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RESOURCES · WORKED EXERCISES

Three worked exercises to practise

These exercises come from the app's content. Try on your own first, then open the solution: every step is explained.

Exercise 1 — French: the four moments of a conversation

Level: 6e (first year of secondary school) · Subject: French (speaking) · Skill: recognise the four steps of a dialogue to ask for information.

Question

Aminata wants to ask a woman at the market for information: she is looking for the way to the pharmacy.

  1. What does she do first of all?
  2. Put the four moments of a good dialogue in order: thank, ask, greet, listen.
  3. Write the short dialogue between Aminata and the woman, following that order.
See the solution

1. First of all, Aminata greets the woman. Before asking anyone for anything, you greet them: it is a sign of respect, and the person will be more willing to answer.

2. The order is: greet → ask → listen → thank.

  • Greet: you open the conversation.
  • Ask: you ask your question clearly and politely.
  • Listen: you let the person answer fully, without interrupting.
  • Thank: you close the conversation by saying thank you, even if the answer did not help.

3. Example dialogue (in French, as in class):

— Bonjour Madame.
— Bonjour ma fille.
— S'il vous plaît, pouvez-vous m'indiquer où se trouve la pharmacie ?
— Bien sûr : tu vas tout droit, puis tu tournes à gauche après la boutique de tissus.
— Merci beaucoup, Madame. Bonne journée !

Key takeaway

A successful conversation has four moments: greet, ask, listen, thank. Forgetting the first or the last makes the request impolite, even if the question itself is well asked.

Exercise 2 — History: in what order does the historian work?

Level: 6e · Subject: history · Skill: know the historian's method.

Question

Here, in the wrong order, are the steps of the historian's work:

  1. Interpreting and explaining the facts
  2. Writing
  3. Processing the information
  4. Collecting information

Put these steps in order by writing the sequence of their numbers.

See the solution

The order is 4 → 3 → 1 → 2.

To find it, imagine a student preparing a presentation: first they look for information, then they sort it, then they think about what it means, and finally they write their text neatly. The historian does the same:

  1. Collecting information (4): they look for documents and testimonies.
  2. Processing the information (3): they sort, classify and check.
  3. Interpretation (1): they understand and explain the facts.
  4. Writing (2): they write the account of what they have established.

Key takeaway

You cannot explain before you have checked, nor write before you have understood. The order collect, process, interpret, write also works for your own presentations.

Exercise 3 — Mathematics: equal quotients at the market

Level: lower secondary · Subject: mathematics · Skill: use cross-multiplication to compare quotients and solve an equation.

Reminder

For numbers a, b, c, d with b and d not equal to 0: a/b = c/d if and only if a × d = b × c. We say the "cross products" are equal.

Question

At the Adjamé market, Tanti Rose sells sachets. Awa compares her offers.

  1. Tanti Rose offers 3 sachets for 1,500 F, or 5 sachets for 2,500 F. Do both offers give the same price per sachet? Use cross-multiplication.
  2. She now offers 4 sachets for 2,200 F. Is it the same price per sachet as 3 sachets for 1,500 F? Which offer is better?
  3. Moussa has to solve the equation x/3 = 5/7. Find x.
See the solution

1. We compare 1,500/3 and 2,500/5.

  • 1,500 × 5 = 7,500
  • 3 × 2,500 = 7,500

The cross products are equal, so 1,500/3 = 2,500/5: both offers come to the same price per sachet, 500 F.

2. We compare 1,500/3 and 2,200/4.

  • 1,500 × 4 = 6,000
  • 3 × 2,200 = 6,600

The cross products are different, so the prices per sachet are not the same. At 1,500 F for 3 sachets, you pay 500 F per sachet; at 2,200 F for 4, you pay 550 F. The first offer is better.

3. x/3 = 5/7 gives, by cross-multiplication, x × 7 = 3 × 5, that is 7x = 15. So x = 15/7.

Key takeaway

Cross-multiplication does two things: it checks whether two quotients are equal, and it finds an unknown value in an equality of quotients. In everyday life, it lets you compare offers without working out each unit price.

Keep practising

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