Quadratic inequalities
Edexcel GCSE Maths revision on Quadratic inequalities. Aligned to the Pearson Edexcel GCSE Mathematics 1MA1 specification. This bank has 16 practice questions on this topic.
Sample questions (3 of 16)
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Question 1
Which range of values satisfies the inequality x squared is less than 9?
- A) -3 < x < 3
- B) x < -3 or x > 3
- C) x > -3 and x < 9
- D) x < 3 or x > -3
Show answer
Answer: -3 < x < 3
The correct answer is -3 < x < 3. To solve this, identify the roots of x squared equals 9, which are 3 and -3, and observe that the curve is below the horizontal axis between these two points. A common error is to assume the range must be outside the roots, which applies to 'greater than' inequalities.
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Question 2
What are the integer values of x that satisfy the inequality x squared minus 4 is less than or equal to 0?
Show answer
Answer: 5
The integer values are -2, -1, 0, 1, and 2, which total 5 distinct values. By factorising x squared minus 4 into (x minus 2)(x plus 2) less than or equal to 0, we identify the interval -2 <= x <= 2, which contains five integers.
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Question 3
Which set of x values satisfies the inequality x squared minus 5x plus 6 is greater than 0?
- A) x < 2 or x > 3
- B) 2 < x < 3 is set
- C) x > 2 and x < 3
- D) x < 3 or x > 2
Show answer
Answer: x < 2 or x > 3
The correct answer is x < 2 or x > 3. Since the quadratic is positive (greater than 0), the solution lies outside the roots found by factorising to (x-2)(x-3). Choosing the region between the roots is a common mistake when the expression is greater than zero.
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.