HSC Maths Standard 1 Measurement, Networks and Statistics: exam question types and methods

What this guide covers

Measurement, Networks and Statistical Analysis are the most visual parts of the Standard 1 course: many questions come with a diagram, a network or a scatterplot. Multiple-choice items test one step (the right ratio, the right conversion, the right algorithm step); Section II questions chain several steps and ask you to interpret the answer. Do the practice quiz first, then use this guide to target your gaps.

Question types you should expect

1. Rates and unit conversions

Write the rate with its units and convert one unit at a time. Key conversions: km/h to m/s divide by 3.6; watts to kilowatts divide by 1000; energy in kWh is kilowatts times hours; fuel consumption is litres per 100 km, so divide the litres by the distance and multiply by 100.

Revise rates in practical contexts.

2. Right-angled triangles and bearings

Draw the diagram, mark north for bearing questions, label the sides opposite, adjacent and hypotenuse relative to the angle you know, then choose SOH CAH TOA. True bearings are three digits measured clockwise from north; compass bearings such as S40°E start from north or south and turn towards east or west.

Revise right-angled triangles, trigonometry and bearings.

3. Scale drawings and irregular areas

Building plans are in millimetres. Multiply plan lengths by the scale factor, then convert to metres before finding areas. For an irregular boundary, apply the trapezoidal rule to each strip: $A \approx \dfrac{h}{2}(d_f + d_l)$, and add the strips.

Revise scale drawings, plans and the trapezoidal rule.

4. Networks

Expect to read degree, path and weight from a network diagram, find a minimum spanning tree and find a shortest path. Show the order in which you added edges (for Prim's or Kruskal's) and state the total weight. For shortest paths, label each vertex with its smallest total from the start and trace back from the finish.

Revise networks and minimum spanning trees and shortest paths in networks.

5. Bivariate data and surveys

Describe an association using form (linear or not), direction (positive or negative) and strength (strong, moderate, weak). Find the equation of a line of fit from two points on the line, not two data points. Predictions inside the data range (interpolation) are usually reasonable; predictions beyond it (extrapolation) may not be. For surveys, look for leading or loaded questions, unclear time frames and unrepresentative samples.

Revise bivariate data, scatterplots and lines of fit and the statistical investigation process and surveys.

Worked example

Question (exam style, 3 marks). From the top of a 40 m cliff, the angle of depression to a boat is 25°. How far is the boat from the base of the cliff, to the nearest metre?

Answer. The angle of elevation from the boat to the cliff top is also 25° (alternate angles). The cliff height is opposite the angle and the distance $d$ is adjacent, so $\tan 25^\circ = \dfrac{40}{d}$ and $d = \dfrac{40}{\tan 25^\circ} \approx 85.8$. The boat is about 86 m from the base of the cliff.

Keep going

Continue with the Financial Mathematics and Algebra practice, then work through the practice questions on each dot point page.