AQA · Mathematics · 8300
GCSE Maths: Equations: trial and improvement
Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Equations: trial and improvement (Corbettmaths Video 116), and every card links back to the exact page it came from. Practice tests generate fresh variations of these questions, so the numbers change every attempt. Source material © Corbettmaths — used with attribution.
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What is the trial and improvement method used for?
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To find approximate numerical solutions to equations that cannot be solved algebraically.
When using trial and improvement, what is the first step in finding a solution?
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Find two consecutive integers between which the solution lies.
In trial and improvement, after finding the integer interval, you test values to refine the answer to the required ?.
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decimal places
What does it mean if x² + 5 = 56 has a solution between 7 and 8?
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The solution is greater than 7 but less than 8; substituting x = 7 gives a value below 56, and x = 8 gives a value above 56.
In trial and improvement, how do you refine from 1 decimal place accuracy to 2 decimal places?
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After finding the solution to 1 d.p., test values around it at 2 decimal places (e.g., if answer is 7.3, test 7.25, 7.30, 7.35) until the required precision is achieved.
Why must you show all your working in trial and improvement questions?
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To demonstrate the systematic testing process and show how you narrowed down to the final answer; marks are awarded for method as well as the final result.
If trial and improvement gives x = 7.25 → result too low, x = 7.35 → result too high, what is x to 1 decimal place?
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x = 7.3, because the solution lies between 7.25 and 7.35, both of which round to 7.3 at 1 d.p.
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