Tuition
<stage5_exam_md>
# Tuition — Stage 5 Mathematics Examination
**Stage:** 5 (Year 10) | **Subject:** Mathematics | **Topic:** Financial Mathematics — Tuition Costs
**Time allowed:** 60 minutes | **Total marks:** 50
**Instructions**
- Answer all questions. Show all necessary working.
- Calculators permitted. Give monetary answers correct to the nearest cent unless stated otherwise.
---
## Section A — Multiple Choice (5 marks)
_Circle the correct answer. Each question is worth 1 mark._
**Question 1**
A tutoring centre charges $45 per hour. What is the cost of 6 hours of tuition?
A) $225 B) $250 C) $270 D) $290
**Question 2**
A weekly tuition fee of $80 rises by 10%. What is the new weekly fee?
A) $8 B) $88 C) $90 D) $108
**Question 3**
Which expression gives the final value of $P invested at r% p.a. compound interest for n years?
A) P(1 + r)n B) P(1 + r/100)^n C) P × r × n D) P(1 − r/100)^n
**Question 4**
A tuition invoice shows $110 including 10% GST. What was the price before GST?
A) $99 B) $100 C) $101 D) $121
**Question 5**
Which lesson offers the better hourly rate?
A) 30-minute lesson for $25 B) 45-minute lesson for $36 C) Both equal D) Cannot be determined
---
## Section B — Short Answer (17 marks)
**Question 6** (2 marks)
Tuition costs $120 per week for 40 teaching weeks. Calculate the total annual cost.
**Question 7** (2 marks)
A term fee increases from $80 to $92. Calculate the percentage increase.
**Question 8** (3 marks)
A family borrows $5000 at 4.5% p.a. simple interest for 3 years to pay tuition fees. Calculate the interest owed.
**Question 9** (3 marks)
$8000 is invested at 3% p.a. compounded annually for 2 years to fund future tuition. Find the final balance and the interest earned.
**Question 10** (2 marks)
An early-payment discount of 15% applies to a term fee of $640. Find the discounted fee.
**Question 11** (2 marks)
A fee of $220 includes 10% GST. Calculate the pre-GST amount.
**Question 12** (3 marks)
A course costs $3600. A 20% deposit is paid, and the balance is repaid in 12 equal monthly instalments. Find the monthly instalment.
---
## Section C — Extended Response (28 marks)
**Question 13** (8 marks)
Plan A charges a flat $50 per hour. Plan B charges $200 per month plus $35 per hour.
a) Write an equation for when the two plans cost the same. (3)
b) Solve the equation to find the number of hours per month where the costs are equal. (3)
c) State which plan is cheaper for a student taking 10 hours per month, with justification. (2)
**Question 14** (10 marks)
The table below shows annual tuition fees at a college.
> Image pending generation for this question.
a) Show that the fee rose by 10% each year from 2021 to 2022. (2)
b) Calculate the total percentage increase from 2021 to 2024, correct to one decimal place. (3)
c) Assuming the same pattern continues, predict the 2025 fee. (2)
d) Explain why the dollar increase each year grows even though the percentage stays constant. (3)
**Question 15** (10 marks)
Annual tuition is $5400. A scholarship covers 60% of the fee. The remaining amount is paid by the family in 10 equal fortnightly payments.
a) Calculate the scholarship contribution. (2)
b) Calculate the amount the family must pay. (2)
c) Calculate each fortnightly payment. (2)
d) If the scholarship instead covered 75%, how much less would each fortnightly payment be? (4)