VCE General & Further Maths Question Thread!

[random_person]

Recall that:

x

x

=

= x

= x

This is a 20% reduction. A

[n.a]

Sorry to be annoying, but why is 0.8 x actual figure a 20% reduction? What am I missing?

[Aaron]

Sorry to be annoying, but why is 0.8 x actual figure a 20% reduction? What am I missing?

100% of something is the original amount (e.g. 1.0). 0.8 = 80% (100-80=20) of the existing amount.

Same situation where 200% of something is double the original (2x)

[n.a]

OMG thanks! I felt so dumb...I realised the answer seconds after I posted the question. Must be my sleep signals messing with my brain. Thanks Aaron and random_person! 

[random_person]

If you are unsure, you can plug in a value for the actual figure. It can be any value, but use 100 (Makes calculations much easier).

= x

We want to make the actual figure 100 (Any value to work out the percentage reduction).

= x =

Now, because the number has gone down from 100 to 80, it has decreased by 20. Right?

So, now we can work out the percentage that it has decreased.

% = x = % reduction.

This is a really long way, but if you are unsure, you can keep doing it this way! Make up any value for the actual value and it will work

[n.a]

Thanks so much! I get it now! You're a great teacher,  .

[AngelWings]

In regard to that question, n.a., it also appeared in 2011 Exam 1 somewhere if I recall correctly. Check that out too for extra practice!

[I am a unicorn]

Hello

For part (d) of this textbook question I having some trouble... What is a residual plot?
The book doesn't explain it very well

The table below shows the scores obtained by nine students on two tests. We want to be able to predict Test B scores from Test A scores.
Test A score (x) 18 15 9 12 11 19 11 14 16
Test B score (y) 15 17 11 10 13 17 11 15 19
Use your calculator to perform each of the following steps of a regression analysis.
a Construct a scatterplot. Name the variables test a and test b.
b Determine the equation of the least squares line along with the values of r and r 2.
c Display the regression line on the scatterplot.
d Obtain a residual plot.

Thankyou

[Peanut Butter]

Hello

For part (d) of this textbook question I having some trouble... What is a residual plot?
The book doesn't explain it very well

The table below shows the scores obtained by nine students on two tests. We want to be able to predict Test B scores from Test A scores.
Test A score (x) 18 15 9 12 11 19 11 14 16
Test B score (y) 15 17 11 10 13 17 11 15 19
Use your calculator to perform each of the following steps of a regression analysis.
a Construct a scatterplot. Name the variables test a and test b.
b Determine the equation of the least squares line along with the values of r and r 2.
c Display the regression line on the scatterplot.
d Obtain a residual plot.

Thankyou

This can easily be done on your calculator

Once you have set up your scatterplot: click menu > analyse (4) > residuals (7) > residual plot (2)

Your residual plot will then appear!!

[StupidProdigy]

This can easily be done on your calculator

Once you have set up your scatterplot: click menu > analyse (4) > residuals (7) > residual plot (2)

Your residual plot will then appear!!

You can also get the residual plot by changing the variable on the y axis to 'stat.resid' (I think it's called that..) if you're using a ti-nspire

[random_person]

 What is a residual plot?

The question asked what is a residual plot, but thanks for showing how to do it on a calculator

What is a residual plot?
A residual plot tells you how far each data value is away from your line of best fit. So, lets say your trend line passes through (4, 5) and your actual data value is at (4, 3) then the actual value is two units below the trend line, right? So on your residual plot, you would have a value at (0, -2). We then do this with all the actual values and plot them on the graph.

What is a residual plot used for?
A residual plot is used to determine whether a certain mathematical model is the best way of representing the data. For this, we look for patterns in the residual plot. If there is a pattern, then we need to apply a transformation to either the x or y axis. In further, you learn x^2, 1/x and log(x) transformations (and after you transform all your x/y values then find a new line of best fit and see if the residual plot shows a random pattern for the new model).

Hope this helps!

[n.a]

Hi,  I'm back!

Can someone have a look at the 2010 Exam 1? I'm wondering about the following questions:

1. Question 3. Can someone explain how to do that please?
2. Question 8. The correct answer is B, but I was pretty darn sure it was C. Isn't the y-intercept at 167? Am I reading it wrong?
3. Question 9. I got the answer right, but just generally, when doing a question like that, am I just supposed to sort of see a similar pattern between the actual data and the residual plots? Is that how it works? Coz that's what I've been doing....but is there a better way?

Thanks!

[BakedDwarf]

Is the distribution of this histogram bimodal? If not, what is it?

[random_person]

Hi,  I'm back!

Can someone have a look at the 2010 Exam 1? I'm wondering about the following questions:

1. Question 3. Can someone explain how to do that please?
2. Question 8. The correct answer is B, but I was pretty darn sure it was C. Isn't the y-intercept at 167? Am I reading it wrong?
3. Question 9. I got the answer right, but just generally, when doing a question like that, am I just supposed to sort of see a similar pattern between the actual data and the residual plots? Is that how it works? Coz that's what I've been doing....but is there a better way?

Thanks!

Question 3

Question 3 Stimulus

Question 3

The 68% 95% 99.7% rule tells us that in a normally distributed data set:
68% of the data is within 1 standard deviation
95% of the data is within 2 standard deviations
99.7% of the data is within 3 standard deviations.

Because the question is asking you to use this rule, we say that the data is approximately normally distributed. Now using the boxplot, we can see that the median is 180 degrees. In a normally distributed data set, the mean=median. So the mean is 180 degrees. To find the standard deviation, we can find the interval which 68% of the data values lie. Approximately 38% of the data lie between 179 and 181 so 1 degree is incorrect. Keep doing this, and once we hit 68% at about 2 standard deviations making B the right answer.

Question 8

Question 8 Stimulus

Question 8

You are making a very common mistake! Look carefully at your x and y axis, and we can see that the origin is not located at (0, 0) and its located at (20, 160). This means that the y intercept will be a lot less than 167. The best way to do this is to find the gradient, and use the point (20, 167) to find the real y intercept.

Question 9

Question 9 Stimulus

Question 9

You can continue to do it that way, but the easiest way to do this question is to just rule out the incorrect answers by looking at different features of the graph. For example, we can see that there needs to be two values below the x axis, when x = 23.5. This rules out A and C. Next, we can see that four numbers have to be above the line y = 0 and four have to be below, because that is how it is with the original graph. This rules out D and E also

[n.a]

Thank you so much! That was very clear and easy to understand! Unfortunately, I ended up doing my SAC before I could see your reply! but thanks anyway! There weren't any similar questions, thank God!