ORT mathematics practice

Mathematics, one clear step at a time.

Practise four foundations with original questions, worked solutions and explanations of common mistakes. Start here, then choose a guide for the topic you need.

Where should I start?

Begin with fractions and percentages, then practise equations and geometry. Solve each example before revealing its explanation, check your working and use the linked guide to revisit a weak topic.

Choose a foundation

Fractions

Add parts using a common denominator.

Percentages

Identify the whole before finding a percentage.

Equations

Keep both sides equal as you isolate the unknown.

Area and perimeter

Separate the space inside a shape from its boundary.

Try it before opening the solution

1 / Fractions

What is 3/8 + 1/4?

Show the solution

5/8

  1. Rewrite 1/4 as 2/8 so the parts have the same size.
  2. Add the numerators: 3/8 + 2/8 = 5/8.
  3. The result is greater than 1/2 and less than 1, which is consistent with the two addends.

A common mistake

Adding the denominators would give 4/12. The denominator names the size of each part; it is not added.

2 / Percentages

A notebook costs 250 som. What is an 18% discount, and what is the new price?

Show the solution

45 som discount; 205 som new price.

  1. 18% means 18 out of 100, so use 0.18.
  2. Calculate the discount: 250 × 0.18 = 45.
  3. Subtract it from the price: 250 − 45 = 205.

A common mistake

45 som is the discount, not the final price. Read what the question is asking for.

3 / Equations

Solve 5x + 7 = 3x + 19.

Show the solution

x = 6

  1. Subtract 3x from both sides: 2x + 7 = 19.
  2. Subtract 7 from both sides: 2x = 12.
  3. Divide by 2 and check: 5 × 6 + 7 = 3 × 6 + 19 = 37.

A common mistake

Change both sides with the same operation. Moving a term without accounting for its sign can change the equation.

4 / Geometry

A rectangle has perimeter 30 cm and width 6 cm. Find its length and area.

Show the solution

Length 9 cm; area 54 cm².

  1. Use P = 2(a + b): 30 = 2(a + 6).
  2. Divide by 2: a + 6 = 15, so a = 9 cm.
  3. Use A = a × b: 9 × 6 = 54 cm².

A common mistake

Perimeter is measured in cm, while area is measured in cm². They describe different quantities.

Read a fuller explanation

Common questions

Can I use these examples without an account?

Yes. Read the questions and solutions here freely. Sign in when you want to use saved tests, courses or personal decks.

What should I do after a wrong answer?

Find the first step that went wrong, read the relevant guide and try a different example. A mistake is a useful clue about what to practise next.

Check the underlying ideas

OpenStax explains school mathematics; the exam organiser publishes official ORT information.

Sample questions here are public. Saved test attempts require signing in.

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