Secondary 4 percentage questions become easier when students identify the original quantity before reaching for a formula. This Mathematics tuition guide for Punggol families explains percentage increase, decrease, reverse percentage, repeated growth, depreciation and compound interest through original worked examples.

Many students can calculate 20% of a number but become uncertain when the question says “after a 20% discount”, “increased by 15%”, “the final price is $204” or “grows by 4% per year”. The arithmetic is often simple. The real difficulty is deciding what 100% refers to.

At eduKatePunggol, Secondary 4 Mathematics is taught in focused groups of up to three students in 1.5-hour lessons near Punggol MRT. This guide supports the wider Secondary 4 Mathematics year plan. Match practice to the student’s actual subject level and school syllabus.

Percentage change starts from a reference value

If a price increases from $80 to $100, the increase is $20.

The percentage increase is measured against the original $80:

(20/80) × 100% = 25%.

A common mistake is to divide by the final value, 100, which would give 20%. The phrase “percentage increase” normally compares the change with the starting quantity.

Worked example 1: percentage decrease

A jacket falls in price from $120 to $90. Find the percentage decrease.

The decrease is $30.

Percentage decrease = (30/120) × 100% = 25%.

The denominator is the original $120, not the reduced $90.

A multiplier makes repeated percentage change clearer

An increase of 12% means the new value is 112% of the old value:

new value = old value × 1.12.

A decrease of 12% means:

new value = old value × 0.88.

This multiplier approach becomes especially useful for compound growth and reverse percentage.

Worked example 2: reverse percentage

After a 15% discount, an item costs $204. Find the original price.

After the discount, 85% of the original remains.

Let the original price be P:

0.85P = 204.

Therefore:

P = 204/0.85 = 240.

The original price was $240.

A common wrong move is to add 15% of 204. But 204 is already the reduced value, not the original 100% base.

Repeated percentage change compounds

Suppose $1000 grows by 5% per year for two years.

After one year:

1000 × 1.05 = 1050.

After two years:

1050 × 1.05 = 1102.50.

This is the same as:

1000(1.05)² = 1102.50.

The second 5% is calculated on the new amount, not on the original $1000 only.

Worked example 3: compound interest

$5000 is invested at 3% per year compounded annually for 4 years.

Amount = 5000(1.03)⁴ ≈ $5627.54.

The total interest earned is:

5627.54 − 5000 = $627.54.

Read whether the question asks for the final amount or only the interest. They are not the same answer.

Worked example 4: depreciation

A machine worth $18,000 depreciates by 8% each year. Find its value after 3 years.

The multiplier is 0.92.

Value = 18000(0.92)³ ≈ $14,015.23.

Do not subtract 24% of the original unless the question explicitly describes a simple linear decrease. Repeated percentage decrease compounds.

Two percentage changes do not simply cancel

If a value rises by 20% and then falls by 20%, it does not return to the start.

Start with 100:

100 × 1.20 = 120.

Then reduce by 20%:

120 × 0.80 = 96.

The final value is 4% below the original. The second percentage is applied to a different base.

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How we diagnose percentage mistakes

Base-value error: the student divides by the final quantity instead of the original.

Multiplier error: 15% decrease becomes ×0.15 instead of ×0.85.

Reverse-percentage error: the final value is treated as 100%.

Compounding error: repeated growth is treated as one simple percentage.

Question-reading error: amount, interest, profit, loss or final value are confused.

Why the three-student format helps

In a group of up to three students, one learner can explain what 100% represents, another can build the multiplier and another can check whether the final answer is reasonable. The tutor can see whether the mistake is arithmetic or interpretation.

What a 90-minute lesson could look like

An illustrative lesson could begin with ten minutes of percentage bases, twenty minutes on multipliers and reverse percentage, twenty minutes on repeated growth, twenty minutes on independent mixed questions and twenty minutes for financial contexts, error review and continuation work.

Repair, stabilisation and extension

Repair: use simple whole-number percentages and identify the original 100% explicitly.

Stabilisation: mix increase, decrease, reverse percentage and compound change so the student must choose the correct base.

Extension: compare multiple percentage changes, explain why equal percentage rise and fall do not cancel, and use algebra to solve missing original values.

Try a short independent set

• Increase $240 by 15%.
• After a 20% discount, an item costs $72. Find the original price.
• $2000 grows by 4% per year for 2 years. Find the final amount.

Answers: $276; $90; and $2163.20.

What progress should look like

• the original 100% base is identified correctly;
• increase and decrease multipliers are formed correctly;
• reverse percentage uses division by the remaining multiplier;
• compound change uses repeated multiplication;
• final amount and interest are distinguished;
• answers are checked for reasonableness.

Punggol class details and consultation inputs

eduKatePunggol Secondary Mathematics tutorials run for 1.5 hours in groups of up to three students near Punggol MRT. Confirm current class availability, fees and meeting arrangements directly.

Bring the student’s subject level, examination year and recent percentage questions. A reverse-percentage question with original working is particularly useful because it reveals what the student treated as 100%.

Frequently asked questions

Why divide for reverse percentage?

Because the final value is a known fraction of the original. If 85% of P is 204, then P = 204/0.85.

Does a 10% rise followed by a 10% fall cancel?

No. The second percentage is applied to the changed value, so the bases differ.

Find the 100% before doing the percentage

Return to the Secondary 4 Mathematics year plan for the wider SEC runway. For powers used in repeated growth, see the indices and standard-form guide.

Choose the base, build the multiplier and check what the question actually asks for. Families can WhatsApp eduKatePunggol with recent work to discuss a suitable next step.