Course 2 · Number & Algebra

Quiz 2.1 · Percentages

Solutions — Quiz 2.1 Percentages

Full worked solutions for all 12 questions. Each solution shows every step — not just the answer. Read the method carefully for any question you got wrong.

📋 12 questions

🧮 Calculator allowed

📐 Lessons 2.1 & 2.2

💡 How to use these solutions: For every question you got wrong, work through the steps carefully and identify where your working diverged. The most common errors are shown in the “Watch out” notes below each solution.

Question 1 — Class test result

Question: In a class test, 3 of the 25 students scored full marks. What percentage of students did NOT score full marks?

✓ Worked Solution

Step 1 — Find the percentage who DID score full marks:
3 ÷ 25 × 100 = 12%

Step 2 — Subtract from 100%:
100 − 12 = 88%

⚠️ Watch out: Don’t answer 12% — the question asks for the students who did NOT score full marks, which is the complement.

Question 2 — Population from Oceania

Question: A country has a population of 12 million people. 8% of the population were born in Oceania. How many thousands of people is this?

✓ Worked Solution

Step 1 — Find 8% of 12,000,000:
8 ÷ 100 × 12,000,000 = 0.08 × 12,000,000 = 960,000 people

Step 2 — Express in thousands:
960,000 ÷ 1,000 = 960 thousand

⚠️ Watch out: 12 million = 12,000,000. Don’t calculate 8% of just “12”.

Question 3 — Dark chocolates

Question: A box contains 28 chocolates. 21 of them are milk chocolate and the rest are dark chocolate. What percentage of the chocolates are dark?

✓ Worked Solution

Step 1 — Find the number of dark chocolates:
28 − 21 = 7 dark chocolates

Step 2 — Express as a percentage:
7 ÷ 28 × 100 = 25%

Question 4 — Cross country selection

Question: At a school athletics carnival, 12 out of 60 students were selected for the cross country team. What percentage were NOT selected?

✓ Worked Solution

Step 1 — Percentage selected:
12 ÷ 60 × 100 = 20%

Step 2 — Not selected:
100 − 20 = 80%

Question 5 — School captain election

Question: Three candidates ran for school captain. They received 29, 120 and 61 votes respectively. What percentage of the total votes did the winner receive? (Nearest whole percent.)

✓ Worked Solution

Step 1 — Find the total votes:
29 + 120 + 61 = 210 votes

Step 2 — Identify the winner:
The winner received 120 votes (highest)

Step 3 — Calculate the percentage:
120 ÷ 210 × 100 = 57.142…% ≈ 57%

⚠️ Watch out: Add all three vote totals to find the denominator — don’t use just the top two. Round only at the final step.

Question 6 — School enrolments

Question: In a school, 9/20 of the total enrolments are boys. What percentage of enrolments are NOT boys?

✓ Worked Solution

Step 1 — Convert the fraction to a percentage:
9 ÷ 20 × 100 = 45% are boys

Step 2 — Find the complement:
100 − 45 = 55% are not boys

Question 7 — Language preferences

Question: In a survey of students, 1/4 preferred History, 7/20 preferred Geography, and the rest preferred Japanese. What percentage preferred Japanese?

✓ Worked Solution

Step 1 — Convert to percentages:
History: 1/4 = 1 ÷ 4 × 100 = 25%
Geography: 7/20 = 7 ÷ 20 × 100 = 35%

Step 2 — Japanese = the remainder:
100 − 25 − 35 = 40%

💡 Tip: Convert all fractions to percentages first, then use the fact that all percentages must add to 100%.

Question 8 — University plans

Question: In a Year 12 class of 60 students, 24 said they plan to go to university. What percentage do NOT plan to go to university?

✓ Worked Solution

Step 1 — Percentage planning to go:
24 ÷ 60 × 100 = 40%

Step 2 — Not going:
100 − 40 = 60%

Question 9 — Teacher salary increase

Question: A teacher’s annual salary is $78,400. The salary is increased by 4.5%. What is the new annual salary? (Nearest dollar.)

✓ Worked Solution

Method A (two steps):
Step 1 — Increase amount: 4.5 ÷ 100 × 78,400 = 0.045 × 78,400 = $3,528
Step 2 — New salary: 78,400 + 3,528 = $81,928

Method B (multiplier — same answer):
78,400 × 1.045 = $81,928

⚠️ Common error: Answering $3,528 (just the increase amount) instead of the new salary. Re-read the question: it asks for the new annual salary, not the raise.

Question 10 — School enrolment growth

Question: A primary school had 480 students enrolled last year. This year enrolments have increased by 12.5%. How many students are enrolled this year?

Options: (a) 540 (b) 480 (c) 600 (d) 520

✓ Worked Solution — Answer: (a) 540

Step 1 — Increase amount:
12.5 ÷ 100 × 480 = 0.125 × 480 = 60 extra students

Step 2 — New total:
480 + 60 = 540 students

💡 Distractor check: Option (c) 600 would be a 25% increase. Option (d) 520 is a common error from calculating 12.5% incorrectly as 40 students. Option (b) 480 ignores the increase entirely.

Question 11 — School resources discount

Question: A school orders art supplies normally priced at $3,250. The supplier offers a 16% discount for schools. What is the discounted price? (Nearest dollar.)

✓ Worked Solution

Method A (two steps):
Discount amount: 16 ÷ 100 × 3,250 = 0.16 × 3,250 = $520
Discounted price: 3,250 − 520 = $2,730

Method B (multiplier):
16% decrease → multiply by (1 − 0.16) = 0.84
3,250 × 0.84 = $2,730

⚠️ Common error: Answering $520 (just the discount amount). The question asks for the discounted price — the amount the school actually pays.

Question 12 — GST on school furniture

Question: A school purchases storage cupboards at a pre-GST price of $2,640. GST of 10% is added. What is the total price including GST?

Options: (a) $2,904 (b) $2,640 (c) $2,800 (d) $2,376

✓ Worked Solution — Answer: (a) $2,904

GST amount: 10 ÷ 100 × 2,640 = $264

Total including GST: 2,640 + 264 = $2,904
Or: 2,640 × 1.10 = $2,904

💡 Distractor check: Option (d) $2,376 = 2,640 × 0.90 — this is what you’d get if you REMOVED 10% instead of adding it. GST is always an increase.

📊 Score guide

11–12

Excellent

Ready to move on

8–10

Good

Review errors & continue

0–7

Needs work

Re-read lessons 2.1 & 2.2

Q1–8

Finding a percentage, expressing as a percentage, percentage complements — all from Lesson 2.1.

Q9–12

Percentage increase, percentage decrease, GST — all from Lesson 2.2. If you struggled here, re-read the multiplier method.