Year 10 - Exponential equations - Free practice
Year 10 Exponential Equations Worksheets
Same-base solving, index manipulation, growth/decay setup.
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Six questions across Foundation, Standard and Extension, with full worked solutions, calibrated to the Victorian Curriculum.
Textbook questions won't lift a test mark.
They come sorted by topic, so your child knows the method before they read the question.
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- ✓Any topic, any time, designed to mimic actual test questions
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About this worksheet
Why we built it
Year 10 exponential equations focus on the same-base technique - getting both sides expressed as a power of the same number and equating exponents. These worksheets give your student varied same-base problems plus the lead-up to logarithms in Year 10A.
What's covered
Sub-skills your student will practise
- ✓Solving by writing both sides as the same base
- ✓Working with negative and fractional exponents
- ✓Setting up growth and decay equations
- ✓Equations leading to a quadratic in disguise
- ✓Word problems involving exponential change
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From our families
Parents on the practice questions.
“Tuterly has been exactly what we needed since Tom started secondary school. Once the topic tests began, he was struggling to keep up. Now he has unlimited practice, all matched to what his class is actually covering, and his Maths results have improved noticeably.”
Rebecca M.
Year 8 · Maths
“My daughter used to leave revision until the night before. Having a platform she can dip into for fifteen minutes after dinner has completely changed that. She's calmer going into assessments, and honestly, so am I.”
Priya S.
Year 9 · Maths
“I like that I can just keep doing questions until it clicks. If I get something wrong, it shows me why, and then gives me another one like it.”
Ella, student
Year 10 · Maths
Frequently asked
Questions parents ask about exponential equations
What's an exponential equation?
An equation where the unknown is in the exponent - 2^x = 32, 3^(x + 1) = 81. Year 10 introduces the same-base method to solve these without logarithms.
What's the same-base method?
Rewrite both sides as a power of the same base, then equate exponents. For 2^x = 32: rewrite 32 as 2^5, so 2^x = 2^5, therefore x = 5. Works whenever both sides can be expressed in a common base.
What does Year 10 do when same-base doesn't work?
Mostly the questions are chosen so same-base does work. For cases where it doesn't (2^x = 7), logarithms are needed - that's Year 10A territory.
Where do exponential equations show up outside school?
Compound interest, population growth, radioactive decay, viral spread, cooling. Anywhere a quantity changes by a fixed proportion per unit of time, there's an exponential equation underneath.
Want a real plan for the term?
Worksheets are great for repetition. A Tuterly tutor can spot the specific moves your student keeps getting wrong and fix them in one or two sessions.
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Talk to us about Year 10 exponential equations.
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