Year 10 - Exponential equations - Free practice
Year 10 Exponential Equations Worksheets
Same-base solving, index manipulation, growth/decay setup.
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10 questions — 4 Foundation, 4 Standard, 2 Extension — with full worked solutions, calibrated to the Victorian Curriculum.
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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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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