Algebra
Solve 3x + 4 = 19.
Show answer and worked explanation
x = 5
- Subtract 4 from both sides: 3x = 15.
- Divide both sides by 3: x = 5.
- Check by substitution: 3 × 5 + 4 = 19.
Revision tip: Apply each operation to both sides of the equation.
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Original practice examples
Try it. Then check your reasoning.
Work through these questions first. Open each explanation when you are ready to check.
Probability
A bag contains 4 red counters and 6 blue counters. One counter is selected at random. What is the probability that it is red?
Show answer and worked explanation
2/5
- There are 4 + 6 = 10 counters in total.
- The probability of red is 4/10.
- Simplify the fraction: 4/10 = 2/5.
Revision tip: Use the total number of equally likely outcomes as the denominator.
Geometry
A right-angled triangle has perpendicular sides of 6 cm and 8 cm. Find the hypotenuse.
Show answer and worked explanation
10 cm
- Use Pythagoras: c² = 6² + 8².
- Calculate c² = 36 + 64 = 100.
- Take the positive square root: c = 10 cm.
Revision tip: The hypotenuse is opposite the right angle and is the longest side.
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- Sort mistakes into calculation errors, missing knowledge and misunderstood questions. Revise the specific method behind each one.
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The tool includes AQA GCSE Mathematics (8300), AQA Level 2 Further Mathematics (8365), Cambridge IGCSE Mathematics (0580), Cambridge IGCSE Additional Mathematics (0606), Pearson Edexcel GCSE Mathematics (1MA1) and International GCSE Further Pure Mathematics (4PM1).
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