Designed by Mr.Shen

UOJMC Training | Lesson 1

Competition preparation: Finance, Rates, Statistics, and Logical Deduction.

Finance & Rates

Budgeting & Substitution

In UOJMC questions, you are often given a large set of data or a physics formula and expected to extract exactly what you need.

Scenario A: Kaia's Budget

Kaia has the following weekly expenses. Assume her income perfectly matches her expenses each week.

Mortgage: \$270
Phone/Net: \$25
Local Rates: \$60
Travel: \$40
Insurance: \$60
Household: \$60
Food: \$90
Savings: \$50
Electricity: \$60
Discretionary: \$60
Scenario B: Electrical Power

The amount of power $p$ (in watts) is determined by $p = vi$, where $v$ is voltage and $i$ is current.

Knowledge Check

1. What is Kaia's total income per week?

\$

2. What percentage of Kaia's budget is her mortgage? (Round to 2 decimal places)

%

3. If a circuit requires 70W of power, and current is fixed at 5A, how much voltage ($v$) is required?

Volts
Solutions:
1. Add all expenses: \$270+60+60+90+60+25+40+60+50+60 = \$775.
2. Mortgage / Total = $270 \div 775 = 0.34838...$ which is 34.84%.
3. Use $p=vi$. Substitute values: $70 = v \times 5$. Divide by 5: $v = $ 14.

Stats, Sets & Logic

Venn Diagrams & Averages

You must be able to translate English paragraphs into mathematical sets, and calculate standard averages from raw data.

Scenario A: The Sports Survey

1000 Year 9 students are surveyed.

  • 15% play cricket.
  • 20% play tennis.
  • 1 in 8 play touch rugby.

Hint: You are also told that exactly a quarter of the tennis players also play cricket.

Scenario B: Plant Growth

Fred measures his plant's daily growth (in mm) over a week:

MonTueWedThuFriSatSun
7627643

Knowledge Check

1. How many students play touch rugby?

2. How many play cricket BUT NOT tennis?

3. What was the TOTAL plant growth (mm)?

4. What was the AVERAGE (mean) daily growth?

Solutions:
1. 1 in 8 students: $1000 \div 8 =$ 125.
2. Total Tennis = 200. A quarter play both ($200 \div 4 = 50$). Total Cricket = 150. Cricket ONLY = $150 - 50 =$ 100.
3. Sum the days: $7+6+2+7+6+4+3 =$ 35.
4. Mean = Total $\div$ Number of days: $35 \div 7 =$ 5.

Boss Level: Tables & Probability

Tama's Jewellery Store

This challenge tests your ability to read a table, infer missing unit values, and calculate probability fractions.

Sales Data
Item TypeNumber SoldTotal Profit
Bracelets18\$270
Rings23\$460
Necklaces13\$169
Anklets5\$40

Assume that for each type of jewellery, the exact same profit is made on every individual item of that type sold.

The Final Gauntlet

1. What is the grand total profit made during that day?

\$

2. Quinn buys exactly ONE of each item. How much profit does Tama make from Quinn?

\$

3. Jenny picks one item sold at random. What is the probability she picks a ring? (State as a fraction).

/
Solutions:
1. Sum the profit column: \$270+460+169+40 = \$939.
2. Calculate profit per item: Bracelet (\$270/18=15$), Ring (\$460/23=20$), Necklace (\$169/13=13$), Anklet (\$40/5=8$). Sum them: $15+20+13+8 =$ \$56.
3. Total items sold = $18+23+13+5=59$. Number of rings = $23$. Fraction is 23 / 59.

Homework Circuit

1. Budget & Finance

Leo's weekly expenses are: Rent \$300, Groceries \$120, Transport \$50, Utilities \$80, Insurance \$40, Entertainment \$70, Savings \$100. Assume his weekly income exactly matches his total expenses.

a) What is his weekly income?
\$
b) What percentage of his total budget is spent on Rent? (Round to 2 d.p.)
%

2. Sets & Logic

800 students are surveyed about sports. 25% play Basketball, 30% play Soccer, and 1 in 10 play Hockey. You are also told that exactly $\frac{1}{5}$ of the Soccer players also play Basketball.

a) How many students play Hockey in total?
b) How many students play Soccer but do NOT play Basketball?

3. Practical Arithmetic

6 friends share \$50 cash equally. Because the smallest physical coin available in New Zealand is the 10c coin, they each receive the maximum equal amount possible in physical cash.

How much total change is left over?
\$

4. Compound Interest

\$5,000 is invested at an interest rate of 8% per year, compounded annually. No money is added or taken out.

What is the total INTEREST (profit) earned after exactly 2 years?
\$

5. Data Analysis

A weather station records the following daily rainfall (in mm) over 7 days:
5, 8, 2, 5, 10, 0, 5

What is the mean (average) daily rainfall?

6. Tables & Probability

Item TypeNumber SoldTotal Profit
Muffins20\$80
Croissants15\$75
Donuts10\$30

Assume for each type of item, the exact same profit is made on every individual item sold.

a) If a customer buys exactly ONE of each item type, how much total profit does the bakery make from that customer?
\$
b) If one item sold that day is picked at random, what is the probability it is a Donut? (State as a simple fraction).
/

7. Formula Substitution

Electrical power $p$ (in watts) is calculated using the formula $p = vi$, where $v$ is voltage and $i$ is current.

What is the voltage ($v$) required if a circuit uses 60W of power and has a current of 4A?

8. Simple Probability

A single letter is chosen at random from the word MATHEMATICS.

What is the probability that the chosen letter is an 'M'? (State as a fraction).
/

Marking Schedule

Score: / 11
1a: Sum of expenses = 760.
1b: $300 \div 760 = 0.3947... \rightarrow$ 39.47%.
2a: $800 \div 10 =$ 80 Hockey players.
2b: Total Soccer = 240. $\frac{1}{5}$ of 240 = 48 play both. $240 - 48 =$ 192.
3: $50 \div 6 = 8.333$. Smallest coin 10c means max cash given to each person is \$8.30. $8.30 \times 6 = 49.80$. Change left over = 0.20.
4: Year 1: $5000 \times 1.08 = 5400$. Year 2: $5400 \times 1.08 = 5832$. Profit = $5832 - 5000 =$ 832.
5: Total rainfall = 35. $35 \div 7$ days = 5.
6a: Muffin unit=\$4. Croissant=\$5. Donut=\$3. Sum = 12.
6b: 10 Donuts $\div$ 45 total items = 10/45 or 2/9.
7: $60 = v \times 4 \rightarrow 60 \div 4 =$ 15.
8: Word has 11 letters. There are two 'M's. Fraction is 2/11.