← Maths Standard 2 syllabus

NSWMaths Standard 2

Year 11: Measurement

9 dot points across 9 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you calculate the area of a circle, a sector and shapes built from circular and straight-sided parts?

Calculate the area of circles, sectors and composite figures, including the annulus, by adding and subtracting the areas of simpler shapes
A focused answer to the HSC Maths Standard 2 dot point on area. The area of a circle, the fraction method for a sector, the annulus (ring) as a difference of two circles, and composite shapes built by adding or subtracting simpler parts, with worked Australian examples and clear rounding.
15 min answer →

How do you measure energy in joules and kilowatt-hours, work out what an appliance costs to run, and balance the kilojoules you eat against the energy your body needs each day?

Solve problems involving energy and mass, including the joule and the watt, energy consumption measured in kilowatt-hours, the energy content of food measured in kilojoules, and daily energy requirements based on basal metabolic rate and level of activity
A focused answer to the HSC Maths Standard 2 dot point on energy and nutrition. The joule and the watt, measuring electricity use in kilowatt-hours, costing an appliance from its power rating and tariff, reading food energy in kilojoules, and estimating daily energy needs from basal metabolic rate times an activity factor, with worked Australian examples.
15 min answer →

How accurate is a measurement, and how do you state its error and the range the true value must lie in?

Describe the limit of reading of an instrument, calculate the absolute error and percentage error of a measurement, and find the greatest possible error and the upper and lower bounds
A focused answer to the HSC Maths Standard 2 dot point on measurement error. The limit of reading of an instrument, absolute error as half the smallest division, percentage error, and the greatest possible error giving the upper and lower bounds, with worked Australian examples on rulers, scales and measuring jugs.
13 min answer →

How do you use rates and ratios to compare value, measure how fast something happens, share a quantity fairly, and read distances off a scale map or plan?

Review and use rates and ratios, including identifying rates from a context (such as best buys, fuel consumption, heart rate and pay rates), working with unit rates, simplifying ratios, dividing a quantity in a given ratio, and using scale factors on maps and plans
A focused answer to the HSC Maths Standard 2 dot point on rates and ratios. Reading a rate from a context, finding unit rates to settle best buys, fuel consumption in litres per 100 km, heart and pay rates, simplifying ratios, dividing a quantity in a given ratio, and using a map or plan scale to convert between drawing and real distances, with worked Australian examples.
15 min answer →

How do you write very large and very small numbers in standard form, and round a measurement to a stated number of significant figures?

Write numbers in scientific (standard) form as a number between 1 and 10 times a power of 10, convert back to a numeral, round to a given number of significant figures, and operate with numbers in standard form
A focused answer to the HSC Maths Standard 2 dot point on scientific notation and significant figures. Standard form for large and small numbers, converting both ways, counting and rounding to significant figures including the tricky carry and zero cases, and multiplying and dividing in standard form, with worked Australian and scientific examples.
14 min answer →

How do you find the surface area of a prism, cylinder, sphere, pyramid or cone, and when must you first find a slant height?

Calculate the surface area of right prisms, cylinders, spheres and pyramids, and of right cones using the slant height, including solids formed as a combination of these
A focused answer to the HSC Maths Standard 2 dot point on surface area. Surface area of right prisms from a net, open and closed cylinders, spheres, pyramids and cones, finding a cone's slant height with Pythagoras, and the surface area of composite solids, with worked Australian examples and the formulae you are given on the reference sheet.
15 min answer →

How do you estimate the area of a block of land or a body of water with one irregular boundary, using the trapezoidal rule with a single strip and with several strips?

Calculate the approximate area of an irregularly shaped region using the trapezoidal rule, A = h/2 (d_f + d_l), and apply the rule repeatedly to find the approximate area between an irregular boundary and a straight line, where d_f and d_l are the first and last measurements and h is the strip width
A focused answer to the HSC Maths Standard 2 dot point on the trapezoidal rule. The single-application formula A = h/2(d_f + d_l), what each letter means, applying the rule repeatedly across several equal strips, the ends-once interior-twice pattern, and worked Australian examples for a block beside a lake, a multi-strip estimate and offsets from a survey line.
14 min answer →

How do you choose the right metric unit and convert correctly between units of length, area, volume, mass and speed?

Use units of measurement and convert between them, including length, area, volume, capacity, mass and compound units such as speed, multiplying or dividing by the correct power of 10
A focused answer to the HSC Maths Standard 2 dot point on units and unit conversion. The SI system and prefixes, the metric conversion ladder for length, mass and capacity, squaring the factor for area and cubing it for volume, the litre link to cubic centimetres, and converting compound units like km/h to m/s, with worked Australian examples.
14 min answer →

How do you calculate the volume of prisms, cylinders, pyramids, cones, spheres and composite solids, and convert that volume into a capacity?

Calculate the volume of right prisms, cylinders, pyramids, cones, spheres and composite solids, and convert between units of volume and capacity
A focused answer to the HSC Maths Standard 2 dot point on volume and capacity. Volume of prisms and cylinders by V = Ah, the one-third for pyramids and cones, the sphere formula, composite solids by adding or subtracting parts, and the volume-to-capacity link 1 cm cubed = 1 mL, with worked Australian examples and the rounding markers expect.
15 min answer →