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Form 2 Laws of Indices Practice

Form 2 · 20 practice questions with instant marking and worked solutions.

Laws of Indices is an important part of the Form 2 mathematics curriculum. This topic develops index notation, laws of indices and simplifying radicals. Begin by identifying what every number, symbol, diagram and unit represents. Translate the information into a mathematical relationship before calculating. Each line of working should have a purpose. Finally use estimation, substitution, an inverse operation, or a second representation to check the result. This habit separates a misunderstanding from a copying error and makes correction more useful.

A reliable approach to Laws of Indices has four stages. First, mark the given information and the quantity required. Second, choose an appropriate representation, property or formula. Third, carry out the operations in a clear order while retaining signs and units. Fourth, return to the original context and decide whether the result is possible. For a graph or table, read the title, scale and labels before using a value. For algebra, inspect brackets, negative signs and the order of operations before simplifying.

The twenty original questions in this topic use a shared mathematical specification in Chinese and English. Difficulty rises from level 1 to level 5. Early questions establish the language and direct skills of Laws of Indices; middle questions add two-step reasoning, conversions and common variations; later questions connect ideas and require a deliberate check. In multiple-choice work, calculate before looking at the choices. In fill-in and short-answer work, retain decisive steps. For true-or-false statements, support the decision with a calculation or counterexample.

Effective revision is more than recording a score. After completing the Laws of Indices set, group errors by concept tags and decide whether each problem arose from interpretation, forming an expression, calculation, or presenting the answer. Retry the item on a later day without opening the solution, then test the same method with a different value. If the same tag appears repeatedly, return to the explanation and rebuild the concept. If signs or units are the issue, use a fixed pre-submission checklist.

Laws of Indices should also connect with the rest of mathematics. Number and algebra supply calculation tools; measurement and geometry give spatial meaning; data handling asks what a result means. A learner who can explain aloud why every step is valid has moved beyond imitation. Estimate a reasonable range, complete an exact solution, and compare the two. Agreement between context, estimate and exact answer is strong evidence that the solution is sound.

Start practising

  1. 1 Basic
    In Laws of Indices, calculate $3^{2}$. Choose the correct answer.
  2. 2 Basic
    In Laws of Indices, calculate $4^{3}$. Give the numerical value only.

  3. 3 Basic
    In Laws of Indices, calculate $2^{2}$. Show the essential working and give the numerical value.

  4. 4 Basic
    In Laws of Indices, the value of $3^{3}$ is 28. Is this statement true?
  5. 5 Standard
    In Laws of Indices, calculate $4^{3}$. Choose the correct answer.
  6. 6 Standard
    In Laws of Indices, calculate $2^{4}$. Give the numerical value only.

  7. 7 Standard
    In Laws of Indices, calculate $3^{3}$. Show the essential working and give the numerical value.

  8. 8 Standard
    In Laws of Indices, the value of $4^{4}$ is 256. Is this statement true?
  9. 9 Advanced
    In Laws of Indices, calculate $2^{4}$. Choose the correct answer.
  10. 10 Advanced
    In Laws of Indices, calculate $3^{5}$. Give the numerical value only.

  11. 11 Advanced
    In Laws of Indices, calculate $4^{4}$. Show the essential working and give the numerical value.

  12. 12 Advanced
    In Laws of Indices, the value of $2^{5}$ is 33. Is this statement true?
  13. 13 Challenging
    In Laws of Indices, calculate $3^{5}$. Choose the correct answer.
  14. 14 Challenging
    In Laws of Indices, calculate $4^{6}$. Give the numerical value only.

  15. 15 Challenging
    In Laws of Indices, calculate $2^{5}$. Show the essential working and give the numerical value.

  16. 16 Challenging
    In Laws of Indices, the value of $3^{6}$ is 729. Is this statement true?
  17. 17 Elite
    In Laws of Indices, calculate $4^{6}$. Choose the correct answer.
  18. 18 Elite
    In Laws of Indices, calculate $2^{7}$. Give the numerical value only.

  19. 19 Elite
    In Laws of Indices, calculate $3^{6}$. Show the essential working and give the numerical value.

  20. 20 Elite
    In Laws of Indices, the value of $4^{7}$ is 16385. Is this statement true?

The report lists what you got wrong and why. Only you can see it.

Common mistakes

Common mistakes in Laws of Indices

This topic needs particular care with index notation, laws of indices and simplifying radicals. The first mistake is applying a remembered rule before reading all conditions. The second is compressing working so much that a sign, bracket, decimal point or unit disappears. The third is accepting an impossible answer without checking: for example, a probability above one, a negative physical length, an angle outside the geometric constraints, or a result far from the estimate. Separate the conditions, model, calculation and check, and finish by stating what the answer represents.

More Form 2 topics

Form 2 mixed revision → My mistakes →

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Repeating the same mistake usually means an earlier concept never landed. We find that step in the trial lesson.

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