Further Maths

Univariate Data

100

This makes up the 5-figure summary.

What is the minimum, Q1, median, Q3 and the maximum.

200

The type of data to describe your shoe size.

What is numerical discrete data?

300

Draw or explain the features of a  bimodal histogram

2 peaks

400

Which measure of spread is used to calculate the middle 50% of data (on a boxplot) and what is its formula?

What is the IQR?

IQR = Q3-Q1

500

The following were scores from a class' maths tests:

100, 84, 38, 94, 90, 72, 99, 98.

What is the most effective measure of centre to use for this data and why?

What is the median as it less affected by outliers?

Relationships between numerical data

100

When describing the correlation between 2 numerical variables, what are the 3 key things we can describe this with?  

Strength, Form and Direction

200

The type of variable that is placed on the horizontal or x axis when drawing a scatterplot.

What is the explanatory variable?

300

This is another name for the r value when looking at scatterplots.

What is Pearson's correlation coefficient?

400

Explain what an r = 0.9606 represents when talking about the correlation between 2 numerical variables

This represents a strong and positive relationship between the 2 variables.

500

For the equation y = -5 - 4x, the value of the gradient and the value of y when x equals 10 are this.

What is -4 and -45?

Sequences & Series

100

The amount of interest paid if $1000 has been invested for 2 years at 10% simple interest.

What is $200?

200

Write the recurrence relation for this sequence:

30, 23.5, 17, 10.5.....

t₀ = 30, t_n+1 = tn - 6.5

300

The number of times an account is compounded if it is compounded every 3 months for 5 years.

What is 20?

400

The value of a compound interest investment, in dollars, after n years, V_n , can be modelled by the recurrence relation shown below.

V₀ = 100000, V_n+1 = 1.01V_n

The interest rate, per annum, for this investment is:

1% 

500

The value of a car bought for $45000, has travelled 25000km and is depreciating at a rate of 0.15c per kilometre.

What is $41250?

Networks

100

This is defined as the number of edges that comes out of each vertex in an undirected graph.

What is degree?

200

The number of vertices if a planar graph contains 5 faces and 12 edges is this.

What is 9?

300

Greedy Algorithms can be used to solve these problems.

What shortest path problems?

400

Describe the special relationships between edges and vertices in a minimum spanning tree?

There is always one less edge than vertice

500

Describe the edge that connects 2 graphs and if removed will make them unconnected?

What is a bridge?

Matrices

100

The rows x columns of a matrix is called this.

What is the dimension or order of a matrix?

200

The determinant of the matrix 

3     -2

1     -3

What is -7?

300

What conditions do we need for an inverse matrix to exist?

The determinant is not equal to 0 and the original matrix is a square matrix.

400

Add these 2 matrices together

3     -2             +               4       - 4

1     -3                              1         3

7         - 6

2           0

500

If using a communication matrix C to find how many employees can talk directly to each other, how do we find how many employees can talk via another employee?

How do we then establish what these connection paths are?

We need to calculate C² matrix to find the number of connections.

We refer back to the original matrix C, to find these paths