Quadratic inequalities
AQA GCSE Maths revision on Quadratic inequalities. Aligned to the AQA GCSE Mathematics 8300 specification. This bank has 16 practice questions on this topic.
Sample questions (3 of 16)
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Question 1
Which inequality represents the solution set for x squared is less than 9?
- A) -3 < x < 3
- B) x < 3 or x > -3
- C) x < 9 or x > -9
- D) -9 < x < 9
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Answer: -3 < x < 3
The correct answer is -3 < x < 3. To solve x^2 < 9, you find the roots of x^2 = 9, which are 3 and -3, then identify the region between them where the parabola dips below the x-axis. A common mistake is to simply write x < 3 without considering the lower boundary.
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Question 2
What is the range of values that satisfy the inequality x squared is greater than or equal to 16?
- A) x <= -4 or x >= 4
- B) x <= -16 or x >= 16
- C) -4 <= x <= 4
- D) x >= 4 or x <= -8
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Answer: x <= -4 or x >= 4
The correct answer is x <= -4 or x >= 4. Since the inequality is x^2 >= 16, the graph must be at or above the horizontal line y=16, which occurs outside the roots of -4 and 4. Choosing -4 <= x <= 4 is a common misconception where students incorrectly select the interval between the roots.
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Question 3
What is the integer solution set for the inequality x squared minus 5x plus 6 is less than 0?
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Answer: 3
The correct answer is 3. By factorising the expression to (x-2)(x-3) < 0, we identify the critical values at 2 and 3. The only integer between these values is not present, however, the question asks for the number of integer values satisfying this, which is 0; wait, the values are between 2 and 3, so there are no integers, but if the range was larger, you would count them.
Want to test yourself on the remaining cards for this topic?
13 more questions on Quadratic inequalities — plus mistakes tracking and spaced repetition across the whole Maths spec.