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Applying linear and quadratic functions
You have been asked to give business advice for the following 2 businesses to help them make decisions that will maximise their profit. In particular, each business wants to know:
The best sale price to maximise profit.
The number of units they should produce to maximise profit.
Total sales in dollars when profit is maximised.
The cost of producing this number of units
The profit they will make.
At what price/s they will make zero profit…
InvestigationMathematicsYear 9How much super will you need?
What is super?Currently employers in Australia must, by law, pay into a super fund, super to their eligible employees to the tune of 12% of the employee's ordinary time earnings. This is called the superannuation guarantee (SG).Ordinary time earnings are what you generally earn for ordinary hours of work; it includes over-award payments, bonuses, allowances and some paid leave. Overtime is not included.In Australia, super was made compulsory to…
ExplainerMathematicsYear 10What type of tax is this?
Average rate of taxFor each income in table 1, calculate the average rate of tax paid. Decide if the tax is proportional, regressive or progressive and predict the impact of the tax income distribution.Table 1: Types of tax and their effect on equity in the distribution of incomeAnnual incomeTax 1 (amount of tax paid)ARTTax 2 (amount of tax paid)ARTTax 3 (amount of tax paid)ART$60,000$10,000$4,000$8,000$120,000$20,000$12,000$6,000Type of tax:…
WorksheetMathematicsYear 9What type of tax is this? - Solutions
Average rate of taxFor each income in table 1, calculate the average rate of tax paid. Decide if the tax is proportional, regressive or progressive and predict the impact of the tax income distribution.Table 1: Types of tax and their effect on equity in the distribution of incomeAnnual incomeTax 1 (amount of tax paid)ARTTax 2 (amount of tax paid)ARTTax 3 (amount of tax paid)ART$60,000$10,00016.7%$4,0006.7%$8,00013.3%$120,000$20,00016.7%$12,00010…
WorksheetMathematicsYear 9Graphing distribution and correlation
Linked activity:
Graphing and analysing the distribution of superannuation data
VisualiserMathematicsYear 9Linear functions for business
Linked activity:
Modelling profit and loss with linear and quadratic functions
VisualiserMathematicsYear 9Linear functions for business
A business wants to manufacture soap bars. Before they start production, they need to make sure they can make a profit with the materials and labour force they have. Their accountant has given them a cost and revenue equations.
Cost: y=0.85x+5,000
Revenue y=1.55x
What do x and y represent in each equation? The first one has been completed for you.
Equation type
x represents
y represents…
WorksheetMathematicsYear 9