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Indices and Standard Form

Secondary 3 practice

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Indices and Standard Form practice questions

Secondary 3 topics from the O-Level Mathematics 4052 syllabus. Every question below has a full worked solution.

When a student gets a question wrong in Math Amigo, it does not show the answer straight away. It reads the working, identifies the step that went wrong, and asks a question that points at the correction. The worked solution is there once a genuine attempt has been made.

Practise Indices and Standard Form free

What this topic covers

Worked examples

Example 1

Simplify 6x−1y3÷3xy26x^{-1}y^{3} \div 3xy^{2}. Express your answer with positive indices.
Show the worked solution
  • 6x−1y3÷3xy26x^{-1}y^{3} \div 3xy^{2}
  • =6x−1y33xy2write as fraction= \frac{6x^{-1}y^{3}}{3xy^{2}} \quad \scriptsize\textit{write as fraction}
  • =63×x−2×yLaw 2: subtract indices= \frac{6}{3} \times x^{-2} \times y \quad \scriptsize\textit{Law 2: subtract indices}
  • =2×x−2×y= 2 \times x^{-2} \times y
  • =2yx2Law 5: a−n=1an= \frac{2y}{x^{2}} \quad \scriptsize\textit{Law 5: } a^{-n} = \frac{1}{a^n}

Answer: 2y/x22y/x^2

Example 2

Evaluate 24315243^{\frac{1}{5}} without a calculator.
Show the worked solution
  • 24315243^{\frac{1}{5}}
  • =2435fractional index: a1n=an= \sqrt[5]{243} \quad \scriptsize\textit{fractional index: } a^{\frac{1}{n}} = \sqrt[n]{a}
  • =3= 3

Answer: 33

Example 3

Solve 82x=48^{2x} = 4.
Show the worked solution
  • 82x=48^{2x} = 4
  • (23)2x=22express both sides as powers of 2(2^{3})^{2x} = 2^{2} \quad \scriptsize\textit{express both sides as powers of 2}
  • 26x=222^{6x} = 2^{2}
  • 6x=2equate exponents6x = 2 \quad \scriptsize\textit{equate exponents}
  • x=13x = \frac{1}{3}

Answer: 1/31/3

Questions parents ask

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The free plan is permanent and does not ask for a card. It has daily limits on the AI feedback, and the paid plans lift them.

Which syllabus does this follow?

O-Level Mathematics (4052), for Singapore secondary students. Math Amigo covers Secondary 1 to 4, both O-Level Mathematics and Additional Mathematics.

Will it just show my child the answer?

No. On a wrong answer it looks at the working, points to the step that went wrong, and asks a question that helps the student find the correction. The full worked solution is available after a genuine attempt.

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