NSWMaths Standard 2

Year 11: Algebra

12 dot points across 12 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you estimate blood alcohol content from a formula or a table, and work out how long until it is safe and legal to drive?

Use the blood alcohol content formulae for males and females to estimate BAC by substitution, read BAC from a body-weight table, and use the time formula BAC divided by 0.015 to estimate the hours until BAC reaches zero or a legal limit
A focused answer to the HSC Maths Standard 2 dot point on blood alcohol content. Estimate BAC with the male and female formulae by substitution, read a BAC body-weight table, and use the time-to-zero formula BAC over 0.015 to find the hours to wait before driving, with the NSW 0.05 and zero limits and worked Australian examples.
16 min answer →

How do you rearrange a formula to make a different variable the subject by undoing the operations around it?

Change the subject of a formula by rearranging it to isolate any chosen variable, including a subject that appears in a power, a root or a fraction, and check the rearrangement by substitution
A focused answer to the HSC Maths Standard 2 dot point on changing the subject of a formula. Rearrange a formula to isolate any variable using inverse operations and keeping it balanced, with the subject in a power, a root or a fraction, multi-step transposing, and checking by substitution, with worked Australian examples.
15 min answer →

What does it mean for one quantity to vary directly with another, how do you find the constant of variation k from a single data pair and write the equation y = kx, why is the graph always a straight line through the origin, and how is direct variation different from inverse variation y = k/x?

Recognise and model direct variation y = kx, where one quantity is a constant multiple of another, find the constant of variation k from a data pair, write and use the equation, identify direct variation from a constant ratio in a table or a straight-line graph through the origin, and contrast it with simple inverse variation y = k/x
A focused answer to the HSC Maths Standard 2 dot point on direct variation. How y = kx works, finding the constant of variation k from a data pair, why the graph is a straight line through the origin, recognising direct variation from a table or graph, and a brief contrast with inverse variation y = k/x, with worked pay, cost and speed examples.
18 min answer →

How are distance, speed and time linked by one formula, and how do you rearrange it and keep the units consistent?

Use the relationship between distance, speed and time to solve problems, rearranging the formula to find any of the three quantities and converting between km/h and m/s
A focused answer to the HSC Maths Standard 2 dot point on distance, speed and time. The $D = ST$ triangle and how to rearrange it for distance, speed or time, average speed over a whole journey, keeping units consistent, converting between km/h and m/s with the factor 3.6, and reading a distance-time graph, with worked Australian examples.
13 min answer →

What is the gradient of a straight line, what do its sign and size tell you, and how do you find the gradient from a graph or from two points and read the y-intercept?

Find the gradient of a straight line as rise over run, interpret the sign of the gradient and what steepness means, read the y-intercept from a graph, and calculate the gradient between two points
A focused answer to the HSC Maths Standard 2 dot point on gradient and intercept. Gradient as rise over run, what positive, negative, zero and undefined gradients mean and what steepness tells you, reading the y-intercept off a graph, and the gradient formula between two points, with worked ramp, hourly-pay and phone-plan examples.
16 min answer →

What do m and b mean in the equation y = mx + b, how do you read them straight off an equation or a graph, and how do you sketch a line quickly from its gradient and y-intercept?

Use the gradient-intercept form y = mx + b: read the gradient m and the y-intercept b directly from the equation (rearranging first if needed), write the equation of a line from its graph, and sketch a line from m and b
A focused answer to the HSC Maths Standard 2 dot point on the gradient-intercept formula. How to read the gradient m and y-intercept b straight from y = mx + b, rearrange an equation into that form first, write the equation of a drawn line, sketch a line from m and b, and build a real cost model, with worked Australian examples.
17 min answer →

How do you turn a linear relationship into a straight-line graph, plotting points from a table of values, recognising the line, sketching horizontal and vertical lines, and finding the intercepts?

Graph linear functions by constructing a table of values and plotting the points, recognise a linear relationship, sketch horizontal and vertical lines, and graph a line using its x- and y-intercepts
A focused answer to the HSC Maths Standard 2 dot point on graphing linear functions. Build a table of values, plot the points and rule a straight line, sketch horizontal lines and vertical lines, graph a line from its x- and y-intercepts, and read values off the graph, with worked Australian cost and distance examples.
17 min answer →

How do you turn a real situation with a fixed cost plus a steady rate into the equation y = mx + b, what do the gradient and y-intercept mean in that context, and how do you use the model to predict a value and read it backwards?

Construct a linear model y = mx + b for a practical situation made of a fixed amount plus a constant rate, interpret the gradient as the rate and the y-intercept as the fixed starting amount in context, and use the model to predict an output and to find the input that gives a required output
A focused answer to the HSC Maths Standard 2 dot point on linear models. How to build y = mx + b from a fixed amount plus a rate, interpret the gradient and y-intercept in words with units, predict a value and read the model backwards, with worked plumber, taxi, mobile-plan and tank-filling examples.
18 min answer →

How do you work out the right dose of medicine for a child or infant, and the drip rate for an IV infusion, by substituting into a given formula?

Use the paediatric dosage formulae (Fried's rule for infants, Young's rule by age and Clark's rule by weight) and the IV flow-rate formula to calculate doses and drip rates by substitution
A focused answer to the HSC Maths Standard 2 dot point on medication dosages. Substitute into Young's rule (by age), Clark's rule (by weight) and Fried's rule (for infants) to find a child's dose, use the IV flow-rate formula for drops per minute, and back-solve for an age or weight, with worked Australian examples and clear rounding.
16 min answer →

How do you find an unknown that is not the subject of a formula by substituting the known values first and then solving the equation that is left?

Substitute known values into a formula and then solve the resulting equation to find an unknown quantity that is not the subject of the formula
A focused answer to the HSC Maths Standard 2 dot point on solving equations after substitution. Substitute the known values into a formula first, then solve the equation that is left to find an unknown that is not the subject, with the order of operations, units and rounding, the substitute-or-rearrange choice, and worked Australian examples.
15 min answer →

How do you solve a linear equation by keeping it balanced and undoing the operations in reverse order?

Solve linear equations using inverse operations, including one-step, two-step and multi-step equations, equations with brackets and fractions, and equations with the variable on both sides
A focused answer to the HSC Maths Standard 2 dot point on solving linear equations. Inverse operations and keeping the equation balanced, one-step, two-step and multi-step equations, brackets, clearing fractions with the lowest common denominator, the variable on both sides, and checking by substitution, with worked Australian examples.
14 min answer →

How do you evaluate a formula correctly once you replace its pronumerals with numbers?

Substitute numerical values into a formula or algebraic expression and evaluate it, including expressions with powers, fractions and negative numbers
A focused answer to the HSC Maths Standard 2 dot point on substitution. Replacing pronumerals with values, the order of operations, the rule for powers of negatives, brackets and fractions, calculator layout, units and rounding, with worked Australian examples for a tradie's quote, a tank's surface area and stopping distance.
12 min answer →