29

Whenever in doubt- especially for proof questions-

Answer 29

See if you can form a quadratic expression.

Question 30

For proof questions - talking about prime numbers

Answer 30

Quite likely to just throw in numbers till you can prove or disprove the statement.

Question 31

Hypothesis testing questions

Answer 31

Be careful! And define the probability or the mean clearly.

Is it population mean or sample mean?

Question 32

To calculate the domain of a composite function

Answer 32

Of fg (x)
Calculate the domain of g(x) and any values for which the composite function may not work for.

Question 33

For iterative equations- you have to use the

Answer 33

Equation of the gradient.

Question 34

Probability questions - when you have to find out how many times to repeat something to get a certain percentage

Answer 34

(1-p)^n = 1-%.

Question 35

How to calculate midrange

Answer 35

It is the max+ min/2

Question 36

Usefulness of mean, median and mode

Answer 36

Mean:

• Uses all values.
• Can be affected by any outliers

Median:
- No affected by outliers

Mode:

• Not affected by outliers
• Can be bimodal though.