Exam-style question
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B5: A student solves (x - 1)(x + 4) ? 0 and writes x ? 1 or x ? -4. Explain the error and give the correct solution set.
Model answer
What a good answer should say
- The critical values are x = -4 and x = 1.
- Since the quadratic product is less than or equal to zero between the roots, the correct solution is -4 ?
- x ?
- 1.
This answer is tied to the objective: B5 Solve linear and quadratic inequalities in a single variable and interpret such inequalities graphically, including inequalities with brackets and fractions; express solutions through correct use of and and or, or through set notation; represent linear and quadratic inequalities graphically..
Explanation
Why this works
Use the explanation to connect the worked answer back to B5 Solve linear and quadratic inequalities in a single variable and interpret such inequalities graphically, including inequalities with brackets and fractions; express solutions through correct use of and and or, or through set notation; represent linear and quadratic inequalities graphically..
This B5 question is specific to quadratic inequalities because it checks sign regions, endpoint inclusion and the difference between inside and outside intervals.
Maths method check
- Topic focus: Pure Mathematics.
- Question style: exam_style.
- Reasoning demand: recall.
- Check the operation, notation, units, and final answer form against the question before moving on.
Common mistake
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