The fix is to name the situation before choosing a method.
Ask three questions in order: What is given? What is wanted? Which relationship connects them? The method follows from the third answer, not from a keyword.
This page teaches that routine with two worked examples. The non-calculator working trainer and percentage-base explorer give extra practice in separate parts of it.
Why does a mixed question feel harder?
In a topic exercise, the chapter title does the thinking for you. In a mixed question, nothing does.
You have to recognise the situation, choose a method, then carry it out. Students often practise only the third part, so the first two stay weak.
Recognition improves when you slow down the first ten seconds. Those ten seconds are cheaper than a page of wrong working.
The routine: four steps before any calculation
- Underline the given facts and circle the unknown. Write the unknown as a letter or a short label.
- Name the situation in plain words. For instance: “a percentage change where I know the final price”, or “two quantities linked by area”.
- Ask which relationship connects given and unknown. It may be a multiplier, an equation, a ratio, a formula.
- Write one line saying what you will do, then calculate. Afterwards, check the answer against the situation.
Worked example 1: one question, two topics
Question: A jacket’s price is raised by 20% to RM 96. In a sale it is then reduced to RM 84. (a) Find the original price. (b) Find the percentage reduction from RM 96 to RM 84.
Step 1, given and wanted. Given: RM 96 is after a 20% rise; sale price RM 84. Wanted: (a) the price before the rise; (b) a percentage change.
Step 2, name the situation. Part (a) is a reverse percentage: the final value is known, the original is unknown. Part (b) is a percentage change, where the base is the price before the change, here RM 96.
Step 3, relationship. (a) Final = original × 1.2. (b) Change = (new − old) ÷ old.
Step 4, calculate.
(a) Original = 96 ÷ 1.2 = RM 80. Check: 80 × 1.2 = 96.
(b) Reduction = (96 − 84) ÷ 96 = 12 ÷ 96 = 0.125, so 12.5%.
A plausible wrong turn. Seeing “20%”, a student computes 20% of 96 = 19.2 and subtracts: 96 − 19.2 = 76.8. The method looks familiar, but it treats RM 96 as the original. RM 96 is the price after the rise, so the base is unknown. Step 2, naming the situation, would have shown this.
Worked example 2: a geometry situation that needs algebra
Question: A rectangular garden is 3 m longer than it is wide. Its area is 40 m². Find its width.
Step 1, given and wanted. Given: length = width + 3, area = 40. Wanted: width.
Step 2, name the situation. Two lengths are linked, and their product is known. That is an equation formed from an area formula, probably quadratic.
Step 3, relationship. Area = width × length.
Step 4, calculate. Let the width be w. Then w(w + 3) = 40, so w² + 3w − 40 = 0.
Factorise: (w + 8)(w − 5) = 0, so w = −8 or w = 5.
A width cannot be negative, so w = 5 m. Check: length 8 m, and 5 × 8 = 40.
A plausible wrong turn. A student divides 40 by 3, getting 13.33, and calls that the width. It feels like a method because “area” and “3” are both there, but it ignores that the length also depends on the width.
Clues that can help, and how they can mislead
| Clue in the question | Often points to | Check before using |
|---|---|---|
| “percent”, “increase”, “discount” | A multiplier | Which quantity is the base? |
| “in the ratio”, “share” | Dividing into parts | Is it parts of the total or a comparison? |
| “area”, “perimeter”, “volume” | A formula | Is one dimension given in terms of another? |
| “how many … altogether” | Forming an equation | What stays fixed, what varies? |
| “right angle”, “side lengths” | Pythagoras or trigonometry | Is an angle involved? |
Treat each row as a prompt for one question, never as an instruction.
Check yourself
1. A train journey of 180 km takes 2 hours 15 minutes. Name the situation, then find the average speed.
Show answer
Situation: speed from distance and time. Convert 2 h 15 min to 2.25 h. Speed = 180 ÷ 2.25 = 80 km/h.
2. The price of a bag after a 25% discount is RM 120. What was the original price? Write the situation first.
Show answer
Situation: reverse percentage. After a 25% discount the price is 75% of the original, so original = 120 ÷ 0.75 = RM 160. Check: 75% of 160 = 120.
3. Two numbers differ by 4 and their product is 45. Name the situation and find a pair.
Show answer
Situation: an equation from a product. Let the numbers be n and n + 4. Then n(n + 4) = 45, so n² + 4n − 45 = 0, which factorises as (n + 9)(n − 5) = 0. Positive pair: 5 and 9. Another pair is −9 and −5.
Where to go next
Work the original mixed practice and, before each question, write your one-line sentence. For the percentage part, see reversing a percentage increase. For the algebra part, see forming an equation from a verbal constraint.
If recognising the situation still does not come with practice, a teacher can watch how you read a question and show you what to look for in online one-to-one Mathematics tuition.