# Year 11 General Mathematics · learner cards H–N · all cases invented

These are **fictional arithmetic models**. No wage, allowance, exchange rate, share, business, quote or return below describes a real offer or entitlement. A stated rate is a **given for a classroom calculation**, not a current market or legal fact. Never enter personal pay, spending or investing information. For every card: identify the base and unit, show the operation, check the result, then say what the model leaves unknown. Use the [teacher plan](LESSONS.md) for order and the [print/text aids](print/TEXT-ALTERNATIVES.md) for accessible layouts. The [public formative checks](STUDENT-CHECKS.md) use new data.

## Card H · two rates for one fictional adult shift

A made-up stage-lighting brief models **8 regular paid hours at $28 per hour**, then **2 additional paid hours at 1.5 times the stated base hourly rate**. “1.5 times” applies to the hourly rate for those 2 hours, not to the whole shift total. There are no deductions or other conditions in this arithmetic model. Find regular amount, additional-hours rate, additional-hours amount and gross model total. Do not infer a legal overtime rate, award, safety condition or actual take-home pay.

## Card I · a separate allowance and two hour bands

An invented adult gallery setup models **6 regular paid hours at $31 per hour**, **2 additional paid hours at 1.25 times that base hourly rate**, and a separate **$24 fixed model allowance**. Find each part and the total. Would a $24 allowance mean $24 per hour? No; its unit is one shift in this case. Real allowance eligibility and pay rules are unspecified.

## Card J · mark-up uses cost as its base

A fictional community theatre bought one prop component for **$80 model cost** and applies a **25% mark-up on cost** to set its model selling price. Calculate the $ mark-up, selling price and $ difference between sale and cost. This is a single simplified transaction; tax, other costs and actual profit are not established.

## Card K · mark-up and margin have different bases

An invented art-print model has **$72 stated unit cost** and **$90 stated selling price**. The dollar gap is $18. Calculate **mark-up percentage on cost** and **margin percentage on selling price**. Explain why both can describe this same fictional gap but are different percentages. Additional expenses and tax are omitted, so “margin” here is just the gross price gap as a share of selling price.

## Card L · forward and reverse percentage comparison

A fictional materials-list figure changes from **$125** to **$137.50** between two invented versions. Calculate the dollar change and percentage increase using the **original $125 base**. Then imagine the figure returns from $137.50 to $125. Calculate that percentage decrease using the **new starting $137.50 base**. These are not real inflation data or product prices.

## Card M · a stipulated exchange-rate table, not a quote

For a purely fictional exercise, suppose **AUD $1 = USD $0.64**, with **no fees or spread**. This is an invented classroom rate, not a current or historical quote. Convert **AUD $250 to USD**, then separately convert **USD $96 to AUD**. Show the direction and reverse check. Real exchange rates and fees vary; consult a current official or provider quote for any real transaction. The optional [offline rate switch](print/rate-switch.xlsx) changes this invented rate and shows both directions without live data.

## Card N · share measures are arithmetic, not recommendations

**N1 dividend model.** A fictional company called Paperbird has a stipulated share price of **$24** and a stipulated **annual dividend of $0.84 per share**. A made-up portfolio holds **50 shares**. Calculate the model annual dividend dollars on 50 shares and the dividend yield `annual dividend per share ÷ share price ×100%`. No future dividend, growth or risk is predicted.

**N2 P/E comparison.** Fictional company Cedar has **$30 market price per share** and **$2 annual earnings per share**. Fictional company Slate has **$36 market price per share** and **$3 annual earnings per share**. Find each price-to-earnings ratio `price per share ÷ annual earnings per share`; label it as a ratio, not a percentage. The numbers do not say which share is better. No purchase or sign-up is required.

## Switch contexts without collecting private data

Use the same arithmetic on invented film-set crew hours, game-convention booth costs, repair-shop price cards, community festival supply lists, book-cover printing, fictional travel budget conversions or made-up publishing shares. Each context must name its rate base, units and missing conditions. Home extensions ask for imagined numbers only; never a payslip, family budget, real exchange transaction or actual share portfolio.