C3 (Modelling)
This type of prediction is considered reliable because it uses values within the observed data range.
Interpolation
What statistic measures the strength and direction of a linear relationship between two variables?
Correlation coefficient (rrr)
What is an arithmetic sequence?
A sequence with a constant difference between consecutive terms
What is simple interest?
Interest calculated only on the original principal
What is a vertex in a network?
A point (node) that represents a location or object in the network
What does it indicate if a model produces unrealistic values such as negative quantities in context?
The model is invalid or being used outside its appropriate range
How would you describe a relationship with r=0.92r = 0.92r=0.92?
Strong positive linear relationship
What is a geometric sequence?
A sequence where each term is multiplied by a constant ratio
What is compound interest?
Interest calculated on the principal plus previously earned interest
What does the degree of a vertex represent?
The number of edges connected to the vertex
What does “reasonableness” mean when evaluating a mathematical solution?
Checking whether the answer makes sense in the real-world context
What is extrapolation?
Making predictions outside the range of the original data
When does a geometric series have a sum to infinity?
When the common ratio satisfies ∣r∣<1|r| < 1∣r∣<1
What is the effective interest rate used for?
To compare investments or loans with different compounding periods
What does the maximum flow in a network equal?
The capacity of the minimum cut
Why is a linear model often unsuitable for long-term growth situations?
It assumes constant change and ignores changing growth rates or external factors
What does the gradient of a regression line represent?
The change in the response variable for each unit increase in the explanatory variable
Why does a geometric sequence with an r value between 0 and 1 model decay?
Because each term is a fraction of the previous term, so the values decrease toward zero
Why might a higher nominal interest rate not be the best option?
Because compounding frequency affects the effective rate, which determines the actual return
What condition must be satisfied for a graph to contain an Eulerian circuit?
All vertices must have even degree and the graph must be connected
Why does exponential growth eventually exceed linear growth?
Because exponential growth increases by a percentage, so the increase becomes larger over time, eventually surpassing constant increases
How can an outlier affect a regression model?
It can distort the gradient and intercept and weaken the correlation, reducing reliability
What does the sum to infinity represent in a hopping frog problem?
The total distance travelled by the frog.
How does reducing balance depreciation differ from straight-line depreciation?
It reduces value by a percentage of the remaining value, resulting in larger depreciation earlier
Why does a graph with exactly two vertices of odd degree contain an Eulerian trail but not an Eulerian circuit?
Because the trail must start and end at the two odd vertices, so it cannot form a closed circuit