VCE · Free to read

General Mathematics VCE practice questions

Exam-style questions from Edapt's growing shared question bank, the same bank the Exam Hall draws on. Answers are not published here. Sign up free and write your answer in Edapt to have it marked question by question, to the VCE scale.

Question 1Recursion and financial modelling4 marks
A population of rabbits grows according to the recurrence relation $P_n = 2P_{n-1} + 3P_{n-2}$, where $P_n$ is the population after n years. If the initial population is 10 and the population after 1 year is 20, find the population after 3 years.
What a full answer covers
Use the recurrence relation to find the population after 2 years, then use it again to find the population after 3 years.
Question 2Data analysis3 marks
The following data shows the number of books sold per day. Determine the mean and median number of books sold per day. $\begin{array}{|c|c|} \hline ext{Day} & ext{Number of books} \\ \hline 1 & 15 \\ 2 & 20 \\ 3 & 10 \\ 4 & 25 \\ 5 & 18 \\ \hline \end{array}$
What a full answer covers
To find the mean, add the values and divide by the number of values, then arrange the data in order to find the median.
Question 3Matrices2 marks
If $A = \begin{pmatrix} 2 & 1 \\ 3 & 4 \end{pmatrix}$ and $B = \begin{pmatrix} 5 & 2 \\ 1 & 3 \end{pmatrix}$, find $A + B$.
What a full answer covers
Add corresponding elements of the two matrices to find the sum.
Question 4Data analysis2 marks
The following table shows the number of students in each year level. Determine the percentage of students in year 10. $\begin{array}{|c|c|} \hline ext{Year level} & ext{Number of students} \\ \hline 7 & 120 \\ 8 & 130 \\ 9 & 140 \\ 10 & 110 \\ 11 & 100 \\ 12 & 90 \\ \hline \end{array}$
What a full answer covers
Calculate the total number of students, then find the percentage of students in year 10.
Question 5Matrices12 marks
If $A = \begin{pmatrix} 2 & 1 \\ 3 & 4 \end{pmatrix}$, find $A^{-1}$ and use it to solve the system of equations $\begin{cases} 2x + y = 3 \\ 3x + 4y = 5 \end{cases}$.
What a full answer covers
Find the inverse of matrix A, then use it to solve the system of equations by multiplying both sides by the inverse.
Question 6Networks and decision mathematics9 marks
The following graph represents a network of roads. Determine the minimum spanning tree of the graph using Kruskal's algorithm.
What a full answer covers
Apply Kruskal's algorithm to find the minimum spanning tree, then state the total weight and draw the tree.
Question 7Data analysis3 marks
A bakery sells a variety of bread. The table shows the number of loaves of bread sold per day. Determine the median number of wholemeal loaves sold over the 5 days. $\begin{array}{|c|c|} \hline ext{Day} & ext{Number of wholemeal loaves} \\ \hline 1 & 15 \\ 2 & 18 \\ 3 & 12 \\ 4 & 20 \\ 5 & 16 \\ \hline \end{array}$
What a full answer covers
To find the median, arrange the data in order and find the middle value, then clearly state the answer.
Question 8Recursion and financial modelling8 marks
A person invests $1000 into a savings account that earns a yearly interest rate of $4%$. The interest is compounded yearly. Determine the amount of money in the account after 10 years, and calculate how much interest is earned over the 10 years.
What a full answer covers
Use the compound interest formula to calculate the amount after 10 years, then subtract the principal amount to find the interest earned.
Question 9Networks and decision mathematics10 marks
The following graph represents a road network. Determine the shortest path from node A to node F using Dijkstra's algorithm.
What a full answer covers
Apply Dijkstra's algorithm to find the shortest distances from node A to all other nodes, then determine the shortest path from node A to node F.
Question 10Recursion and financial modelling7 marks
A person borrows $2000 at an interest rate of $6%$ per annum. The interest is compounded monthly. Determine the amount owed after 2 years.
What a full answer covers
Convert the yearly interest rate to a monthly interest rate, then use the compound interest formula to calculate the amount owed after 2 years.

Wrote an answer? Find out what it scores.

Edapt marks your written answers against the VCE scale, question by question, with the marks you would have lost and why. Every feature is free.

General Mathematics VCE practice questions

Wrote an answer? Find out what it scores.

About

Legal