Matrices and Networks
What are the dimensions (order) of this matrix: [[2, 5, 1], [3, 8, 4]]
2×3 (2 rows, 3 columns)
Convert 3.5km to metres.
3500m
What is the mean of the data set: 4, 8, 6, 10, 2?
6
Calculate simple interest on $2000 at 5% p.a. for 3 years.
$300
What is the gradient of the line y = 3x + 7?
3
Add these matrices: [[1, 2], [3, 4]] + [[5, 6], [7, 8]]
[[6, 8], [10, 12]]
Find the area of a rectangle with length 12cm and width 7cm.
84cm²
What is the median of: 3, 9, 5, 1, 7?
5
What is the formula for simple interest?
I = Prn (Principal × rate × number of years)
Find the y-intercept of the line 2y = 4x − 6.
−3
In network terms, what is a "vertex" and what is an "edge"?
A vertex is a point/node in the network; an edge is a line connecting two vertices
Calculate the circumference of a circle with radius 6cm (use π ≈ 3.14).
37.68cm
In a box plot, what does the box itself represent?
the middle 50% of the data
$1500 is invested at 4% p.a. compound interest for 2 years. What is the final balance?
$1622.40
A phone plan costs $30 flat fee plus $0.50 per GB. Write a linear equation for total cost (C) in terms of data used (d).
C = 30 + 0.5d
Multiply the matrix [[2, 1], [0, 3]] by the scalar 4.
[[8, 4], [0, 12]]
Find the volume of a cylinder with radius 4cm and height 10cm (use π ≈ 3.14).
502.4cm³
A data set has Q1 = 12 and Q3 = 20. Calculate the IQR and state the upper fence for outliers.
IQR = 8; upper fence = Q3 + 1.5×IQR = 32
A loan of $5000 is charged 6% p.a. simple interest. After how many years will the total interest equal the original principal?
1/0.06 ≈ 16.67 years
A population grows according to P = 200(1.08)^t, where t is in years. What is the initial population and the annual growth rate?
200; growth rate = 8% p.a.
What type of network could be used to constructing roadways?
Maximum flow
A cone has a base radius of 3cm and a slant height of 5cm. Find its total surface area (use π ≈ 3.14).
75.36cm² (πr² + πrl = 28.26 + 47.1)
Explain the difference between a population and a sample, and give one reason sampling is often used instead of a census.
A population is the entire group being studied; a sample is a subset of it. Sampling is used because it's cheaper/faster/more practical than surveying everyone.
$3000 is invested at 3.5% p.a. compounded annually. Calculate the balance after 5 years, correct to the nearest cent.
$3564.79
Two competing mobile plans are C₁ = 25 + 0.4d and C₂ = 15 + 0.6d. For what value of d do the plans cost the same, and what is that cost?
d = 50, cost = $45